master
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a Code for the Combination of Indirect and Direct Constraints on High Energy Physics Models
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A class for the \(\bar{B} \to X_s\gamma\) decay.
More...
#include <bsgamma.h>
A class for the \(\bar{B} \to X_s\gamma\) decay.
- Author
- HEPfit Collaboration
- Copyright
- GNU General Public License
This class is used to build all the functions needed in order to compute the observables relative to the \(\bar{B} \to X_s\gamma\) decay, following the prescriptions of [163] and [162].
Model parameters
The model parameters of bsgamma are summarized below:
| Label | LaTeX symbol | Description |
| BLNPcorr | \(N_{b\to s\gamma}\) | The non perturbative uncertainty associated to the \(b\to s\gamma\) BR. |
| mukin | \(\mu^{\rm kin}\) | The mass scale for the b quark in the kinetic scheme. |
| BRsem | \(\mathrm{BR}(B\to X_ce\nu)\) | The branching ratio of \(B\to X_c e\nu\). |
| Mbkin | \(m_b^{\rm kin}\) | The b quark mass in the kinetic scheme. |
| Mcatmuc | \(m_c(\mu_c)\) | The c quark at \(\mu_c\). |
| mupi2, rhoD3, muG2, rhoLS3 | \(\mu_{\pi}^{2}, \rho_{D}^{3}, \mu_{G}^{2}, \rho_{LS}^{3}\) | The B meson expectation values for the relevant dim. 5 and 6 operators. |
| mu_b_bsgamma, mu_c_bsgamma | \(\mu_b, \mu_c\) | The renormalization scales \(\mu_b\) and \(\mu_c\). |
In general, the decay rate can be expressed as
\[ \Gamma(\bar{B} \to X_s^p \gamma)_{{E_\gamma > E_0}} = \frac{\left|V_{ts}^\star V_{tb}\right|^2 G_F^2 m_b^5 \alpha_{\rm em}}{32\pi^4} \sum_{i,j=1}^8 C_i(\mu_b)C_j(\mu_b) G_{ij}(E_0,\mu_b)\,. \]
Given the factor \(m_b^5\) present in the normalization, this formulation is not really usefull in a phenomenological analysis; in order to reduce this uncertainty, one can write the branching fraction dividing by the theoretical semileptonic decay rate and multiplying by the experimental semileptonic branching ratio:
\[ {\rm BR}[\bar{B} \to X_s \gamma]_{E_{\gamma} > E_0} = {\rm BR}[\bar{B} \to X_{c\,} e \bar{\nu}]_{\rm exp} \left( \frac{\Gamma[\bar{B} \to X_u e \bar{\nu}]}{\Gamma[\bar{B} \to X_{c\,} e \bar{\nu}]} \right)_{\rm th} \left( \frac{\Gamma(\bar{B} \to X_s^p \gamma)_{{E_\gamma > E_0}}}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \right)_{\rm th}\\ = {\rm BR}[\bar{B} \to X_c e \bar{\nu}]_{\rm exp} \left| \frac{ V^*_{ts} V_{tb}}{V_{cb}} \right|^2 \frac{6 \alpha_{\rm em}}{\pi\;C} \left[ P(E_0) + N(E_0) \right]\,, \]
where \(C\), taken from the fit in [14] , is the ratio
\[ C = \left| \frac{V_{ub}}{V_{cb}} \right|^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \,, \]
\(P(E_0)\) is given by the perturbative ratio
\[ \frac{\Gamma[ b \to X_s \gamma]_{E_{\gamma} > E_0}}{|V_{cb}/V_{ub}|^2 \; \Gamma[ b \to X_u e \bar{\nu}]} = \left| \frac{ V^*_{ts} V_{tb}}{V_{cb}} \right|^2 \frac{6 \alpha_{\rm em}}{\pi} \; P(E_0)\,, \]
and \(N(E_0)\) denotes the non-perturbative correction [46] , which appears when \(b\) is replaced by \(\bar{B}\) in the previous equation.
The quantity \(P(E_0)\) depends quadratically on the Wilson coefficients, and can be perturbatively expand at NLO in the following form ( \(\tilde{\alpha}_s(\mu) \equiv \frac{ \alpha_s^{(5)}(\mu)}{4\pi}\)):
\[ P(E_0) = P^{(0)}(\mu_b) + \tilde{\alpha}_s(\mu_b)\Big[ P^{(1)}_1(\mu_b) + P^{(1)}_2(\mu_b)\Big] + O\Big(\tilde{\alpha}_s^2(\mu_b)\Big)\,. \]
Here, \(P^{(0)}\) and \(P_1^{(k)}\) mainly originate from the tree-level matrix element of \(Q_7\) [164], while a small contribution stems also from the penguin operators [145] :
\[ P^{(0)} = \Big(C_7^{\rm (0) eff}(\mu_b)\Big)^2 + P^{(0)}_{\rm 4-body}\,,\\ P_1^{(1)} = 2C_7^{\rm (0) eff}(\mu_b)C_7^{\rm (1) eff}(\mu_b)\,.\\ \]
\(P_2^{(1)}\) depends on the LO Wilson coefficients \(C_i^{\rm (0)eff}\) throught the following relation [164] :
\[ P_2^{(1)} = \sum_{i,j=1}^8C_i^{\rm (0)eff}C_j^{\rm (0)eff}K_{ij}^{(1)}\,. \]
The \(K_{ij}^{(1)}\) functions are defined in the following way:
\[ K_{i7}^{(1)} = \mathrm{Re} r_i^{(1)} - \frac{1}{2}\gamma_{i7}^{\rm (0) eff}L_b + 2\phi_{i7}^{(1)}(\delta)\,, \qquad {\rm for}\:\:i\leq 6,\\ K_{77}^{(1)} = -\frac{182}{9} + \frac{8}{9}\pi^2 - \gamma_{77}^{\rm (0) eff}L_b + 4\phi_{77}^{(1)}(\delta)\,,\\ K_{78}^{(1)} = \frac{44}{9} - \frac{8}{27}\pi^2 - \frac{1}{2}\gamma_{87}^{\rm (0) eff}L_b + 2\phi_{78}^{(1)}(\delta)\,,\\ K_{ij}^{(1)} = 2(1+\delta_{ij})\phi_{ij}^{(1)}(\delta)\,, \qquad {\rm for}\:\:i,j \neq 7\,, \]
where we have defined the quantities
\[ L_b= \ln{\bigg(\frac{\mu_b}{ m_b^{kin}}\bigg)^2}, \qquad \delta = 1 - \frac{2E_0}{ m_b^{kin}}\,, \]
and all the relevant ingredients can be collected in [53], [127], [168], [143] .
The class is organized as follows: after the Wilson coefficients are computed in computeCoeff() and the cache is checked in checkCache(), the parameters are updated in updateParameters() and the ratio \(C\) is computed in C_sem().
The perturbative part of the Branching Ratio is computed order by order:
- at Leading Order it is computed in P0(), in which are taken into account both the leading term due to \(C_7\) and the subleading term due to the 4-body contribution, computed in P0_4body() ;
- at Next to Leading Order it is computed in P11() and P21(), where the latter is build from the Kij_1() function, which make use of the functions Phi11_1(), Phi12_1(), Phi13_1(), Phi14_1(), Phi15_1(), Phi16_1(), Phi17_1(), Phi18_1(), Phi22_1(), Phi23_1(), Phi24_1(), Phi25_1(), Phi26_1(), Phi27_1(), Phi28_1(), Phi33_1(), Phi34_1(), Phi35_1(), Phi36_1(), Phi37_1(), Phi38_1(), Phi44_1(), Phi45_1(), Phi46_1(), Phi47_1(), Phi48_1(), Phi55_1(), Phi56_1(), Phi57_1(), Phi58_1(), Phi66_1(), Phi67_1(), Phi68_1(), Phi77_1(), Phi78_1() and Phi88_1() . The subleading terms due to the 4-body contributions are currently hard-coded in Phi23_1_4body(), Phi24_1_4body(), Phi25_1_4body() and Phi26_1_4body(), and switched off due to setting the marco FOUR_BODY to false.
The \(V_{ub}\) corrections at LO are automatically taken into account in P0_4body() , while at NLO they are computed in the function Vub_NLO(), which considers contributions from 2-body, 3-body and 4-body decays, with the former switched off due to setting the marco FOUR_BODY to false.
All the perturbative corrections are eventually added in the function P(). The non-perturbative corrections are computed in the function N(). The observables are finally computed in the computeThValue() function.
Definition at line 165 of file bsgamma.h.
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| gslpp::complex | a (double z) |
| | The funcion \( a(z) \) as defined in [53] . More...
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| gslpp::complex | b (double z) |
| | The funcion \( b(z) \) as defined in [53] . More...
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| | Bsgamma (const StandardModel &SM_i, int obsFlag) |
| | Constructor. More...
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| | Bsgamma (const StandardModel &SM_i, QCD::quark quark_i, int obsFlag) |
| | Constructor. More...
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| double | C_sem () |
| | The ratio \(C = | \frac{V_{ub}}{V_{cb}} |^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \) as defined in [128] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino). More...
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| void | computeCoeff (double mu) |
| | Compute the Wilson Coefficient. More...
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| double | computeThValue () |
| | Computes the Branching Ratio for the \(b \to q \gamma\) decay. More...
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| double | delddel_Phi22_1 (double E0) |
| | Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines. More...
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| double | delddel_Phi28_1 (double z, double E0) |
| | Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines. More...
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| double | delddel_Phi88_1 (double E0) |
| | Derivative of the function Phi88_1() used to compute effects of massive quark loops on gluon lines. More...
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| double | delta (double E0) |
| | The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \). More...
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| double | Delta (double r) |
| | The \(\Delta(r)\) function from Z. Phys. C 48, 673 (1990). More...
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| double | dY1 (double E0) |
| | The \( \delta Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
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| double | EW_NLO (double mu) |
| | The NLO electroweak correction to the BR as defined in [126] . More...
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| double | f (double r) |
| | The \(f(\rho)\) function from hep-ph/0611123. More...
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| double | F_1 (double z) |
| | The \( F_{1}(z,1) \) interpolated function from arXiv:1503.01791. More...
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| double | F_2 (double z) |
| | The \( F_{2}(z,1) \) interpolated function from arXiv:1503.01791. More...
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| double | f_b (double z) |
| | The \( f_{b}(z) \) function from arXiv:1503.01791. More...
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| double | f_c (double z) |
| | The \( f_{c}(z) \) function from arXiv:1503.01791. More...
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| double | f_NLO_1 (double z) |
| | The \( f_{\rm NLO}(z,1) \) function from arXiv:1503.01791. More...
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| double | f_q (double z, double E0) |
| | The \( f_{q}(z,1) \) function from arXiv:1503.01791. More...
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| double | f_u (double r) |
| | The \(f_u\) function obtained after multiplying the fitted function \(U_C\) of arXiv:0803.0960 for \(C_FT_R\) and subtracting the \(r \to 0\) limit. More...
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| double | ff7_dMP (double E0) |
| | The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [143] . More...
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| double | ff7_sMP (double E0) |
| | The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [143] . More...
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| double | ff8_dMP (double E0) |
| | The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [143] . More...
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| double | ff8_sMP (double E0) |
| | The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [143] . More...
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| gslpp::complex | Gamma_t (double t) |
| | The function \( \Gamma \) as defined in [127] . More...
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| double | getKb_abs2_1mt (double t) |
| | The function \(|k_b(t)|^2(1 - t)\). More...
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| double | getKb_abs2_1mt2 (double t) |
| | The function \(|k_b(t)|^2(1 - t)^2\). More...
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| double | getKb_abs2_t2_1mt (double t) |
| | The function \(|k_b(t)|^2t^2(1 - t)\). More...
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| double | getKb_abs2_t2_1mt2 (double t) |
| | The function \(|k_b(t)|^2t^2(1 - t)^2\). More...
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| double | getKb_abs2_t_1mt (double t) |
| | The function \(|k_b(t)|^2t(1 - t)\). More...
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| double | getKb_abs2_t_1mt2 (double t) |
| | The function \(|k_b(t)|^2t(1 - t)^2\). More...
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| double | getKb_re_1mt (double t) |
| | The function \(Re(k_b(t))(1-t)\). More...
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| double | getKb_re_1mt2 (double t) |
| | The function \(Re(k_b(t))(1-t)^2\). More...
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| double | getKb_re_t (double t) |
| | The function \(Re(k_b(t))t\). More...
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| double | getKb_re_t2_1mt (double t) |
| | The function \(Re(k_b(t))t^2(1-t)\). More...
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| double | getKb_re_t2_1mt2 (double t) |
| | The function \(Re(k_b(t))t^2(1-t)^2\). More...
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| double | getKb_re_t_1mt (double t) |
| | The function \(Re(k_b(t))t(1-t)\). More...
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| double | getKb_re_t_1mt2 (double t) |
| | The function \(Re(k_b(t))t(1-t)^2\). More...
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| double | getKc_abs2_1mt (double t) |
| | The function \(|k_c(t)|^2(1 - t)\). More...
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| double | getKc_abs2_1mt2 (double t) |
| | The function \(t|k_c(t)|^2(1 - t)^2\). More...
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| double | getKc_abs2_t (double t) |
| | The function \(|k_c(t)|^2 t\). More...
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| double | getKc_abs2_t_1mt (double t) |
| | The function \(|k_c(t)|^2t(1 - t)\). More...
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| double | getKc_im_1mt (double t) |
| | The function \(Im(k_c(t))(1-t)\). More...
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| double | getKc_im_1mt2 (double t) |
| | The function \(Im(k_c(t))(1-t)^2\). More...
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| double | getKc_im_Kb_1mt (double t) |
| | The function \(Re(k_b(t))Im(k_c(t))(1-t)\). More...
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| double | getKc_im_Kb_1mt2 (double t) |
| | The function \(Re(k_b(t))Im(k_c(t))(1-t)^2\). More...
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| double | getKc_im_Kb_t_1mt (double t) |
| | The function \(Re(k_b(t))Im(k_c(t)t(1-t)\). More...
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| double | getKc_im_Kb_t_1mt2 (double t) |
| | The function \(Re(k_b(t))Im(k_c(t)t(1-t)^2\). More...
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| double | getKc_im_t (double t) |
| | The function \(Im(k_c(t))t\). More...
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| double | getKc_im_t_1mt (double t) |
| | The function \(Im(k_c(t))t(1-t)\). More...
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| double | getKc_im_t_1mt2 (double t) |
| | The function \(Im(k_c(t))t(1-t)^2\). More...
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| double | getKc_re_1mt (double t) |
| | The function \(Re(k_c(t))(1-t)\). More...
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| double | getKc_re_1mt2 (double t) |
| | The function \(Re(k_c(t))(1-t)^2\). More...
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| double | getKc_re_Kb_1mt (double t) |
| | The function \(Re(k_b(t))Re(k_c(t))(1-t)\). More...
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| double | getKc_re_Kb_1mt2 (double t) |
| | The function \(Re(k_b(t))Re(k_c(t))(1-t)^2\). More...
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| double | getKc_re_Kb_t_1mt (double t) |
| | The function \(Re(k_b(t))Re(k_c(t)t(1-t)\). More...
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| double | getKc_re_Kb_t_1mt2 (double t) |
| | The function \(Re(k_b(t))Re(k_c(t)t(1-t)^2\). More...
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| double | getKc_re_t (double t) |
| | The function \(Re(k_c(t))t\). More...
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| double | getKc_re_t_1mt (double t) |
| | The function \(Re(k_c(t))t(1-t)\). More...
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| double | getKc_re_t_1mt2 (double t) |
| | The function \(Re(k_c(t))t(1-t)^2\). More...
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| double | h27_2 (double z, double E0) |
| | The \( h_{27}^{(2)}(z,\delta) \) function from arXiv:1009.5685 and arXiv:1503.01791. More...
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| double | Int_b1 (double E0) |
| | Integral of the functions getKb_re_1mt() and getKb_re_1mt2(). More...
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| double | Int_b2 (double E0) |
| | Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2(). More...
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| double | Int_b3 (double E0) |
| | Integral of the functions getKb_re_t() and getKb_re_t_1mt(). More...
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| double | Int_b4 (double E0) |
| | Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2(). More...
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| double | Int_bb1 (double E0) |
| | Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2(). More...
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| double | Int_bb2 (double E0) |
| | Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2(). More...
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| double | Int_bb4 (double E0) |
| | Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2(). More...
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| gslpp::complex | Int_bc1 (double E0) |
| | Integral of the functions getKc_re_Kb_1mt(), getKc_im_Kb_1mt() and getKc_re_Kb_1mt2(), getKc_im_Kb_1mt2(). More...
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| gslpp::complex | Int_bc2 (double E0) |
| | Integral of the functions getKc_re_Kb_t_1mt(), getKc_im_Kb_t_1mt() and getKc_re_Kb_t_1mt2(), getKc_im_Kb_t_1mt2(). More...
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| gslpp::complex | Int_c1 (double E0) |
| | Integral of the functions getKc_re_1mt(), getKc_im_1mt() and getKc_re_1mt2(), getKc_im_1mt2(). More...
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| gslpp::complex | Int_c2 (double E0) |
| | Integral of the functions getKc_re_t_1mt(), getKc_im_t_1mt() and getKc_re_t_1mt2(), getKc_im_t_1mt2(). More...
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| gslpp::complex | Int_c3 (double E0) |
| | Integral of the functions getKc_re_t(), getKc_im_t() and getKc_re_t_1mt(), getKc_im_t_1mt(). More...
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| double | Int_cc (double E0) |
| | Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt(). More...
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| double | Int_cc1 (double E0) |
| | Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^(). More...
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| double | Int_cc1_part1 (double E0) |
| | Integral of the functions getKc_abs2_1mt(). More...
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| double | Int_Phi77_2rem (double E0) |
| | The integral of omega77() More...
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| double | K77_2_z1 (double E0, double mu) |
| | The \( K_{77}^{(2),z=1} \) function computed in the limit \( m_b = m_c \). More...
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| gslpp::complex | kappa (double Mq, double t) |
| | The function \( k \) as defined in [168] . More...
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| gslpp::complex | Kij_1 (int i, int j, double E0, double mu) |
| | The \( K_{ij}^{(1)} \) function from [164] . More...
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| double | Kij_2 (int i, int j, double E0, double mu_b, double mu_c) |
| | The \( K_{ij}^{(2)} \) function from arXiv:1503.01791. More...
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| double | mddel_f_NLO (double z, double E0) |
| | The \( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791. More...
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| double | N (double E0, double mu) |
| | The non perturbative part of the \(BR\) as defined in [46] , \(N\). More...
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| double | N_27 () |
| | The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [127] , \(N_{27}\). More...
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| double | N_77 (double E0, double mu) |
| | The non perturbative part of the \(BR\) due to \(Q_7-Q_7\) interference as defined in arXiv:0911.2175, \(N_{77}\). More...
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| double | omega (double E0) |
| | The cutoff energy function \( \omega \) as defined in [145] . More...
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| double | omega77 (double z) |
| | The \( \omega_{77} \) function, linear combination of the functions \( F^{(2,a)} \), \( F^{(2,na)} \) and \( F^{(2,nf)} \) from hep-ph/0505097. More...
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| double | P (double E0, double mu_b, double mu_c, orders order) |
| | The perturbative part of the \(BR\) as defined in [164] , \(P\). More...
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| double | P0 (double E0) |
| | The perturbative part \( P^{(0)} \) of the BR as defined in [164] . More...
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| double | P0_4body (double E0, double t) |
| | The 4-body LO contribution as defined in [145] . More...
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| double | P11 () |
| | The perturbative part \( P_1^{(1)} \) of the BR as defined in [164] . More...
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| double | P12 () |
| | The perturbative part \( P_1^{(2)} \) of the BR as defined in [164] . More...
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| double | P21 (double E0, double mu) |
| | The perturbative part \( P_2^{(1)} \) of the BR as defined in [164] . More...
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| double | P21_CPodd (double E0, double mu) |
| | The CP odd part of the perturbative part \( P_2^{(1)} \) of the BR as defined in [164] . More...
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| double | P22 (double E0, double mu_b, double mu_c) |
| | The perturbative part \( P_2^{(2)} \) of the BR as defined in [164] . More...
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| double | P32 (double E0, double mu) |
| | The perturbative part \( P_3^{(2)} \) of the BR as defined in [164] . More...
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| double | Phi11_1 (double E0) |
| | The \( \Phi_{11}^{(1)} \) function from [127] . More...
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| double | Phi12_1 (double E0) |
| | The \( \Phi_{12}^{(1)} \) function from [127] . More...
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| gslpp::complex | Phi13_1 (double E0) |
| | The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [56] . More...
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| gslpp::complex | Phi14_1 (double E0) |
| | The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [56] . More...
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| gslpp::complex | Phi15_1 (double E0) |
| | The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [56] . More...
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| gslpp::complex | Phi16_1 (double E0) |
| | The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [56] . More...
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| gslpp::complex | Phi17_1 (double E0, double z) |
| | The \( \Phi_{17}^{(1)} \) function from [127] . More...
|
| |
| gslpp::complex | Phi18_1 (double E0, double z) |
| | The \( \Phi_{18}^{(1)} \) function from [127] . More...
|
| |
| double | Phi22_1 (double E0) |
| | The \( \Phi_{22}^{(1)} \) function from [127] . More...
|
| |
| double | Phi22_2beta0 (double E0, double mu) |
| | The \( \Phi_{22}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
|
| |
| gslpp::complex | Phi23_1 (double E0) |
| | The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi23_1_4body (double E0) |
| | The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [143] . More...
|
| |
| gslpp::complex | Phi24_1 (double E0) |
| | The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi24_1_4body (double E0) |
| | The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [143] . More...
|
| |
| gslpp::complex | Phi25_1 (double E0) |
| | The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi25_1_4body (double E0) |
| | The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [143] . More...
|
| |
| gslpp::complex | Phi26_1 (double E0) |
| | The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi26_1_4body (double E0) |
| | The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [143] . More...
|
| |
| gslpp::complex | Phi27_1 (double E0, double z) |
| | The \( \Re \Phi_{27}^{(1)} \) function from [127] . More...
|
| |
| gslpp::complex | Phi28_1 (double E0, double z) |
| | The \( \Phi_{28}^{(1)} \) function from [127] . More...
|
| |
| double | Phi28_2beta0 (double E0, double mu) |
| | The \( \Phi_{28}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
|
| |
| double | Phi33_1 (double E0) |
| | The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| double | Phi34_1 (double E0) |
| | The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| double | Phi35_1 (double E0) |
| | The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| gslpp::complex | Phi36_1 (double E0) |
| | The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi37_1 (double E0) |
| | The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi38_1 (double E0) |
| | The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi44_1 (double E0) |
| | The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| double | Phi45_1 (double E0) |
| | The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| gslpp::complex | Phi46_1 (double E0) |
| | The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi47_1 (double E0) |
| | The \( \Phi_{47}^{(1)} \) function from [127] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi48_1 (double E0) |
| | The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi55_1 (double E0) |
| | The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| gslpp::complex | Phi56_1 (double E0) |
| | The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi57_1 (double E0) |
| | The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi58_1 (double E0) |
| | The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| gslpp::complex | Phi66_1 (double E0) |
| | The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [56] . More...
|
| |
| gslpp::complex | Phi67_1 (double E0) |
| | The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| gslpp::complex | Phi68_1 (double E0) |
| | The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] . More...
|
| |
| double | Phi77_1 (double E0) |
| | The \( \Phi_{77}^{(1)} \) function from [127] . More...
|
| |
| double | Phi77_2beta0 (double E0, double mu) |
| | The \( \Phi_{77}^{(2)\beta_0} \) function from [164] .. More...
|
| |
| double | Phi77_2rem (double E0) |
| | The part of the \( K_{77}^{(2)} \) function with no \( \beta_0 \) dependance, as defined in [164] . More...
|
| |
| double | Phi78_1 (double E0) |
| | The \( \Phi_{78}^{(1)} \) function from [127] . More...
|
| |
| double | Phi88_1 (double E0) |
| | The \( \Phi_{88}^{(1)} \) function from [127] . More...
|
| |
| double | Phi88_2beta0 (double E0, double mu) |
| | The \( \Phi_{88}^{(2)\beta_0} \) function from arXiv:1009.5685. More...
|
| |
| gslpp::complex | r1 (int i, double z) |
| | The funcion \( r_i^{(1)}(z) \) as defined in [53] . More...
|
| |
| gslpp::complex | r1_ew (int i, double z) |
| | The funcion \( r_{i,ew}^{(1)}(z) \) as defined in [126] . More...
|
| |
| double | Rer22 (double z) |
| | The \( Re r_2^{(2)} \) function from [164] . More...
|
| |
| double | rho (double E0) |
| | The cutoff energy function \( \rho \) as defined in [145] . More...
|
| |
| double | T1 (double E0, double t) |
| | The cutoff energy function \( T_1 \) as defined in [145] . More...
|
| |
| double | T2 (double E0, double t) |
| | The cutoff energy function \( T_2 \) as defined in [145] . More...
|
| |
| double | T3 (double E0, double t) |
| | The cutoff energy function \( T_3 \) as defined in [145] . More...
|
| |
| void | updateParameters () |
| | The update parameter method for bsgamma. More...
|
| |
| double | Vub_NLO (double E0) |
| | The total NLO Vub part of the \(BR\), \(Vub^{NLO}\). More...
|
| |
| double | Vub_NLO_2body () |
| | The 2 body NLO Vub part of the \(BR\) as defined in [127] , \(Vub^{NLO}_{2b}\). More...
|
| |
| double | Vub_NLO_2body_CPodd () |
| | The CP odd part of the 2 body NLO Vub part of the \(BR\) as defined in [127] , \(Vub^{NLO}_{2b,CPodd}\). More...
|
| |
| double | Vub_NLO_3body_A (double E0) |
| | The first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A,CPodd}\). More...
|
| |
| double | Vub_NLO_3body_A_CPodd (double E0) |
| | The CP odd part of the first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A}\). More...
|
| |
| double | Vub_NLO_3body_B (double E0) |
| | The second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B,CPodd}\). More...
|
| |
| double | Vub_NLO_3body_B_CPodd (double E0) |
| | The CP odd part of the second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B}\). More...
|
| |
| double | Vub_NLO_4body (double E0) |
| | The 4 body NLO Vub part of the \(BR\) obtained from [143] , \(Vub^{NLO}_{4b,CPodd}\). More...
|
| |
| double | Vub_NLO_4body_CPodd (double E0) |
| | The CP odd part of the 4 body NLO Vub part of the \(BR\) obtained from [143] , \(Vub^{NLO}_{4b}\). More...
|
| |
| double | Vub_NLO_CPodd (double E0) |
| | The CP odd part of the total NLO Vub part of the \(BR\), \(Vub^{NLO}_{CPodd}\). More...
|
| |
| double | Vub_NNLO (double E0) |
| | The NNLO Vub part of the \(BR\) as defined in xxxxxxxxx, \(Vub^{NLO}\). More...
|
| |
| double | Y1 (double E0, double mu) |
| | The \( Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2 (double E0, double mu) |
| | The \( Y^{(2)}(z_0,\mu) \) function from arXiv:0805.3911v2 and arXiv:1005.5587v1. More...
|
| |
| double | Y2CA (double E0, double mu) |
| | The \( Y^{(2,CA)}(z_0,\mu) \) function from arXiv:1005.5587v1. More...
|
| |
| double | Y2CF (double E0, double mu) |
| | The \( Y^{(2,CF)}(z_0,\mu) \) function from arXiv:1005.5587v1. More...
|
| |
| double | Y2NH (double E0, double mu) |
| | The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NL (double E0, double mu) |
| | The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NV (double E0, double mu) |
| | The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NV_PHI1 (double rho) |
| | The \( \Phi_1(\rho) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NV_PHI2 (double rho) |
| | The \( \Phi_2(\rho) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NV_PHI3 (double rho) |
| | The \( \Phi_3(\rho) \) function from arXiv:0805.3911v2. More...
|
| |
| double | Y2NV_PHI4 (double rho) |
| | The \( \Phi_4(\rho) \) function from arXiv:0805.3911v2. More...
|
| |
| double | zdz_f_NLO (double z, double E0) |
| | The \( z \frac{d}{dz}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791. More...
|
| |
| double | zdz_Phi22_1 (double E0) |
| | Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines. More...
|
| |
| double | zdz_Phi28_1 (double z, double E0) |
| | Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines. More...
|
| |
| double | zeta () |
| | The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \). More...
|
| |
| double | getBinMax () |
| | A get method to get the maximum value of the bin. More...
|
| |
| double | getBinMin () |
| | A get method to get the minimum value of the bin. More...
|
| |
| const StandardModel & | getModel () |
| | A get method to get the model. More...
|
| |
| const std::vector< std::string > | getParametersForObservable () |
| | A get method to get the parameters for the specific observable. More...
|
| |
| void | setBinMax (double max) |
| | A set method to set the maximum value of the bin. More...
|
| |
| void | setBinMin (double min) |
| | A set method to set the minimum value of the bin. More...
|
| |
| void | setParametersForObservable (std::vector< std::string > parametersForObservable_i) |
| | A set method to get the parameters for the specific observable. More...
|
| |
| | ThObservable (const StandardModel &SM_i) |
| | Constructor. More...
|
| |
| | ThObservable (const ThObservable &orig) |
| | The copy constructor. More...
|
| |
| virtual | ~ThObservable () |
| | The default destructor. More...
|
| |
◆ Bsgamma() [1/2]
Constructor.
- Parameters
-
| [in] | SM_i | a reference to an object of type StandardModel |
| [in] | quark_i | final quark type of the decay |
| [in] | obsFlag | flag to choose which observable to compute |
Definition at line 22 of file bsgamma.cpp.
26 if (obsFlag > 0 and obsFlag < 3)
obs = obsFlag;
27 else throw std::runtime_error(
"obsFlag in bsgamma can only be 1 (BR) or 2 (ACP)");
38 <<
"rhoD3" <<
"muG2" <<
"rhoLS3" <<
"BLNPcorr" <<
"mu_b_bsgamma" <<
"mu_c_bsgamma");
55 w_INT = gsl_integration_cquad_workspace_alloc (100);
◆ Bsgamma() [2/2]
Constructor.
- Parameters
-
| [in] | SM_i | a reference to an object of type StandardModel |
| [in] | obsFlag | flag to choose which observable to compute |
Definition at line 58 of file bsgamma.cpp.
62 if (obsFlag > 0 and obsFlag < 3)
obs = obsFlag;
63 else throw std::runtime_error(
"obsFlag in bsgamma can only be 1 (BR) or 2 (ACP)");
84 w_INT = gsl_integration_cquad_workspace_alloc (100);
◆ a()
The funcion \( a(z) \) as defined in [53] .
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( a(z) \)
Definition at line 233 of file bsgamma.cpp.
235 double zeta3 = gsl_sf_zeta_int(3);
247 double pi2=M_PI*M_PI;
250 else return 16./9. * ( ( 5./2. - pi2/3. - 3.*zeta3
251 + ( 5./2. - 3./4.*pi2 )*L + L2/4. + L3/12. )*z
252 + ( 7./4. + 2./3.*pi2 - pi2*L/2. - L2/4. + L3/12. )*z2
253 + ( -7./6. - pi2/4. + 2*L - 3./4.*L2 )*z3
254 + ( 457./216. - 5./18*pi2 - L/72. - 5./6.*L2 )*z4
255 + ( 35101./8640. - 35./72.*pi2 - 185./144.*L - 35./24.*L2 )*z5
256 + ( 67801./8000. - 21./20.*pi2 - 3303./800.*L - 63./20.*L2 )*z6 +
258 + ( 1./2. - pi2/6. - L + L2/2. )*z2
259 + z3 + 5./9.*z4 + 49./72.*z5 + 231./200.*z6) );
◆ b()
The funcion \( b(z) \) as defined in [53] .
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( b(z) \)
Definition at line 262 of file bsgamma.cpp.
273 double pi2=M_PI*M_PI;
276 else return -8./9. * ( ( -3. + pi2/6. - L )*z - 2./3.*pi2*
pow(z,3./2.)
277 + ( 1./2. + pi2 -2.*L - L2/2. )*z2
278 + ( -25./12. - pi2/9. - 19./18.*L + 2.*L2 )*z3
279 + ( -1376./225. + 137./30.*L + 2.*L2 + 2./3.*pi2 )*z4
280 + ( -131317./11760. + 887./84.*L + 5.*L2 + 5./3.*pi2 )*z5
281 + ( -2807617./97200. + 16597./540.*L + 14.*L2 + 14./3.*pi2 )*z6 +
283 + ( -10./9. + 4./3.*L )*z3 + z4 + 2./3.*z5 + 7./9.*z6) );
◆ C_sem()
| double Bsgamma::C_sem |
( |
| ) |
|
The ratio \(C = | \frac{V_{ub}}{V_{cb}} |^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]}{\Gamma[\bar{B} \to X_u e \bar{\nu}]} \) as defined in [128] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino).
- Returns
- \(C\)
Definition at line 2325 of file bsgamma.cpp.
2328 return (1. - 8. * z + 8. * z*z*z - z*z*z*z - 12. * z*z *
log(z)) * ( 0.903
◆ checkCache()
| void Bsgamma::checkCache |
( |
| ) |
|
|
private |
The caching method for bsgamma.
Definition at line 87 of file bsgamma.cpp.
◆ computeCoeff()
| void Bsgamma::computeCoeff |
( |
double |
mu | ) |
|
Compute the Wilson Coefficient.
- Parameters
-
| [in] | mu | low scale of the decay |
Definition at line 1901 of file bsgamma.cpp.
◆ computeThValue()
| double Bsgamma::computeThValue |
( |
| ) |
|
|
virtual |
Computes the Branching Ratio for the \(b \to q \gamma\) decay.
- Returns
- \(BR\)
Implements ThObservable.
Definition at line 2429 of file bsgamma.cpp.
2440 throw std::runtime_error(
"Bsgamma::computeThValue(): Observable type not defined. Can be only 1 or 2");
◆ delddel_Phi22_1()
| double Bsgamma::delddel_Phi22_1 |
( |
double |
E0 | ) |
|
Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.
- Parameters
-
- Returns
- \( 4(1-\delta(E_0)) \frac{d\Phi_{22}^{(1)}}{d\,\delta} \)
Definition at line 1638 of file bsgamma.cpp.
1640 double d =
delta(E0);
◆ delddel_Phi28_1()
| double Bsgamma::delddel_Phi28_1 |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.
- Parameters
-
- Returns
- \( 2(1-\delta(E_0)) \frac{d\Phi_{28}^{(1)}}{d\,\delta} \)
Definition at line 1650 of file bsgamma.cpp.
1652 double d =
delta(E0);
1653 double Sq =
sqrt( (1. - d) * (1. - d - 4.*z) );
1654 double Log =
log( (
sqrt(1. - d) +
sqrt(1. - d - 4.*z) ) / 2. /
sqrt(z) );
1655 double Log2 = Log*Log;
1657 return 4. / (27. * Sq * (1 - d - 4. * z)) * Sq * Sq *
1658 (-8. * (-1. + d) * Log * z * (-1. + d + 4. * z) +
1659 Sq * (1. + d*d + (4. + 8. * Log2 - 2. * M_PI*M_PI) * z +
1660 4. * (-4. * Log2 + M_PI*M_PI) * z * z -
1661 2. * d * (1. + (2. + 4. * Log2 - M_PI*M_PI) * z)));
◆ delddel_Phi88_1()
| double Bsgamma::delddel_Phi88_1 |
( |
double |
E0 | ) |
|
Derivative of the function Phi88_1() used to compute effects of massive quark loops on gluon lines.
- Parameters
-
- Returns
- \( 4(1-\delta(E_0)) \frac{d\Phi_{88}^{(1)}}{d\,\delta} \)
Definition at line 1683 of file bsgamma.cpp.
1685 double d =
delta(E0);
1688 return 4./27. * (1. - d) * (5. - 8./(1. - d) + 5. * d - 2. * d * d -
1689 2. * (2. - 4./(1. - d) + 2. * d) *
log(
Mb_kin/
Ms) + (4. * Ld)/(1. - d)
1690 - d * Ld - (2. + d) * Ld);
◆ delta()
| double Bsgamma::delta |
( |
double |
E0 | ) |
|
The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \).
- Parameters
-
- Returns
- \( \delta(E0) \)
Definition at line 105 of file bsgamma.cpp.
◆ Delta()
| double Bsgamma::Delta |
( |
double |
r | ) |
|
The \(\Delta(r)\) function from Z. Phys. C 48, 673 (1990).
- Parameters
-
| [in] | r | ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(\Delta(r)\)
Definition at line 1713 of file bsgamma.cpp.
1717 double Lmr =
log(1. - r);
1718 double Lpr =
log(1. + r);
1723 return -3./8. + 1./8. * M_PI*M_PI;
1725 return 1./4. * (1. - r) * (1. - r3) * ( gsl_sf_dilog(r) + Lr * Lmr - 1./2. * Lr2 - 1./3. * M_PI*M_PI )
1726 - 1./4. * (1. + r) * (1. + r3) * ( gsl_sf_dilog(-1./r) - Lr * Lpr + Lr2 )
1727 + 1./4. * Lr2 - 1./4. * r2 * Lr - 3./8. * r2 + 1./24. * M_PI*M_PI;
◆ dY1()
| double Bsgamma::dY1 |
( |
double |
E0 | ) |
|
The \( \delta Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( \delta Y^{(1)}(z_0,\mu) \)
Definition at line 1274 of file bsgamma.cpp.
1276 double z0 = 1. -
delta(E0);
1277 double Li2 = gsl_sf_dilog(z0);
1279 return + 2./9. * z0*(z0*z0 + 24.)- 8./3. * (z0 - 1.)*
log(1. - z0) - 8./3. *
Li2;
◆ EW_NLO()
| double Bsgamma::EW_NLO |
( |
double |
mu | ) |
|
The NLO electroweak correction to the BR as defined in [126] .
- Parameters
-
| [in] | mu | low scale of the decay |
- Returns
- \( P_3^{(2)} \)
Definition at line 2081 of file bsgamma.cpp.
2086 double ga_eff_ew_7[7] = {-832./729., -208./243., -20./243., -176./729., -22712./243., -6272./729., 16./9.};
2088 double Lz = 2. *
log(
Mz/mu);
2092 r[0] =
r1_ew(1,
zeta()) - ga_eff_ew_7[0] * Lb;
2093 r[1] =
r1_ew(2,
zeta()) - ga_eff_ew_7[1] * Lb;
2094 r[2] =
r1_ew(3,
zeta()) - ga_eff_ew_7[2] * Lb;
2095 r[3] =
r1_ew(4,
zeta()) - ga_eff_ew_7[3] * Lb;
2096 r[4] =
r1_ew(5,
zeta()) - ga_eff_ew_7[4] * Lb;
2097 r[5] =
r1_ew(6,
zeta()) - ga_eff_ew_7[5] * Lb;
2098 r[6] =
r1_ew(7,
zeta()) - ga_eff_ew_7[6] * Lb;
2100 for(
int i=0;i<7;i++){
◆ f()
| double Bsgamma::f |
( |
double |
r | ) |
|
The \(f(\rho)\) function from hep-ph/0611123.
- Parameters
-
| [in] | r | ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(f(\rho)\)
Definition at line 1693 of file bsgamma.cpp.
1699 double zeta3 = gsl_sf_zeta_int(3);
1703 return 7126./81. - 356./27. * M_PI*M_PI - 16./3. * zeta3;
1705 return - 16./3. * Poly.
Li3(r2)
1706 + 8. * r * (35./9. * r2 + 9.) * ( gsl_sf_dilog(r) - atanh(r) * Lr - 1./4. * M_PI*M_PI)
1707 + 2. * (8./3. * Lr - 6. * r4 - 35./9. * r3 - 9. * r - 62./9. ) * gsl_sf_dilog(r2)
1708 - 8. * (3. * r4 + 31./9.) *
log(1. - r2) * Lr + 32./9. * Lr*Lr*Lr
1709 + 8. * (3. * r4 + 25./9.) * Lr*Lr + 64./9. * r2 * Lr
1710 + 4. * M_PI*M_PI * r4 + 172./9. * r2 + 5578./81.;
◆ F_1()
| double Bsgamma::F_1 |
( |
double |
z | ) |
|
The \( F_{1}(z,1) \) interpolated function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( F_{1}(z,1) \)
Definition at line 1624 of file bsgamma.cpp.
1626 return - 23.74697061848885 + 35./12. *
f_q(z,0.)
1627 + (2129./936. - 9./52. * M_PI*M_PI) *
f_NLO_1(z)
◆ F_2()
| double Bsgamma::F_2 |
( |
double |
z | ) |
|
The \( F_{2}(z,1) \) interpolated function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( F_{2}(z,1) \)
Definition at line 1631 of file bsgamma.cpp.
1633 return - 3.006537367876035 - 592./81. *
f_q(z,0.)
1634 - 10.344289655256379 *
f_NLO_1(z)
◆ f_b()
| double Bsgamma::f_b |
( |
double |
z | ) |
|
The \( f_{b}(z) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( f_{b}(z) \)
Definition at line 1614 of file bsgamma.cpp.
1616 return -1.836 + 2.608 * z + 0.8271 * z * z - 2.441 * z *
log(z);
◆ f_c()
| double Bsgamma::f_c |
( |
double |
z | ) |
|
The \( f_{c}(z) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( f_{c}(z) \)
Definition at line 1619 of file bsgamma.cpp.
1621 return 9.099 + 13.20 * z - 19.68 * z * z + 25.71 * z *
log(z);
◆ f_NLO_1()
| double Bsgamma::f_NLO_1 |
( |
double |
z | ) |
|
The \( f_{\rm NLO}(z,1) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( f_{\rm NLO}(z,1) \)
Definition at line 1454 of file bsgamma.cpp.
◆ f_q()
| double Bsgamma::f_q |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
The \( f_{q}(z,1) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
| [in] | E0 | energy cutoff |
- Returns
- \( f_{q}(z,1) \)
Definition at line 1609 of file bsgamma.cpp.
◆ f_u()
| double Bsgamma::f_u |
( |
double |
r | ) |
|
The \(f_u\) function obtained after multiplying the fitted function \(U_C\) of arXiv:0803.0960 for \(C_FT_R\) and subtracting the \(r \to 0\) limit.
- Parameters
-
| [in] | r | ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(f_u\)
Definition at line 1730 of file bsgamma.cpp.
1740 double Pi2 = M_PI*M_PI;
1741 double zeta3 = gsl_sf_zeta(3.);
1744 return 6335./288. - 1./2. * M_PI*M_PI - 16. * zeta3;
1746 return -5./6. * Pi2 * r + ( 14. + 16./9. * Pi2) * r2
1747 + (64./9. * Lr + 128./9. *
log(2.) - 95./54.) * Pi2 * r3
1748 + (-16./3. * Lr2 + 365./9. * Lr + 4. * Pi2 * Lr
1749 - 4375./54. - 25./9. * Pi2 + 32. * zeta3) * r4
1750 - 224./45. * Pi2 * r5 + (-128./27. * Lr2 + 16./15. * Lr
1751 + 15608./2025. + 128./81. * Pi2) * r6 - 16./7. * Pi2 * r7;
◆ ff7_dMP()
| double Bsgamma::ff7_dMP |
( |
double |
E0 | ) |
|
The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [143] .
- Parameters
-
- Returns
- \(ff^7_{d,MP}\)
Definition at line 695 of file bsgamma.cpp.
702 return 4. * d * (18. - 33.*d + 2.*d2 + 13.*d3 - 6.* d2 * (2. + d) *
log(d))
◆ ff7_sMP()
| double Bsgamma::ff7_sMP |
( |
double |
E0 | ) |
|
The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [143] .
- Parameters
-
- Returns
- \(ff^7_{s,MP}\)
Definition at line 709 of file bsgamma.cpp.
716 return (-2. * d * (72. + 39.*d - 76.*d2 - 35.*d3
717 + 6.*d*(18. + 13.*d + 2.*d2)*
log(d))) / (243.*(d - 1.));
◆ ff8_dMP()
| double Bsgamma::ff8_dMP |
( |
double |
E0 | ) |
|
The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [143] .
- Parameters
-
- Returns
- \(ff^8_{d,MP}\)
Definition at line 723 of file bsgamma.cpp.
730 double l1d =
log(1. - d);
731 double Li2 = gsl_sf_dilog(d);
733 return -136./27. * d - 724./81. * d2 + 20./27. * d3
734 + (-8./9. + 16./9. * d - 8./9. * d2) * l1d* l1d
735 + (32./27. * d + 76./27. * d2 - 16./81. * d3) * ld
736 + (-104./27. - 80./9. * d + 40./9. * d2 + (32./27.
737 + 32./9. * d - 16./9. * d2) * ld) * l1d
738 + (-64./27. * d - 152./27. * d2 + 32./81. * d3
739 + (-64./27. - 64./9. * d + 32./9. * d2) * l1d) *
log(
Ms/
Mb_kin)
740 + (32./27. + 32./9. * d - 16./9. * d2) *
Li2;
◆ ff8_sMP()
| double Bsgamma::ff8_sMP |
( |
double |
E0 | ) |
|
The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [143] .
- Parameters
-
- Returns
- \(ff^8_{s,MP}\)
Definition at line 746 of file bsgamma.cpp.
753 double l1d =
log(1. - d);
754 double Li2 = gsl_sf_dilog(d);
756 return -340./243. * d - 104./81. * d2 + 16./729. * d3
757 + (-4./27. + 8./27. * d - 4./27. * d2) * l1d* l1d
758 + (8./27. * d + 4./9. * d2) * ld
760 + (-268./243. - 40./27. * d + 20./27. * d2 + (8./27.
761 + 16./27. * d - 8./27. * d2) * ld
762 + (-16./27. - 32./27. * d + 16./27. * d2) *
log(
Ms/
Mb_kin)) * l1d
763 + (8./27. + 16./27. * d - 8./27. * d2) *
Li2;
◆ Gamma_t()
The function \( \Gamma \) as defined in [127] .
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \( \Gamma \)
Definition at line 345 of file bsgamma.cpp.
347 if (t<4)
return -2. * atan(
sqrt(t/(4.-t)) ) * atan(
sqrt(t/(4.-t)) );
◆ getKb_abs2_1mt()
| double Bsgamma::getKb_abs2_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2(1 - t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2(1 - t)\)
Definition at line 461 of file bsgamma.h.
◆ getKb_abs2_1mt2()
| double Bsgamma::getKb_abs2_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2(1 - t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2(1 - t)^2\)
Definition at line 472 of file bsgamma.h.
◆ getKb_abs2_t2_1mt()
| double Bsgamma::getKb_abs2_t2_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2t^2(1 - t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2t^2(1 - t)\)
Definition at line 505 of file bsgamma.h.
◆ getKb_abs2_t2_1mt2()
| double Bsgamma::getKb_abs2_t2_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2t^2(1 - t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2t^2(1 - t)^2\)
Definition at line 516 of file bsgamma.h.
◆ getKb_abs2_t_1mt()
| double Bsgamma::getKb_abs2_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2t(1 - t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2t(1 - t)\)
Definition at line 483 of file bsgamma.h.
◆ getKb_abs2_t_1mt2()
| double Bsgamma::getKb_abs2_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(|k_b(t)|^2t(1 - t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_b(t)|^2t(1 - t)^2\)
Definition at line 494 of file bsgamma.h.
◆ getKb_re_1mt()
| double Bsgamma::getKb_re_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))(1-t)\)
Definition at line 582 of file bsgamma.h.
◆ getKb_re_1mt2()
| double Bsgamma::getKb_re_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))(1-t)^2\)
Definition at line 593 of file bsgamma.h.
◆ getKb_re_t()
| double Bsgamma::getKb_re_t |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))t\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))t\)
Definition at line 527 of file bsgamma.h.
◆ getKb_re_t2_1mt()
| double Bsgamma::getKb_re_t2_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))t^2(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))t^2(1-t)\)
Definition at line 549 of file bsgamma.h.
◆ getKb_re_t2_1mt2()
| double Bsgamma::getKb_re_t2_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))t^2(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))t^2(1-t)^2\)
Definition at line 560 of file bsgamma.h.
◆ getKb_re_t_1mt()
| double Bsgamma::getKb_re_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))t(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))t(1-t)\)
Definition at line 538 of file bsgamma.h.
◆ getKb_re_t_1mt2()
| double Bsgamma::getKb_re_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))t(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))t(1-t)^2\)
Definition at line 571 of file bsgamma.h.
◆ getKc_abs2_1mt()
| double Bsgamma::getKc_abs2_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(|k_c(t)|^2(1 - t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_c(t)|^2(1 - t)\)
Definition at line 318 of file bsgamma.h.
◆ getKc_abs2_1mt2()
| double Bsgamma::getKc_abs2_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(t|k_c(t)|^2(1 - t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_c(t)|^2(1 - t)^2\)
Definition at line 340 of file bsgamma.h.
◆ getKc_abs2_t()
| double Bsgamma::getKc_abs2_t |
( |
double |
t | ) |
|
|
inline |
The function \(|k_c(t)|^2 t\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_c(t)|^2t\)
Definition at line 307 of file bsgamma.h.
◆ getKc_abs2_t_1mt()
| double Bsgamma::getKc_abs2_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(|k_c(t)|^2t(1 - t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(|k_c(t)|^2t(1 - t)\)
Definition at line 329 of file bsgamma.h.
◆ getKc_im_1mt()
| double Bsgamma::getKc_im_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Im(k_c(t))(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Im(k_c(t))(1-t)\)
Definition at line 428 of file bsgamma.h.
◆ getKc_im_1mt2()
| double Bsgamma::getKc_im_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Im(k_c(t))(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Im(k_c(t))(1-t)^2\)
Definition at line 450 of file bsgamma.h.
◆ getKc_im_Kb_1mt()
| double Bsgamma::getKc_im_Kb_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Im(k_c(t))(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Im(k_c(t))(1-t)\)
Definition at line 615 of file bsgamma.h.
◆ getKc_im_Kb_1mt2()
| double Bsgamma::getKc_im_Kb_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Im(k_c(t))(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Im(k_c(t))(1-t)^2\)
Definition at line 637 of file bsgamma.h.
◆ getKc_im_Kb_t_1mt()
| double Bsgamma::getKc_im_Kb_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Im(k_c(t)t(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Im(k_c(t)t(1-t)\)
Definition at line 659 of file bsgamma.h.
◆ getKc_im_Kb_t_1mt2()
| double Bsgamma::getKc_im_Kb_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Im(k_c(t)t(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Im(k_c(t)t(1-t)^2\)
Definition at line 681 of file bsgamma.h.
◆ getKc_im_t()
| double Bsgamma::getKc_im_t |
( |
double |
t | ) |
|
|
inline |
The function \(Im(k_c(t))t\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Im(k_c(t))t\)
Definition at line 362 of file bsgamma.h.
◆ getKc_im_t_1mt()
| double Bsgamma::getKc_im_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Im(k_c(t))t(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Im(k_c(t))t(1-t)\)
Definition at line 384 of file bsgamma.h.
◆ getKc_im_t_1mt2()
| double Bsgamma::getKc_im_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Im(k_c(t))t(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Im(k_c(t))t(1-t)^2\)
Definition at line 406 of file bsgamma.h.
408 return kappa(
Mc,t).
imag() * t * (1. - t) * (1. - t);
◆ getKc_re_1mt()
| double Bsgamma::getKc_re_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_c(t))(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_c(t))(1-t)\)
Definition at line 417 of file bsgamma.h.
◆ getKc_re_1mt2()
| double Bsgamma::getKc_re_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_c(t))(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_c(t))(1-t)^2\)
Definition at line 439 of file bsgamma.h.
◆ getKc_re_Kb_1mt()
| double Bsgamma::getKc_re_Kb_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Re(k_c(t))(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Re(k_c(t))(1-t)\)
Definition at line 604 of file bsgamma.h.
◆ getKc_re_Kb_1mt2()
| double Bsgamma::getKc_re_Kb_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Re(k_c(t))(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Re(k_c(t))(1-t)^2\)
Definition at line 626 of file bsgamma.h.
◆ getKc_re_Kb_t_1mt()
| double Bsgamma::getKc_re_Kb_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Re(k_c(t)t(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Re(k_c(t)t(1-t)\)
Definition at line 648 of file bsgamma.h.
◆ getKc_re_Kb_t_1mt2()
| double Bsgamma::getKc_re_Kb_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_b(t))Re(k_c(t)t(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_b(t))Re(k_c(t)t(1-t)^2\)
Definition at line 670 of file bsgamma.h.
◆ getKc_re_t()
| double Bsgamma::getKc_re_t |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_c(t))t\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_c(t))t\)
Definition at line 351 of file bsgamma.h.
◆ getKc_re_t_1mt()
| double Bsgamma::getKc_re_t_1mt |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_c(t))t(1-t)\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_c(t))t(1-t)\)
Definition at line 373 of file bsgamma.h.
◆ getKc_re_t_1mt2()
| double Bsgamma::getKc_re_t_1mt2 |
( |
double |
t | ) |
|
|
inline |
The function \(Re(k_c(t))t(1-t)^2\).
- Parameters
-
| [in] | t | dummy variable to be integrated out |
- Returns
- \(Re(k_c(t))t(1-t)^2\)
Definition at line 395 of file bsgamma.h.
397 return kappa(
Mc,t).
real() * t * (1. - t) * (1. - t);
◆ h27_2()
| double Bsgamma::h27_2 |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
The \( h_{27}^{(2)}(z,\delta) \) function from arXiv:1009.5685 and arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
| [in] | E0 | energy cutoff |
- Returns
- \( h_{27}^{(2)}(z,\delta) \)
Definition at line 1586 of file bsgamma.cpp.
1588 double d =
delta(E0);
1592 return ( 41./27. - 2./9. * M_PI*M_PI
1593 - 2.24 *
sqrt(z) - 7.04 * z + 23.72 *
pow(z,3./2.)
1594 + ( -9.86 * z + 31.28 * z * z ) *
log(z));
1595 }
else return - 0.1755402735503456 - 1.4553730660088837 * d
1596 + 1.1192806367180177 * d2
1597 + ( 0.7259818237183779 - 7.230418135384073 * d
1598 + 5.977206932166958 * d2 ) *
sqrt(z)
1599 + ( 13.786205094458156 + 113.71026116073105 * d
1600 - 100.3588074342665 * d2 ) * z
1601 + ( -145.05588751363894 - 307.05884309429547 * d
1602 + 388.54181686721904 * d2 ) *
pow(z,3./2.)
1603 + ( 475.2039505292043 + 312.9832308573048 * d
1604 - 775.8088176670707 * d2 ) * z * z
1605 + ( -509.7299390734172 - 126.08888075477071 * d
1606 + 646.2084041395774 * d2 ) *
pow(z,5./2.);
◆ Int_b1()
| double Bsgamma::Int_b1 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_re_1mt() and getKb_re_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))(1-t)^2\)
Definition at line 359 of file bsgamma.cpp.
362 double t1 = (1. -
delta(E0));
365 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
369 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_b2()
| double Bsgamma::Int_b2 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))t(1-t)^2\)
Definition at line 379 of file bsgamma.cpp.
382 double t1 = (1. -
delta(E0));
385 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
389 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_b3()
| double Bsgamma::Int_b3 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_re_t() and getKb_re_t_1mt().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t + \int_{1-\delta(E_0)}^1 Re(k_b(t))t(1-t)\)
Definition at line 399 of file bsgamma.cpp.
402 double t1 = (1. -
delta(E0));
405 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
409 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_b4()
| double Bsgamma::Int_b4 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))t^2(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))t^2(1-t)^2\)
Definition at line 419 of file bsgamma.cpp.
422 double t1 = (1. -
delta(E0));
425 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
429 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_bb1()
| double Bsgamma::Int_bb1 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2(1-t)^2\)
Definition at line 439 of file bsgamma.cpp.
442 double t1 = (1. -
delta(E0));
445 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
449 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_bb2()
| double Bsgamma::Int_bb2 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2t(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2t(1-t)^2\)
Definition at line 459 of file bsgamma.cpp.
462 double t1 = (1. -
delta(E0));
465 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
469 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_bb4()
| double Bsgamma::Int_bb4 |
( |
double |
E0 | ) |
|
Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |(k_b(t)|^2t^2(1-t) + \int_{1-\delta(E_0)}^1 |(k_b(t)|^2t^2(1-t)^2\)
Definition at line 479 of file bsgamma.cpp.
482 double t1 = (1. -
delta(E0));
485 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
489 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_bc1()
Integral of the functions getKc_re_Kb_1mt(), getKc_im_Kb_1mt() and getKc_re_Kb_1mt2(), getKc_im_Kb_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))k_c(t)(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))k_c(t)(1-t)^2\)
Definition at line 499 of file bsgamma.cpp.
502 double t1 = (1. -
delta(E0));
505 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
509 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
513 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
517 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_bc2()
Integral of the functions getKc_re_Kb_t_1mt(), getKc_im_Kb_t_1mt() and getKc_re_Kb_t_1mt2(), getKc_im_Kb_t_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))k_c(t)t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))k_c(t)t(1-t)^2\)
Definition at line 527 of file bsgamma.cpp.
530 double t1 = (1. -
delta(E0));
533 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
537 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
541 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
545 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_c1()
Integral of the functions getKc_re_1mt(), getKc_im_1mt() and getKc_re_1mt2(), getKc_im_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)(1-t) + \int_{1-\delta(E_0)}^1 k_c(t)(1-t)^2\)
Definition at line 555 of file bsgamma.cpp.
558 double t1 = (1. -
delta(E0));
561 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
565 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
569 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
573 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_c2()
Integral of the functions getKc_re_t_1mt(), getKc_im_t_1mt() and getKc_re_t_1mt2(), getKc_im_t_1mt2().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)t(1-t) + \int_{1-\delta(E_0)}^1 k_c(t)t(1-t)^2\)
Definition at line 583 of file bsgamma.cpp.
586 double t1 = (1. -
delta(E0));
589 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
593 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
597 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
601 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_c3()
Integral of the functions getKc_re_t(), getKc_im_t() and getKc_re_t_1mt(), getKc_im_t_1mt().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} k_c(t)t + \int_{1-\delta(E_0)}^1 k_c(t)t(1-t)\)
Definition at line 611 of file bsgamma.cpp.
614 double t1 = (1. -
delta(E0));
617 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
621 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
625 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
629 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_cc()
| double Bsgamma::Int_cc |
( |
double |
E0 | ) |
|
Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2t + 2\int_{1-\delta(E_0)}^1 |k_c(t)|^2t(1-t)\)
Definition at line 639 of file bsgamma.cpp.
642 double t1 = (1. -
delta(E0));
645 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
649 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_cc1()
| double Bsgamma::Int_cc1 |
( |
double |
E0 | ) |
|
Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2(1-t) + \int_{1-\delta(E_0)}^1 |k_c(t)|^2(1-t)^2\)
Definition at line 659 of file bsgamma.cpp.
662 double t1 = (1. -
delta(E0));
666 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
670 if (gsl_integration_cquad(&
INT, t1, 1., 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_cc1_part1()
| double Bsgamma::Int_cc1_part1 |
( |
double |
E0 | ) |
|
Integral of the functions getKc_abs2_1mt().
- Parameters
-
- Returns
- \(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2(1-t)\)
Definition at line 680 of file bsgamma.cpp.
683 double t1 = (1. -
delta(E0));
686 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ Int_Phi77_2rem()
| double Bsgamma::Int_Phi77_2rem |
( |
double |
E0 | ) |
|
The integral of omega77()
- Parameters
-
- Returns
- \( \int_0^{1-\delta(E_0)} omega_{77} \)
Definition at line 1799 of file bsgamma.cpp.
1802 double t1 = (1. -
delta(E0));
1805 if (gsl_integration_cquad(&
INT, 0., t1, 1.e-2, 1.e-1,
w_INT, &
avaINT, &
errINT, NULL) != 0)
return std::numeric_limits<double>::quiet_NaN();
◆ K77_2_z1()
| double Bsgamma::K77_2_z1 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( K_{77}^{(2),z=1} \) function computed in the limit \( m_b = m_c \).
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | b quark scale |
- Returns
- \( K_{77}^{(2),z=1} \)
Definition at line 1826 of file bsgamma.cpp.
1829 double Pi2 = M_PI*M_PI;
1830 double xm = 8./9. * M_PI *
alsUps;
1833 return ( K77_1 - 4. *
Phi77_1(E0) ) * K77_1 - 1178948./729. + 18593./729. * Pi2
1834 - 628./405. * Pi2*Pi2 + 428./27. * Pi2 *
log(2.) + 61294./81. * gsl_sf_zeta(3.)
1835 - 880./9. * Lb * Lb + ( 440./27. * Pi2 - 14698./27. ) * Lb
◆ kappa()
The function \( k \) as defined in [168] .
- Parameters
-
| [in] | Mq | quark mass |
| [in] | t | dummy variable to be integrated out |
- Returns
- \( k \)
Definition at line 353 of file bsgamma.cpp.
◆ Kij_1()
The \( K_{ij}^{(1)} \) function from [164] .
- Parameters
-
| [in] | i | first index |
| [in] | j | second index |
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( K_{ij}^{(1)} \)
Definition at line 1094 of file bsgamma.cpp.
1096 if (i > 8 || j>8 || i<1 || j<1)
throw std::runtime_error(
"Bsgamma::Kij_1(): indices (i,j) must be included in (1,..,8)");
1098 double gamma_i7[8] = {-208./243., 416./81., -176./81., -152./243., -6272./81., 4624./243., 32./3., -32./9.};
1123 K_ij[2][6] =
r1(3,
zeta()) - gamma_i7[2]*Lb + 2.*
Phi37_1(E0);
1129 K_ij[3][6] =
r1(4,
zeta()) - gamma_i7[3]*Lb + 2.*
Phi47_1(E0);
1134 K_ij[4][6] =
r1(5,
zeta()) - gamma_i7[4]*Lb + 2.*
Phi57_1(E0);
1138 K_ij[5][6] =
r1(6,
zeta()) - gamma_i7[5]*Lb + 2.*
Phi67_1(E0);
1141 K_ij[6][6] = -182./9. + 8./9.*M_PI*M_PI - gamma_i7[6]*2.*Lb + 4.*
Phi77_1(E0);
1142 K_ij[6][7] =
r1(8,
zeta()) - gamma_i7[7]*Lb + 2.*
Phi78_1(E0);
1146 if (j >= i )
return K_ij[i-1][j-1];
◆ Kij_2()
| double Bsgamma::Kij_2 |
( |
int |
i, |
|
|
int |
j, |
|
|
double |
E0, |
|
|
double |
mu_b, |
|
|
double |
mu_c |
|
) |
| |
The \( K_{ij}^{(2)} \) function from arXiv:1503.01791.
- Parameters
-
| [in] | i | first index |
| [in] | j | second index |
| [in] | E0 | energy cutoff |
| [in] | mu_b | b quark scale |
| [in] | mu_c | c quark scale |
- Returns
- \( K_{ij}^{(2)} \)
Definition at line 1839 of file bsgamma.cpp.
1843 throw std::runtime_error(
"Bsgamma::Kij_2(): index i must be included in (1,2,7,8)");
1846 throw std::runtime_error(
"Bsgamma::Kij_2(): index j must be included in (1,2,7,8)");
1850 if (i > j) {temp=i; i=j; j=temp;}
1852 double K_ij[8][8] = {{0.}};
1854 double d =
delta(E0);
1860 double xm = 8./9. * M_PI *
alsUps;
1862 double A1 = 22.604961348474838;
1863 double A2 = 75.60281607240395;
1869 K_ij[1][6] = A2 +
F_2(z) - 27./2. *
f_q(z,E0) +
f_b(z) +
f_c(z)
1874 - 254./81.) * Lb - 5948./729. * Lb2;
1880 K_ij[0][0] = 1./36. * K_ij[1][1];
1881 K_ij[0][1] = -1./6. * K_ij[1][1];
1882 K_ij[0][6] = - 1./6. * K_ij[1][6] + A1 +
F_1(z)
1884 + 94./81.) * Lb - 34./27. * Lb2;
1885 K_ij[0][7] = -1./6. * K_ij[1][7];
1888 + 2./3. * (
f(r) -
f(1.)) - 128./3. * (
Delta(r) -
Delta(1.))
1889 - 16. * (
f_u(r) -
f_u(1.));
1890 K_ij[6][7] = 2./3. *
Y2(E0,
mu_b) + (16./9.*M_PI*M_PI - 164./9. - 32./6. * Lb) *
Y1(E0,
mu_b)
1891 - 32./81. *
alsUps * M_PI * (3. + 7.*d - 3.*d*d + d*d*d - 4.*d*
log(d) );
1898 return K_ij[i-1][j-1];
◆ mddel_f_NLO()
| double Bsgamma::mddel_f_NLO |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
The \( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
| [in] | E0 | energy cutoff |
- Returns
- \( (1. - \delta)\frac{d}{d\delta}f_{\rm NLO}(z,\delta) \)
Definition at line 1555 of file bsgamma.cpp.
1557 double d =
delta(E0);
1559 double sqrt1d =
sqrt(1. - d);
1560 double sqrt1d4z =
sqrt(1. - d - 4. * z);
1561 double sqrtz =
sqrt(z);
1562 double LogSqrt =
log((sqrt1d + sqrt1d4z)/(2. * sqrtz));
1563 double SumSqrt = sqrt1d + sqrt1d4z;
1564 double ProdSqrt = sqrt1d * sqrt1d4z;
1566 return 2. * (1. - d) * ( -2./27. * d * (-3. + 2. * d)
1567 - 2./27. * (3. - 3. * d + d2)
1568 + 1./9. * (2. - d) * (-7. + 2. * M_PI * M_PI) * z
1569 - 1./9. * d * (-7. + 2. * M_PI * M_PI) * z
1570 + 4. * d * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z))
1571 * ProdSqrt * z / (3. * SumSqrt)
1572 + 4./9. * (3. - 2. * M_PI * M_PI) * z * z
1573 + 4./3. * ProdSqrt * z * LogSqrt
1574 - 16. * d * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z))
1575 * (2. - d - 4. * z) * z * LogSqrt / (9. * SumSqrt)
1576 + 2. * d * z * (-2. + 2. * d + 4. * z) * LogSqrt / (3. * ProdSqrt)
1577 + 16. * (-1./(2. * sqrt1d) - 1./(2. * sqrt1d4z)) * z
1578 * (1 - 4. * z + 6. * z * z) * LogSqrt / (9. * SumSqrt)
1579 + 8./9. * d * z * LogSqrt * LogSqrt
1580 - 8./9. * (2. - d - 4. * z) * z * LogSqrt * LogSqrt
1581 + 4./3. * (1. - 2. * z) * z
1582 * ( (1./(2. * sqrt1d) + 1./(2. * sqrt1d4z)) * ProdSqrt/SumSqrt
1583 - (-2. + 2. * d + 4. * z) * LogSqrt/(2. * ProdSqrt)));
◆ N()
| double Bsgamma::N |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The non perturbative part of the \(BR\) as defined in [46] , \(N\).
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | b quark scale |
- Returns
- \(N\)
Definition at line 2320 of file bsgamma.cpp.
◆ N_27()
The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [127] , \(N_{27}\).
- Returns
- \(N_{27}\)
Definition at line 2265 of file bsgamma.cpp.
2267 double mcnorm = 1.131;
◆ N_77()
| double Bsgamma::N_77 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The non perturbative part of the \(BR\) due to \(Q_7-Q_7\) interference as defined in arXiv:0911.2175, \(N_{77}\).
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | b quark scale |
- Returns
- \(N_{77}\)
Definition at line 2273 of file bsgamma.cpp.
2275 double z = 1. -
delta(E0);
2279 double umz2 = (1.-z)*(1.-z);
2280 double Lz =
log(1. - z);
2284 double corrLambda2_rad;
2285 double corrLambda2_sem;
2286 double corrLambda2_mix;
2291 double Lambda_pert = 64./9. * alsb *
mu_kin *
2293 - 3. * (M_PI*M_PI/6. - 13./12.)) );
2299 double rho1 =
rho_D3 - rho_D3_pert;
2301 double f1EGN = 16./9. * ( 4. - M_PI*M_PI) - 8./3. * Lz2 -
2302 ( 4. * z * ( 30. - 63. * z + 31. * z2 + 5. * z3))/(9. * umz2) -
2303 ( 4. * (30. - 72. * z + 51. * z2 - 2. * z3 - 3. * z4))/(9. * umz2) * Lz;
2304 double f2EGN = -2./9. * ( 87. + 32. * M_PI*M_PI) - 32./3. * Lz2 +
2305 2. * ( 162. - 244. * z + 113. * z2 - 7. * z3)/(3. * (1. - z)) * Lz +
2306 2. * z * ( 54 - 49. * z + 15. * z2)/(1. - z);
2308 corrLambda2_rad =
lambda1 * ( f1EGN/8. - 4./3. * (Lb + 1.) )
2309 +
lambda2 * (f2EGN/8. + 12. * (Lb + 1.) );
2310 corrLambda2_sem = -3. * 4.98 *
lambda2 + (25. - 4. * M_PI*M_PI)/12.*
lambda1;
2313 corrLambda2 = corrLambda2_rad - corrLambda2_sem + corrLambda2_mix;
◆ omega()
| double Bsgamma::omega |
( |
double |
E0 | ) |
|
The cutoff energy function \( \omega \) as defined in [145] .
- Parameters
-
- Returns
- \( \omega(E0) \)
Definition at line 118 of file bsgamma.cpp.
125 return 3./2. * d2 - 2. * d3 + d4;
◆ omega77()
| double Bsgamma::omega77 |
( |
double |
z | ) |
|
The \( \omega_{77} \) function, linear combination of the functions \( F^{(2,a)} \), \( F^{(2,na)} \) and \( F^{(2,nf)} \) from hep-ph/0505097.
- Parameters
-
| [in] | z | integration variable |
- Returns
- \( \omega_{77} \)
Definition at line 1754 of file bsgamma.cpp.
1763 double omz = 1. - z;
1764 double omz2 = omz * omz;
1765 double omz3 = omz2 * omz;
1767 double Lomz =
log (1. - z);
1768 double Lomz2 = Lomz*Lomz;
1769 double Lomz3 = Lomz2*Lomz;
1770 double Ltmz =
log (2. - z);
1771 double Ltmz2 = Ltmz*Ltmz;
1772 double Li2omz = gsl_sf_dilog(1. - z);
1773 double Li2zmo = gsl_sf_dilog(z - 1.);
1775 double Pi2 = M_PI*M_PI;
1777 return 4./9. * (z3 - 4. * z2 + 4. * z + 1.)/omz * ( 2. * Poly.
Li3( 1./(2.-z) )
1778 - Poly.
Li3( z/(2.-z) ) + Poly.
Li3( z/(z-2.) )
1779 + Ltmz * ( Lomz2 - 1./3. * Ltmz2 + 1./6. * Pi2 ) )
1780 + 4./9. * (z3 + 36. * z - 43.)/omz * Poly.
Li3(z)
1781 + 8./9. * (z3 - 2. * z2 + 19. * z - 22.)/omz * Poly.
Li3(1.-z)
1782 - 16./9. * omz2 * Poly.
Li3(z-1.)
1783 - 4./9. * (z3 + 35. * z - 44.)/omz * Li2omz * Lomz
1784 - 4./9. * (z3 - 2. * z2 + 2. * z - 3.)/omz * Li2zmo * Lomz
1785 - 4./27. * (23. * z6 - 106. * z5 + 145. * z4 + 3. * z3
1786 - 180. * z2 + 147. * z - 36.)/(z * omz3) * (Li2omz + Lomz * Lz)
1787 + 2./27. * (z8 - 6. * z7 + 9. * z6 + 27. * z5 - 140. * z4 + 219. * z3
1788 - 124. * z2 + 28. * z - 6.)/(z * omz3) * (Li2zmo + Lomz * Ltmz)
1789 - 8./9. * (z2 + 8. * z - 11.)/omz * Lomz2 * Lz
1790 - 2./9. * (z4 - 3. * z3 - 5. * z2 + 15. * z + 8.)/(z * omz) * Lomz3
1791 - (z6 - 4. * z5 - 46. * z4 + 101. * z3 - 461. * z2 + 1057. * z - 72.)/(27. * z * omz) * Lomz2
1792 + 2./27. * (z3 - 2. * z2 + 4. * z - 5.)/omz * Pi2 * Lomz
1793 + (2. * z5 - 29. * z4 - 113. * z3 + 153. * z2 - 827. * z - 162.)/(27. * z * omz) * Lomz
1794 - (3. * z3 - 8. * z2 + 144. * z - 157.)/(9. * omz) * gsl_sf_zeta(3.)
1795 + (z6 - 4. * z5 + 48. * z4 - 106. * z3 - 58. * z2 + 158. * z - 75.)/(81. * z * omz) * Pi2
1796 + (2. * z4 - 92. * z3 + 88. * z2 - 713. * z - 18.)/(27. * omz);
◆ P()
| double Bsgamma::P |
( |
double |
E0, |
|
|
double |
mu_b, |
|
|
double |
mu_c, |
|
|
orders |
order |
|
) |
| |
The perturbative part of the \(BR\) as defined in [164] , \(P\).
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu_b | b quark scale |
| [in] | mu_c | c quark scale |
| [in] | order | perturbation theory order |
- Returns
- \(P\)
Definition at line 2233 of file bsgamma.cpp.
2259 std::stringstream out;
2261 throw std::runtime_error(
"Bsgamma::P(): order " + out.str() +
" not implemented");
◆ P0()
| double Bsgamma::P0 |
( |
double |
E0 | ) |
|
The perturbative part \( P^{(0)} \) of the BR as defined in [164] .
- Parameters
-
- Returns
- \( P^{(0)} \)
Definition at line 1969 of file bsgamma.cpp.
◆ P0_4body()
| double Bsgamma::P0_4body |
( |
double |
E0, |
|
|
double |
t |
|
) |
| |
The 4-body LO contribution as defined in [145] .
- Parameters
-
| [in] | E0 | cutoff energy |
| [in] | t | squared ratio between b quark and s quark masses |
- Returns
- \( P_{tree}^{(0)} \)
Definition at line 172 of file bsgamma.cpp.
199 double C13 = (C13re*la_u.
real() - C13im*la_u.
imag());
200 double C14 = (C14re*la_u.
real() - C14im*la_u.
imag());
201 double C15 = (C15re*la_u.
real() - C15im*la_u.
imag());
202 double C16 = (C16re*la_u.
real() - C16im*la_u.
imag());
203 double C23 = (C23re*la_u.
real() - C23im*la_u.
imag());
204 double C24 = (C24re*la_u.
real() - C24im*la_u.
imag());
205 double C25 = (C25re*la_u.
real() - C25im*la_u.
imag());
206 double C26 = (C26re*la_u.
real() - C26im*la_u.
imag());
218 return (C33 + 20. * C35 + 2./9. * C44 + 40./9. * C46 + 136. * C55 + 272./9. * C66) *
T1(E0,t) +
221 + 8./9. * C13 - 4./27. * C14 + 128./9. * C15 - 64./27. * C16
222 + 2./3. * C23 + 8./9. * C24 + 32./3. * C25 + 128./9. * C26) *
T2(E0,t) +
224 (C33 + 8./3. * C34 + 32. * C35 + 128./3. * C36 - 2./9. * C44 + 128./3. * C45
225 - 64./9. * C46 + 256. * C55 + 2048./3 * C56 - 512./9. * C66) *
T3(E0,t);
◆ P11()
The perturbative part \( P_1^{(1)} \) of the BR as defined in [164] .
- Returns
- \( P_1^{(1)} \)
Definition at line 1974 of file bsgamma.cpp.
◆ P12()
The perturbative part \( P_1^{(2)} \) of the BR as defined in [164] .
- Returns
- \( P_1^{(2)} \)
Definition at line 2032 of file bsgamma.cpp.
◆ P21()
| double Bsgamma::P21 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The perturbative part \( P_2^{(1)} \) of the BR as defined in [164] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( P_2^{(1)} \)
Definition at line 1980 of file bsgamma.cpp.
◆ P21_CPodd()
| double Bsgamma::P21_CPodd |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The CP odd part of the perturbative part \( P_2^{(1)} \) of the BR as defined in [164] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( P_2^{(1)} \)
Definition at line 2006 of file bsgamma.cpp.
◆ P22()
| double Bsgamma::P22 |
( |
double |
E0, |
|
|
double |
mu_b, |
|
|
double |
mu_c |
|
) |
| |
The perturbative part \( P_2^{(2)} \) of the BR as defined in [164] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu_b | b quark scale |
| [in] | mu_c | c quark scale |
- Returns
- \( P_2^{(2)} \)
Definition at line 2038 of file bsgamma.cpp.
2041 int i,j, temp_i,temp_j;
2055 p22 += (C0[i]*C0[j]).real() *
Kij_2(temp_i+1,temp_j+1,E0,
mu_b,
mu_c);
◆ P32()
| double Bsgamma::P32 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The perturbative part \( P_3^{(2)} \) of the BR as defined in [164] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( P_3^{(2)} \)
Definition at line 2062 of file bsgamma.cpp.
2074 p32 += 2.*(C0[i]*C1[j]).real() *
Kij_1(i+1,j+1,E0,mu).
real();
◆ Phi11_1()
| double Bsgamma::Phi11_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{11}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{11}^{(1)} \)
Definition at line 769 of file bsgamma.cpp.
◆ Phi12_1()
| double Bsgamma::Phi12_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{12}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{12}^{(1)} \)
Definition at line 774 of file bsgamma.cpp.
◆ Phi13_1()
The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{13}^{(1)} \)
Definition at line 779 of file bsgamma.cpp.
◆ Phi14_1()
The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{14}^{(1)} \)
Definition at line 784 of file bsgamma.cpp.
◆ Phi15_1()
The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{15}^{(1)} \)
Definition at line 789 of file bsgamma.cpp.
◆ Phi16_1()
The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{16}^{(1)} \)
Definition at line 794 of file bsgamma.cpp.
◆ Phi17_1()
The \( \Phi_{17}^{(1)} \) function from [127] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( \Phi_{17}^{(1)} \)
Definition at line 799 of file bsgamma.cpp.
◆ Phi18_1()
The \( \Phi_{18}^{(1)} \) function from [127] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( \Phi_{18}^{(1)} \)
Definition at line 804 of file bsgamma.cpp.
◆ Phi22_1()
| double Bsgamma::Phi22_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{22}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{22}^{(1)} \)
Definition at line 809 of file bsgamma.cpp.
◆ Phi22_2beta0()
| double Bsgamma::Phi22_2beta0 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( \Phi_{22}^{(2)\beta_0} \) function from arXiv:1009.5685.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( \Phi_{22}^{(2)\beta_0} \)
Definition at line 1182 of file bsgamma.cpp.
1185 double d =
delta(E0);
1188 double mcmb2 = mcmb*mcmb;
1189 double mcmb3 = mcmb2*mcmb;
1192 + 0.013698269459646965 + 0.3356948452887703 * d
1193 - 0.086677232161681 * d2
1194 + ( 0.3575455009710223 + 1.8248223618702617 * d
1195 - 0.374324331239819 * d2 ) * mcmb
1196 + (-2.3059130759599302 - 5.799640881350228 * d
1197 - 6.226247001127346 * d2 ) * mcmb2
1198 + ( 3.4485885608332834 - 0.5479757965141787 * d
1199 + 17.272487170738795 * d2 ) * mcmb3);
◆ Phi23_1()
The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{23}^{(1)} \)
Definition at line 822 of file bsgamma.cpp.
◆ Phi23_1_4body()
| double Bsgamma::Phi23_1_4body |
( |
double |
E0 | ) |
|
The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [143] .
- Parameters
-
- Returns
- \( \Phi_{23}^{(1),{\rm 4-body}} \)
Definition at line 814 of file bsgamma.cpp.
817 return 0.0039849625073434735;
◆ Phi24_1()
The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{24}^{(1)} \)
Definition at line 836 of file bsgamma.cpp.
◆ Phi24_1_4body()
| double Bsgamma::Phi24_1_4body |
( |
double |
E0 | ) |
|
The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [143] .
- Parameters
-
- Returns
- \( \Phi_{24}^{(1),{\rm 4-body}} \)
Definition at line 828 of file bsgamma.cpp.
831 return 0.012330977673588935;
◆ Phi25_1()
The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{25}^{(1)} \)
Definition at line 850 of file bsgamma.cpp.
◆ Phi25_1_4body()
| double Bsgamma::Phi25_1_4body |
( |
double |
E0 | ) |
|
The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [143] .
- Parameters
-
- Returns
- \( \Phi_{25}^{(1),{\rm 4-body}} \)
Definition at line 842 of file bsgamma.cpp.
845 return 0.06375940011749558;
◆ Phi26_1()
The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{26}^{(1)} \)
Definition at line 864 of file bsgamma.cpp.
◆ Phi26_1_4body()
| double Bsgamma::Phi26_1_4body |
( |
double |
E0 | ) |
|
The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [143] .
- Parameters
-
- Returns
- \( \Phi_{26}^{(1),{\rm 4-body}} \)
Definition at line 856 of file bsgamma.cpp.
859 return 0.11932481422855279;
◆ Phi27_1()
The \( \Re \Phi_{27}^{(1)} \) function from [127] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( \Re \Phi_{27}^{(1)} \)
Definition at line 870 of file bsgamma.cpp.
872 double d =
delta(E0);
875 double Pi2 = M_PI*M_PI;
876 double st0 =
sqrt(1. - 4.*z);
877 double std =
sqrt( (1. - d - 4.*z) * (1. - d) );
878 double L0 =
log( ( 1. + st0 ) / ( 2.*
sqrt(z) ) );
879 double Ld =
log( (
sqrt(1. - d) +
sqrt(1. - d - 4.*z) ) / ( 2.*
sqrt(z) ) );
884 res = -2./27. + (2.*Pi2 - 7.)/9. * z + 4.*(3. - 2.*Pi2)/9. * z * z
885 + 4./3. * z * (1. - 2.*z) * st0 * L0
886 - 8./9. * z * (6.*z*z - 4.*z + 1.) * L0*L0 + 4./3. * Pi2 * z * z *z;
887 }
else res = -2./27. * d * (3. - 3.*d + d2) + (2.*Pi2 - 7.)/9. * z * d * (2. - d)
888 + 4.*(3. - 2.*Pi2)/9. * z * z * d
889 + 4./3. * z * (1. - 2.*z) * ( st0 * L0 - std * Ld )
890 + 4./3. * z * d * std * Ld
891 - 8./9. * z * (6.*z*z - 4.*z + 1.) * ( L0*L0 - Ld*Ld )
892 - 8./9. * z * d * (2. - d - 4.*z) * Ld * Ld;
895 res +=
gslpp::complex::i() * 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2)* (L0-Ld) - 3./4. * (1. - 2. * z) * (st0-std)
896 + d * (2. - d - 4. * z) * Ld - 3./4. * d * std );
898 res +=
gslpp::complex::i() * 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2) * L0 - 3./4. * (1. - 2. * z) * st0 );
◆ Phi28_1()
The \( \Phi_{28}^{(1)} \) function from [127] .
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( \Phi_{28}^{(1)} \)
Definition at line 903 of file bsgamma.cpp.
◆ Phi28_2beta0()
| double Bsgamma::Phi28_2beta0 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( \Phi_{28}^{(2)\beta_0} \) function from arXiv:1009.5685.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( \Phi_{28}^{(2)\beta_0} \)
Definition at line 1202 of file bsgamma.cpp.
1205 double d =
delta(E0);
1208 double mcmb2 = mcmb*mcmb;
1209 double mcmb3 = mcmb2*mcmb;
1210 double mcmb4 = mcmb3*mcmb;
1211 double mcmb5 = mcmb4*mcmb;
1214 + 0.026054745293391798 + 0.1678721564514209 * d
1215 - 0.19700988587274693 * d2
1216 + ( -0.03801105485376407 + 0.601712887338462 * d
1217 - 0.7557529126506585 * d2 ) * mcmb
1218 + ( 2.7551159092192132 - 10.034450524236696 * d
1219 + 11.271837772655209 * d2 ) * mcmb2
1220 + ( -27.045289848315868 + 68.46851531490181 * d
1221 - 72.50921751760909 * d2 ) * mcmb3
1222 + ( 85.86574743951778 - 289.3441408351491 * d
1223 + 297.6777008484198 * d2 ) * mcmb4
1224 + ( -91.5260435658921 + 399.81982774456964 * d
1225 - 399.85440571662446 * d2 ) * mcmb5);
◆ Phi33_1()
| double Bsgamma::Phi33_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{33}^{(1)} \)
Definition at line 908 of file bsgamma.cpp.
917 + 1./18. * d * ( 1./2. - 1./2.*d2 + 1./3.*d3 - 1./15.*d4 );
◆ Phi34_1()
| double Bsgamma::Phi34_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{34}^{(1)} \)
Definition at line 920 of file bsgamma.cpp.
◆ Phi35_1()
| double Bsgamma::Phi35_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{35}^{(1)} \)
Definition at line 925 of file bsgamma.cpp.
934 + 4./9. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
◆ Phi36_1()
The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{36}^{(1)} \)
Definition at line 937 of file bsgamma.cpp.
947 - 2./27. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
◆ Phi37_1()
| double Bsgamma::Phi37_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{37}^{(1)} \)
Definition at line 950 of file bsgamma.cpp.
955 return -4./3. *
Int_b3(E0) + 1./9. * d * (1. - d + 1./3.*d2) + 1./4.*
ff7_sMP(E0);
◆ Phi38_1()
| double Bsgamma::Phi38_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{38}^{(1)} \)
Definition at line 958 of file bsgamma.cpp.
◆ Phi44_1()
| double Bsgamma::Phi44_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{44}^{(1)} \)
Definition at line 963 of file bsgamma.cpp.
◆ Phi45_1()
| double Bsgamma::Phi45_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{45}^{(1)} \)
Definition at line 968 of file bsgamma.cpp.
◆ Phi46_1()
The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{46}^{(1)} \)
Definition at line 973 of file bsgamma.cpp.
◆ Phi47_1()
| double Bsgamma::Phi47_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{47}^{(1)} \) function from [127] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{47}^{(1)} \)
Definition at line 978 of file bsgamma.cpp.
◆ Phi48_1()
| double Bsgamma::Phi48_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{48}^{(1)} \)
Definition at line 984 of file bsgamma.cpp.
◆ Phi55_1()
| double Bsgamma::Phi55_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{55}^{(1)} \)
Definition at line 990 of file bsgamma.cpp.
999 + 8./9. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
◆ Phi56_1()
The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{56}^{(1)} \)
Definition at line 1002 of file bsgamma.cpp.
1012 - 8./27. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
◆ Phi57_1()
| double Bsgamma::Phi57_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{57}^{(1)} \)
Definition at line 1015 of file bsgamma.cpp.
1020 return 16./9. * d * ( 1. - d + 1./3.*d2) + 4. *
ff7_sMP(E0);
◆ Phi58_1()
| double Bsgamma::Phi58_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{58}^{(1)} \)
Definition at line 1023 of file bsgamma.cpp.
◆ Phi66_1()
The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [56] .
- Parameters
-
- Returns
- \( \Phi_{66}^{(1)} \)
Definition at line 1029 of file bsgamma.cpp.
1040 + 2./81. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
◆ Phi67_1()
The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{67}^{(1)} \)
Definition at line 1043 of file bsgamma.cpp.
1048 return 8./3. * (
Int_b3(E0) - 2.*
Int_c3(E0)) - 8./27. * d * ( 1. - d + 1./3.*d2)
◆ Phi68_1()
The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [56] and adding the 4-body contribution from [143] .
- Parameters
-
- Returns
- \( \Phi_{68}^{(1)} \)
Definition at line 1052 of file bsgamma.cpp.
◆ Phi77_1()
| double Bsgamma::Phi77_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{77}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{77}^{(1)} \)
Definition at line 1058 of file bsgamma.cpp.
1064 return -2./3.*
pow(
log(d),2.) - 7./3.*
log(d) - 31./9. + 10./3.*d + d2/3. - 2./9.*d3 + d*(d - 4.)*
log(d)/3.;
◆ Phi77_2beta0()
| double Bsgamma::Phi77_2beta0 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( \Phi_{77}^{(2)\beta_0} \) function from [164] ..
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( \Phi_{77}^{(2)\beta_0} \)
Definition at line 1228 of file bsgamma.cpp.
1231 double d =
delta(E0);
1235 double zeta3 = gsl_sf_zeta_int(3);
1236 double Li2 = gsl_sf_dilog(1. - d);
1238 double Li3 = Poly.
Li3(d);
1241 + ( -3. + 4./3. * d - 1./3. * d2 - 4./3. * Ld ) *
Li2
1242 + ( 13./18. + 2. * d - 1./2. * d2 - 4./3. *
log(1. - d)
1243 + 2./3. * Ld ) * Ld*Ld
1244 - 8./3. * (
Li3 - zeta3)
1245 + ( 4./9. * M_PI*M_PI - 85./18. - 47./9. * d
1246 + 19./18. * d2 + 2./9. * d3 ) * Ld
1247 - 49./6. + 80./9. * d + 1./18. * d2 - 7./9. * d3);
◆ Phi77_2rem()
| double Bsgamma::Phi77_2rem |
( |
double |
E0 | ) |
|
The part of the \( K_{77}^{(2)} \) function with no \( \beta_0 \) dependance, as defined in [164] .
- Parameters
-
- Returns
- \( K_{77}^{(2), {\rm rem}} \)
Definition at line 1814 of file bsgamma.cpp.
1816 double xm = 8./9. * M_PI *
alsUps;
1817 double d =
delta(E0);
1823 ((4. - 6. * d2 + 2. * d3) *
log(d) + 7. - 13. * d + 3. * d2 + 5. * d3 - 2. * d4);
◆ Phi78_1()
| double Bsgamma::Phi78_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{78}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{78}^{(1)} \)
Definition at line 1067 of file bsgamma.cpp.
1073 double Li2 = gsl_sf_dilog(1. - d);
1075 double pi2=M_PI*M_PI;
1077 return 8./9.*(
Li2 - pi2/6. - d*
log(d) + 9./4.*d - d2/4. + d3/12.);
◆ Phi88_1()
| double Bsgamma::Phi88_1 |
( |
double |
E0 | ) |
|
The \( \Phi_{88}^{(1)} \) function from [127] .
- Parameters
-
- Returns
- \( \Phi_{88}^{(1)} \)
Definition at line 1080 of file bsgamma.cpp.
1086 double Li2 = gsl_sf_dilog(1. - d);
1088 double pi2=M_PI*M_PI;
1090 return 1./27.*( -2.*
log(
Mb_kin/
Ms)*( d2 + 2.*d + 4.*
log(1. - d) ) + 4.*
Li2 - 2./3.*pi2 - d*(2. + d)*
log(d)
1091 + 8.*
log(1. - d) - 2./3.*d3 + 3.*d2 +7*d);
◆ Phi88_2beta0()
| double Bsgamma::Phi88_2beta0 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( \Phi_{88}^{(2)\beta_0} \) function from arXiv:1009.5685.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( \Phi_{88}^{(2)\beta_0} \)
Definition at line 1250 of file bsgamma.cpp.
1253 double d =
delta(E0);
1257 double L1d =
log(1. - d);
1258 double Li2 = gsl_sf_dilog(1. - d);
1260 double Li3 = Poly.
Li3(d);
1263 + 4./27. * ( - 2. * (
Li2 - 1./6. * M_PI*M_PI + 3. * L1d
1264 - 1./4. * d * (2. + d) * Ld + 8./3. * d + 5./6. * d2
1266 + ( 5. - 2. * Ld ) * (
Li2 - 1./6. * M_PI*M_PI )
1267 + ( 1./2. * d + 1./4. * d2 - L1d ) * Ld * Ld
1268 - 1./12. * M_PI*M_PI * d * (2. + d)
1269 + ( 151./18. - 1./3. * M_PI*M_PI ) * L1d
1270 + ( - 53./12. * d - 19./12. * d2 + 2./9. * d3 ) * Ld
1271 + 787./72. * d + 227./72. * d2 - 41./72. * d3 ));
◆ r1()
The funcion \( r_i^{(1)}(z) \) as defined in [53] .
- Parameters
-
| [in] | i | function index |
| [in] | z | squared ratio between m_c and m_b^{\rm kin} |
- Returns
- \( r_i(z)^{(1)} \)
Definition at line 286 of file bsgamma.cpp.
288 double Xb = -0.16844083981858157;
298 return -761./729. - 4.*M_PI/9./
sqrt(3.) - 16./27.*Xb +
a(1.)/6. + 5.*
b(1.)/3. + 2.*
b(z) - 148./243.*
gslpp::complex::i()*M_PI;
300 return 56680./243. + 32.*M_PI/3./
sqrt(3.) + 128./9.*Xb - 16.*
a(1.) + 32.*
b(1.) + 896./81.*
gslpp::complex::i()*M_PI;
302 return 5710./729. - 16.*M_PI/9./
sqrt(3.) - 64./27.*Xb - 10./3.*
a(1.) + 44./3.*
b(1.) + 12.*
a(z) + 20.*
b(z)
307 std::stringstream out;
309 throw std::runtime_error(
"Bsgamma::r1(): index " + out.str() +
" not implemented");
◆ r1_ew()
The funcion \( r_{i,ew}^{(1)}(z) \) as defined in [126] .
- Parameters
-
| [in] | i | function index |
| [in] | z | squared ratio between m_c and m_b^{\rm kin} |
- Returns
- \( r_i(z)^{(1)} \)
Definition at line 313 of file bsgamma.cpp.
315 double Xb = -0.16844083981858157;
316 double PI2 = M_PI*M_PI;
321 return 3332./2187. - 4.*(
a(z) +
b(z))/9. + 160./729.*iPI;
323 return 833./729. - (
a(z) +
b(z))/3. + 40./243.*iPI;
325 return 748./729. + 2.*M_PI/9./
sqrt(3.) - 2./81.*PI2 + 8./27.*Xb
326 -
a(1.)/12. + 7.*
b(1.)/6. - 2.*
b(z) + 26./243.*iPI;
328 return 2680./2187. + 8.*M_PI/27./
sqrt(3.) - 8./243.*PI2 + 32./81.*Xb
329 -
a(1.)/9. + 2.*
b(1.)/9. + 56./729.*iPI;
331 return 78301./729. + 8.*M_PI/9./
sqrt(3.) - 40./81.*PI2 + 32./27.*Xb
332 - 13.*
a(1.)/3. + 38.*
b(1.)/3. - 12.*
a(z) - 20.*
b(z) + 3908./243.*iPI;
334 return 62440./2187. + 32.*M_PI/27./
sqrt(3.) - 160./243.*PI2 + 128./81.*Xb
335 - 16.*
a(1.)/9. + 32.*
b(1.)/9. + 896./729.*iPI;
337 return -25./27. - 2./9.*iPI;
339 std::stringstream out;
341 throw std::runtime_error(
"Bsgamma::r1_ew(): index " + out.str() +
" not implemented");
◆ Rer22()
| double Bsgamma::Rer22 |
( |
double |
z | ) |
|
The \( Re r_2^{(2)} \) function from [164] .
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \( Re r_2^{(2)} \)
Definition at line 1150 of file bsgamma.cpp.
1156 double z32 =
sqrt(z)*z;
1162 double Pi2 = M_PI*M_PI;
1163 double zeta3 = gsl_sf_zeta_int(3);
1165 return 67454./6561. - 124./729. * Pi2
1166 - 4./1215. * (11280. - 1520. * Pi2 - 171. * Pi2*Pi2 - 5760. * zeta3
1167 + 6840. * L - 1440. * Pi2*L - 2520. * zeta3*L
1168 + 120. * L2 + 100. * L3 - 30. * L4) * z
1169 - 64./243. * Pi2*( 43. - 12. *
log(2.) - 3. * L) * z32
1170 - 2./1215. * (11475. - 380. * Pi2 + 96. * Pi2*Pi2
1171 + 7200. * zeta3 - 1110. * L - 1560. * Pi2*L + 1440. * zeta3*L
1172 + 990. * L2 + 260. * L3 - 60. * L4) * z2
1173 + 2240./243. * Pi2 * z52
1174 - 2./2187. * (62471. - 2424. * Pi2 - 33264. * zeta3 - 19494. * L
1175 - 504. * Pi2*L - 5184. * L2 + 2160. * L3) * z3
1176 - 2464./6075. * Pi2 * z72
1177 + ( - 15103841./546750. + 7912./3645. * Pi2 + 2368./81. * zeta3
1178 + 147038./6075. * L + 352./243. * Pi2*L + 88./243. * L2
1179 - 512./243. * L3 ) * z4;
◆ rho()
| double Bsgamma::rho |
( |
double |
E0 | ) |
|
The cutoff energy function \( \rho \) as defined in [145] .
- Parameters
-
- Returns
- \( \rho(E0) \)
Definition at line 110 of file bsgamma.cpp.
115 return d + d4/6. +
log(1. - d);
◆ T1()
| double Bsgamma::T1 |
( |
double |
E0, |
|
|
double |
t |
|
) |
| |
The cutoff energy function \( T_1 \) as defined in [145] .
- Parameters
-
| [in] | E0 | cutoff energy |
| [in] | t | squared ratio between b quark and s quark masses |
- Returns
- \( T_1(E0) \)
Definition at line 128 of file bsgamma.cpp.
135 double Li2 = gsl_sf_dilog(d);
137 return 109./18. * d + 17./18. * d2 - 191./108. * d3 + 23./16. * d4
138 + 79./18. *
log(1. - d) - 5./3. *
Li2
◆ T2()
| double Bsgamma::T2 |
( |
double |
E0, |
|
|
double |
t |
|
) |
| |
The cutoff energy function \( T_2 \) as defined in [145] .
- Parameters
-
| [in] | E0 | cutoff energy |
| [in] | t | squared ratio between b quark and s quark masses |
- Returns
- \( T_2(E0) \)
Definition at line 143 of file bsgamma.cpp.
150 double Li2 = gsl_sf_dilog(d);
152 return 187./108. * d + 7./18. * d2 - 395./648. * d3 + 1181./2592. * d4
153 + 133./108. *
log(1. - d) -
Li2/2.
◆ T3()
| double Bsgamma::T3 |
( |
double |
E0, |
|
|
double |
t |
|
) |
| |
The cutoff energy function \( T_3 \) as defined in [145] .
- Parameters
-
| [in] | E0 | cutoff energy |
| [in] | t | squared ratio between b quark and s quark masses |
- Returns
- \( T_3(E0) \)
Definition at line 158 of file bsgamma.cpp.
165 double Li2 = gsl_sf_dilog(d);
167 return 35./162. * d + 1./72. * d2 - 89./1944. * d3 + 341./7776. * d4
168 + 13./81. *
log(1. - d) -
Li2/18.
◆ updateParameters()
| void Bsgamma::updateParameters |
( |
| ) |
|
The update parameter method for bsgamma.
Definition at line 2333 of file bsgamma.cpp.
2392 std::stringstream out;
2394 throw std::runtime_error(
"bqgamma: quark " + out.str() +
" not implemented");
◆ Vub_NLO()
| double Bsgamma::Vub_NLO |
( |
double |
E0 | ) |
|
The total NLO Vub part of the \(BR\), \(Vub^{NLO}\).
- Parameters
-
- Returns
- \(Vub^{NLO}\)
Definition at line 2213 of file bsgamma.cpp.
◆ Vub_NLO_2body()
| double Bsgamma::Vub_NLO_2body |
( |
| ) |
|
The 2 body NLO Vub part of the \(BR\) as defined in [127] , \(Vub^{NLO}_{2b}\).
- Returns
- \(Vub^{NLO}_{2b}\)
Definition at line 2114 of file bsgamma.cpp.
2121 * (
a(z)+
b(z) ).real();
◆ Vub_NLO_2body_CPodd()
| double Bsgamma::Vub_NLO_2body_CPodd |
( |
| ) |
|
The CP odd part of the 2 body NLO Vub part of the \(BR\) as defined in [127] , \(Vub^{NLO}_{2b,CPodd}\).
- Returns
- \(Vub^{NLO}_{2b}\)
Definition at line 2124 of file bsgamma.cpp.
2131 * (
a(z)+
b(z) ).imag();
◆ Vub_NLO_3body_A()
| double Bsgamma::Vub_NLO_3body_A |
( |
double |
E0 | ) |
|
The first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A,CPodd}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{3b}\)
Definition at line 2134 of file bsgamma.cpp.
2136 double d =
delta(E0);
◆ Vub_NLO_3body_A_CPodd()
| double Bsgamma::Vub_NLO_3body_A_CPodd |
( |
double |
E0 | ) |
|
The CP odd part of the first piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,A}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{3b}\)
Definition at line 2143 of file bsgamma.cpp.
◆ Vub_NLO_3body_B()
| double Bsgamma::Vub_NLO_3body_B |
( |
double |
E0 | ) |
|
The second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B,CPodd}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{3b}\)
Definition at line 2148 of file bsgamma.cpp.
2150 double d =
delta(E0);
◆ Vub_NLO_3body_B_CPodd()
| double Bsgamma::Vub_NLO_3body_B_CPodd |
( |
double |
E0 | ) |
|
The CP odd part of the second piece of the 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b,B}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{3b}\)
Definition at line 2161 of file bsgamma.cpp.
2163 double d =
delta(E0);
◆ Vub_NLO_4body()
| double Bsgamma::Vub_NLO_4body |
( |
double |
E0 | ) |
|
The 4 body NLO Vub part of the \(BR\) obtained from [143] , \(Vub^{NLO}_{4b,CPodd}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{4b}\)
Definition at line 2174 of file bsgamma.cpp.
2177 double d =
delta(E0);
2181 double Lumd =
log(1. - d);
2184 double uphib427 = ( 2. * d * (-63. + 30. * d + 35. * d2 - 2. * d3
2185 + 3. * d * (-18. - 7. * d + d2) * Ld) ) / ( 243. * (d - 1.) );
2186 double uphib428 = ( 108. * (d - 1.) * (d - 1.) * Lumd*Lumd
2187 - 12. * Lumd * (- 25. - 18. * Lq - 18. * d * (5. + 4. * Lq)
2188 + 9. * d2 * (5. + 4. * Lq) + (9. + 36. * d - 18. * d2) * Ld)
2189 + d * (24. * (17. + 9. * Lq) + 27. * d * (43. + 26. * Lq)
2190 - d2 * (127. + 72. * Lq) + 9. * (-12. - 39. * d + 4. * d2) * Ld)
2191 + 108. * (-1. - 4. * d + 2. * d2) * gsl_sf_dilog(d) ) / 729.;
◆ Vub_NLO_4body_CPodd()
| double Bsgamma::Vub_NLO_4body_CPodd |
( |
double |
E0 | ) |
|
The CP odd part of the 4 body NLO Vub part of the \(BR\) obtained from [143] , \(Vub^{NLO}_{4b}\).
- Parameters
-
- Returns
- \(Vub^{NLO}_{4b}\)
Definition at line 2204 of file bsgamma.cpp.
◆ Vub_NLO_CPodd()
| double Bsgamma::Vub_NLO_CPodd |
( |
double |
E0 | ) |
|
The CP odd part of the total NLO Vub part of the \(BR\), \(Vub^{NLO}_{CPodd}\).
- Parameters
-
- Returns
- \(Vub^{NLO}\)
Definition at line 2218 of file bsgamma.cpp.
◆ Vub_NNLO()
| double Bsgamma::Vub_NNLO |
( |
double |
E0 | ) |
|
The NNLO Vub part of the \(BR\) as defined in xxxxxxxxx, \(Vub^{NLO}\).
- Parameters
-
- Returns
- \(Vub^{NLO}\)
Definition at line 2223 of file bsgamma.cpp.
◆ Y1()
| double Bsgamma::Y1 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(1)}(z_0,\mu) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(1)}(z_0,\mu) \)
Definition at line 1282 of file bsgamma.cpp.
1286 return 4./9.*(29. - 2.*M_PI*M_PI) + 16./3.*Lb -
dY1(E0);
◆ Y2()
| double Bsgamma::Y2 |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2)}(z_0,\mu) \) function from arXiv:0805.3911v2 and arXiv:1005.5587v1.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2)}(z_0,\mu) \)
Definition at line 1441 of file bsgamma.cpp.
1450 return CF*
Y2CF(E0,mu) + CA*
Y2CA(E0,mu)
1451 + TR * ( NL*
Y2NL(E0,mu) + NV*
Y2NV(E0,mu) + NH*
Y2NH(E0,mu) );
◆ Y2CA()
| double Bsgamma::Y2CA |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2,CA)}(z_0,\mu) \) function from arXiv:1005.5587v1.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2,CA)}(z_0,\mu) \)
Definition at line 1316 of file bsgamma.cpp.
1319 double z0 = 1. -
delta(E0);
1321 double z03 = z02*z0;
1322 double z04 = z03*z0;
1323 double z05 = z04*z0;
1324 double z06 = z05*z0;
1325 double z07 = z06*z0;
1326 double z08 = z07*z0;
1327 double z09 = z08*z0;
1328 double z010 = z09*z0;
1329 double z011 = z010*z0;
1330 double Lz =
log(1. - z0);
1331 double Li2 = gsl_sf_dilog(z0);
1333 return 22.8959 + 76.5729 * Lb + 30.2222 * Lb*Lb + 2.94616 * z0 - 60.4444 * Lb*z0
1334 - 13.2522 * z02 - 6.96907 * z03 - 2.51852 * Lb*z03 + 0.117907 * z04
1335 - 2.02988 * z05 + 2.90402 * z06 - 3.53904 * z07 + 2.55728 * z08
1336 - 0.941549 * z09 + 0.0173599 * z010 + 0.0598012 * z011
1337 + (2.94616 - 30.2222 * Lb- 12.3947 * z0 + 30.2222 * Lb*z0 + 9.44855 * z02) * Lz
1338 - 6.61587 * (1. - z0) * (1. - z0) * Lz*Lz + 30.2222 * Lb*
Li2
1339 + (0.69995 - 1.3999 * z0 + 0.69995 * z02) * Lz*Lz*Lz;
◆ Y2CF()
| double Bsgamma::Y2CF |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2,CF)}(z_0,\mu) \) function from arXiv:1005.5587v1.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2,CF)}(z_0,\mu) \)
Definition at line 1289 of file bsgamma.cpp.
1292 double z0 = 1. -
delta(E0);
1294 double z03 = z02*z0;
1295 double z04 = z03*z0;
1296 double z05 = z04*z0;
1297 double z06 = z05*z0;
1298 double z07 = z06*z0;
1299 double z08 = z07*z0;
1300 double z09 = z08*z0;
1301 double z010 = z09*z0;
1302 double z011 = z010*z0;
1303 double Lz =
log(1. - z0);
1304 double Li2 = gsl_sf_dilog(z0);
1306 return -21.9087 - 112.464 * Lb - 42.6667 * Lb*Lb - 77.7675 * z0 + 10.6667 * Lb*z0
1307 + 68.5848 * z02 - 5.33333 * Lb * z02 - 4.42133 * z03 + 6.22222 * Lb * z03
1308 - 4.0317 * z04 + 6.64376 * z05 - 11.647 * z06 + 15.8697 * z07
1309 - 14.8006 * z08 + 8.85514 * z09 - 2.9929 * z010 + 0.433254 * z011
1310 + (-77.7675 + 85.8251 * z0 - 28.6855 * z02
1311 + Lb * (-21.3333 - 21.3333 * z0 + 5.33333 * z02)) * Lz
1312 + (-12.2881 - 10.6667 * Lb + 6.12213 * z0 + 0.27227 * z02) * Lz*Lz
1313 + (-2.88573 + 5.77146 * z0 - 2.88573 * z02) * Lz*Lz*Lz - 32. * Lb*
Li2;
◆ Y2NH()
| double Bsgamma::Y2NH |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2,NL)}(z_0,\mu) \)
Definition at line 1430 of file bsgamma.cpp.
1433 double zeta3 = gsl_sf_zeta_int(3);
1434 double Cl2 = gsl_sf_clausen(M_PI/3.);
1436 return 8./81. * (244. - 27.*
sqrt(3.)*M_PI - 61.*M_PI*M_PI)
1437 - 64./27.*(18. - M_PI*M_PI)*Lb - 64./9.*Lb*Lb - 64./27.*zeta3
◆ Y2NL()
| double Bsgamma::Y2NL |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2,NL)}(z_0,\mu) \)
Definition at line 1342 of file bsgamma.cpp.
1344 double z0 = 1. -
delta(E0);
1345 double Lz =
log(1. - z0);
1347 double zeta3 = gsl_sf_zeta_int(3);
1348 double Li2 = gsl_sf_dilog(z0);
1350 double Li3 = Poly.
Li3(z0);
1351 double Li3min = Poly.
Li3(1. - z0);
1353 return -16./81. * (328. - 13.*M_PI*M_PI) - 64./27. * (18. - M_PI*M_PI)*Lb
1354 -64./9. * Lb*Lb + 64./3. * zeta3
1355 +4./27. * z0*(7.*z0*z0 - 17.*z0 + 238.) + 8./3. * Lb*
dY1(E0)
1356 -8./27. * (z0*z0*z0 - 6.*z0*z0 + 80.*z0 - 75. + 6.*M_PI*M_PI)*Lz
1357 +16./3. * (z0 - 1.)*Lz*Lz + 16./3. *
log(z0)*Lz*Lz
1358 +32./27. * (3.*z0 - 8.)*
Li2 + 32./3. * Lz*
Li2
1359 -32./9. *
Li3 + 32./3. * Li3min - 32./3. * zeta3;
◆ Y2NV()
| double Bsgamma::Y2NV |
( |
double |
E0, |
|
|
double |
mu |
|
) |
| |
The \( Y^{(2,NL)}(z_0,\mu) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | E0 | energy cutoff |
| [in] | mu | low scale of the decay |
- Returns
- \( Y^{(2,NL)}(z_0,\mu) \)
Definition at line 1407 of file bsgamma.cpp.
1414 double Li2 = gsl_sf_dilog(1. -
rho);
1415 double Li2sqrt = gsl_sf_dilog(1. -
sqrt(
rho));
1418 double Li3ov = Poly.
Li3(1. - 1./
rho);
1420 return -16./81. * (157. - 279.*
rho - M_PI*M_PI*(5. + 9.*rho2 - 42.*rho32))
1421 -64./27. * (18. - M_PI*M_PI)*Lb - 64./9. * Lb*Lb
1422 +16./27. * (22. - M_PI*M_PI + 10.*
rho)*Lr + 16./27. * (8. + 9.*rho2)*Lr*Lr
1423 -16./27. * Lr*Lr*Lr - 8./9. * (1. - 6.*rho2)*
Y2NV_PHI1(
rho)
1426 +32./27. * (5. + 9.*rho2 + 14.*rho32)*
Li2 - 1792./27. * rho32*Li2sqrt
1427 +64./9. *
Li3 + 64./9. * Li3ov + 4./3.*(2.*Lb - Lr)*
dY1(E0);
◆ Y2NV_PHI1()
| double Bsgamma::Y2NV_PHI1 |
( |
double |
rho | ) |
|
The \( \Phi_1(\rho) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | rho | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(\Phi_1(\rho) \)
Definition at line 1362 of file bsgamma.cpp.
1367 return log(y)*
log(y) - M_PI*M_PI;
1369 return - acos( 1. - 1./(2. *
rho) ) * acos( 1. - 1./(2. *
rho) );
◆ Y2NV_PHI2()
| double Bsgamma::Y2NV_PHI2 |
( |
double |
rho | ) |
|
The \( \Phi_2(\rho) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | rho | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(\Phi_2(\rho) \)
Definition at line 1373 of file bsgamma.cpp.
1380 return - acos( 1. - 1./(2. *
rho) ) *
sqrt(4.*
rho - 1.);
◆ Y2NV_PHI3()
| double Bsgamma::Y2NV_PHI3 |
( |
double |
rho | ) |
|
The \( \Phi_3(\rho) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | rho | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(\Phi_3(\rho) \)
Definition at line 1384 of file bsgamma.cpp.
1389 return ( gsl_sf_dilog(-y) +
log(y)*
log(y)/4. + M_PI*M_PI/12. ) *
sqrt(1. - 4.*
rho);
1391 return - gsl_sf_clausen(2. * asin( 1./(2. *
sqrt(
rho)) )) *
sqrt(4.*
rho - 1.);
◆ Y2NV_PHI4()
| double Bsgamma::Y2NV_PHI4 |
( |
double |
rho | ) |
|
The \( \Phi_4(\rho) \) function from arXiv:0805.3911v2.
- Parameters
-
| [in] | rho | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
- Returns
- \(\Phi_4(\rho) \)
Definition at line 1395 of file bsgamma.cpp.
1402 return Poly.
Li3(- y) +
log(y)*
log(y)*
log(y)/12. +
log(y)*M_PI*M_PI/12.;
1404 return Clausen.
Cl3(2. * asin( 1./(2. *
sqrt(
rho)) ));
◆ zdz_f_NLO()
| double Bsgamma::zdz_f_NLO |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
The \( z \frac{d}{dz}f_{\rm NLO}(z,\delta) \) function from arXiv:1503.01791.
- Parameters
-
| [in] | z | squared ratio between \(m_c\) and \(m_b^{\rm kin}\) |
| [in] | E0 | energy cutoff |
- Returns
- \( z \frac{d}{dz}f_{\rm NLO}(z,\delta)) \)
Definition at line 1459 of file bsgamma.cpp.
1461 double d =
delta(E0);
1462 double sqrt1d =
sqrt(1. - d);
1463 double sqrt4z =
sqrt(1. - 4. * z);
1464 double sqrt1d4z =
sqrt(1. - d - 4. * z);
1465 double sqrtz =
sqrt(z);
1466 double sqrt1ovz =
sqrt(1./z);
1467 double sqrt4m1ovz =
sqrt(-4. + 1./z);
1468 double SumSqrt = sqrt1d + sqrt1d4z;
1469 double ProdSqrt = sqrt1d * sqrt1d4z;
1470 double ProdSqrtz = sqrtz * sqrt1d4z;
1471 double LogSumSqrt =
log(SumSqrt/(2. * sqrtz));
1472 double LogSqrt4z =
log((1. + sqrt4z)/(2. * sqrtz));
1473 double LogSqrtov =
log((sqrt4m1ovz + sqrt1ovz)/2.);
1481 double Pi2 = M_PI*M_PI;
1482 double zeta3 = gsl_sf_zeta_int(3);
1484 double zdz_f_NLO_E0;
1487 zdz_f_NLO_E0 = 2./27. * (3. * (-7. + 2. * M_PI*M_PI)
1488 + 2. * (36. - 24. * M_PI*M_PI) * z
1489 + 108. * M_PI*M_PI * z2
1490 - ( 36. * (-
pow(1./z,3./2.)/2. - 1./(2. * sqrt4m1ovz * z2))
1491 * sqrt4m1ovz * (-1. + 2. * z))/((sqrt4m1ovz + sqrt1ovz) *
pow(1./z,3./2.))
1492 - (72. * sqrt4m1ovz * LogSqrtov)/
pow(1./z,3./2.)
1493 - (54. * sqrt4m1ovz * (-1. + 2. * z) * LogSqrtov)/sqrt1ovz
1494 + (18. * sqrt1ovz * (-1. + 2. * z) * LogSqrtov)/sqrt4m1ovz
1495 - (48. * (-
pow(1./z,3./2.)/2. - 1./(2. * sqrt4m1ovz * z2))
1496 * z * (1. - 4. * z + 6. * z2) * LogSqrtov)/(sqrt4m1ovz + sqrt1ovz)
1497 - 24. * z * (-4. + 12. * z) * LogSqrtov * LogSqrtov
1498 - 24. * (1. - 4. * z + 6. * z2) * LogSqrtov * LogSqrtov);
1499 }
else zdz_f_NLO_E0 = 2. * ((2. - d) * d * (-7. + 2. * Pi2) / 9.
1500 + 8./9. * d * (3. - 2. * Pi2) * z
1501 + (8. * d * (-SumSqrt/( 4. *
pow(z,3./2.) ) - 1./ProdSqrtz)
1502 * ProdSqrt *
pow(z,3./2.))/(3. * SumSqrt)
1503 + 4./3. * d * ProdSqrt * LogSumSqrt
1504 - (8. * (1. - d) * d * z * LogSumSqrt)/(3. * ProdSqrt)
1505 - (32. * d * (-SumSqrt/( 4. *
pow(z,3./2.) ) - 1./ProdSqrtz)
1506 * (2. - d - 4. * z) *
pow(z,3./2.) * LogSumSqrt)/(9. * SumSqrt)
1507 - 8./9. * d * (2. - d - 4. * z) * LogSumSqrt * LogSumSqrt
1508 + 32./9. * d * z * LogSumSqrt * LogSumSqrt
1509 + 4./3. * (1. - 2. * z) * z *
1510 ((2. * (-( (1. + sqrt4z)/(4. *
pow(z,3./2.)) )
1511 - 1./(sqrt4z * sqrtz)) * sqrt4z * sqrtz)/(1. + sqrt4z)
1512 - (2. * ( -(SumSqrt/(4. *
pow(z,3./2.)) ) - 1./ProdSqrtz)
1513 * ProdSqrt * sqrtz)/(SumSqrt) - 2. * LogSqrt4z/sqrt4z
1514 + 2. * (1. - d) * LogSumSqrt/ProdSqrt)
1515 + 4./3. * (1. - 2. * z) * (sqrt4z * LogSqrt4z - ProdSqrt * LogSumSqrt)
1516 - 8./3. * z * (sqrt4z * LogSqrt4z - ProdSqrt * LogSumSqrt)
1517 - 8./9. * z * (1 - 4. * z + 6. * z2) *
1518 (( 4. * (-( (1. + sqrt4z)/(4. *
pow(z,3./2.)) )
1519 - 1./(sqrt4z * sqrtz)) * sqrtz * LogSqrt4z)/(1. + sqrt4z)
1520 - (4. * (-SumSqrt/(4. *
pow(z,3./2.)) - 1./ProdSqrtz) * sqrtz * LogSumSqrt)/SumSqrt)
1521 - 8./9. * (LogSqrt4z*LogSqrt4z - LogSumSqrt*LogSumSqrt)
1522 * ( z * (-4. + 12. * z) + (1. - 4. * z + 6. * z2) )) ;
1524 return z * (zdz_f_NLO_E0
1526 - 16./9. * (-4. + Pi2/6. - Pi2 * sqrtz
1527 - Lz - z2 * (19./18. - 4. * Lz) + z * (-2. - Lz)
1528 + z3 * (137./30. + 4. * Lz)
1529 + z4 * (887./84. + 10. * Lz)
1530 + z5 * (16597./540. + 28. * Lz)
1531 - 3. * z2 * (25./12. + Pi2/9. + 19. * Lz/18. - 2. * Lz * Lz)
1532 + 2. * z * (1./2. + Pi2 - 2. * Lz - Lz * Lz/2)
1533 + 4. * z3 * (-1376./225. + 2. * Pi2/3 + 137. * Lz/30. + 2. * Lz * Lz)
1534 + 5. * z4 * (-131317./11760. + 5. * Pi2/3. + 887. * Lz/84. + 5. * Lz * Lz)
1535 + 6. * z5 * (-2807617./97200. + 14. * Pi2/3. + 16597. * Lz/540. + 14. * Lz * Lz))
1537 + 32./9. * (5./2. - Pi2/3. + (5./2. - 3. * Pi2/4.) * Lz
1538 + Lz * Lz/4 + Lz * Lz * Lz/12.
1539 + z5 * (-3303./800. - 63. * Lz/10.)
1540 + z4 * (-185./144. - 35. * Lz/12.)
1541 + z3 * (-1./72. - 5. * Lz/3.)
1542 + z2 * (2. - 3. * Lz/2.)
1543 + 6. * z5 * (67801./8000. - 21. * Pi2/20.
1544 - 3303. * Lz/800. - 63. * Lz * Lz/20.)
1545 + 5. * z4 * (35101./8640. - 35. * Pi2/72.
1546 - 185. * Lz/144. - 35. * Lz * Lz/24.)
1547 + 4. * z3 * (457./216. - 5. * Pi2/18. - Lz/72. - 5. * Lz * Lz/6.)
1548 + 3. * z2 * (-7./6. - Pi2/4. + 2. * Lz - 3. * Lz * Lz/4.)
1549 + z * (-Pi2/2. - Lz/2. + Lz * Lz/4.)
1550 + 5./2. - 3. * Pi2/4. + Lz/2. + Lz * Lz/4.
1551 + 2. * z * (7./4. + 2. * Pi2/3. - Pi2 * Lz/2. - Lz * Lz/4.
1552 + Lz * Lz * Lz/12.) - 3. * zeta3));
◆ zdz_Phi22_1()
| double Bsgamma::zdz_Phi22_1 |
( |
double |
E0 | ) |
|
Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.
- Parameters
-
- Returns
- \( 4z \frac{d\Phi_{22}^{(1)}}{d\,z} \)
Definition at line 1645 of file bsgamma.cpp.
◆ zdz_Phi28_1()
| double Bsgamma::zdz_Phi28_1 |
( |
double |
z, |
|
|
double |
E0 |
|
) |
| |
Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.
- Parameters
-
- Returns
- \( 2z \frac{d\Phi_{28}^{(1)}}{d\,z} \)
Definition at line 1664 of file bsgamma.cpp.
1666 double d =
delta(E0);
1667 double Sq =
sqrt( (1. - d) * (1. - d - 4.*z) );
1668 double Log1 =
log( (
sqrt(1. - d) +
sqrt(1. - d - 4.*z) ) / 2. /
sqrt(z) );
1669 double Log2 =
log( ( 1. +
sqrt(1. - 4.*z) ) / 2. /
sqrt(z) );
1671 return 2./27. * z * (d*d * (-7. - 8. * (-1. + Log1) * Log1 + 2. * M_PI*M_PI)
1672 - 20. * Log2 *
sqrt(1. - 4. * z) + 72. * Log2 *
sqrt(1. - 4. * z) * z
1673 + (48. * Log1 * Sq * z * z) / (-1. + d + 4. * z)
1674 + (8. * z * ( -(3. + 4. * Log1) * Sq*Sq + 2. * (3. + 8. * Log1) * Sq * z
1675 - 24. * Log1 * z * z )) / (-1. + d - Sq + 4. * z)
1676 - 2. * d * (-7. - 3. * Sq + Log1 * (8. + 6. * Sq) + M_PI*M_PI * (2. - 8. * z)
1677 + 12. * z + 8. * Log1*Log1 * (-1. + 4. * z))
1678 + 2. * (-3. * (-1. + Sq + 2. * (1. + Sq) * z)
1679 + Log1 * (4. + Sq * (6. - 52. * z) + 24. * z * z)
1680 + 4. * ( Log2 * Log2 - Log1 * Log1) * (1. + 2. * z * (-4. + 9. * z))));
◆ zeta()
The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \).
- Returns
- \( z \)
Definition at line 228 of file bsgamma.cpp.
◆ ale
◆ AleatMztilde
| double Bsgamma::AleatMztilde |
|
private |
alpha electromagnetic at Mz divided by 4 pi
Definition at line 1746 of file bsgamma.h.
◆ allcoeff
vector that contains the Wilson coeffients
Definition at line 1777 of file bsgamma.h.
◆ allcoeffprime
vector that contains the primed Wilson coeffients
Definition at line 1778 of file bsgamma.h.
◆ Alstilde
alpha strong divided by 4 pi
Definition at line 1748 of file bsgamma.h.
◆ alsUps
◆ avaINT
◆ BLNPcorr
◆ BRsl
BR of the semileptonic decay \(B \to X_c e \nu\)
Definition at line 1757 of file bsgamma.h.
The semileptonic phase space ratio
Definition at line 1758 of file bsgamma.h.
◆ C1_0
LO term of the Wilson coeffients \(C_1\)
Definition at line 1780 of file bsgamma.h.
◆ C1_1
NLO term of the Wilson coeffients \(C_1\)
Definition at line 1789 of file bsgamma.h.
◆ C2_0
LO term of the Wilson coeffients \(C_2\)
Definition at line 1781 of file bsgamma.h.
◆ C2_1
NLO term of the Wilson coeffients \(C_2\)
Definition at line 1790 of file bsgamma.h.
◆ C3_0
LO term of the Wilson coeffients \(C_3\)
Definition at line 1782 of file bsgamma.h.
◆ C3_1
NLO term of the Wilson coeffients \(C_3\)
Definition at line 1791 of file bsgamma.h.
◆ C4_0
LO term of the Wilson coeffients \(C_4\)
Definition at line 1783 of file bsgamma.h.
◆ C4_1
NLO term of the Wilson coeffients \(C_4\)
Definition at line 1792 of file bsgamma.h.
◆ C5_0
LO term of the Wilson coeffients \(C_5\)
Definition at line 1784 of file bsgamma.h.
◆ C5_1
NLO term of the Wilson coeffients \(C_5\)
Definition at line 1793 of file bsgamma.h.
◆ C6_0
LO term of the Wilson coeffients \(C_6\)
Definition at line 1785 of file bsgamma.h.
◆ C6_1
NLO term of the Wilson coeffients \(C_6\)
Definition at line 1794 of file bsgamma.h.
◆ C7_0
LO term of the Wilson coeffients \(C_7\)
Definition at line 1786 of file bsgamma.h.
◆ C7_1
NLO term of the Wilson coeffients \(C_7\)
Definition at line 1795 of file bsgamma.h.
◆ C7_1ew
ew-NLO term of the Wilson coeffients \(C_7\)
Definition at line 1798 of file bsgamma.h.
◆ C7_2
NNLO term of the Wilson coeffients \(C_7\)
Definition at line 1800 of file bsgamma.h.
◆ C7p_0
LO term of the Wilson coeffients \(C'_7\)
Definition at line 1802 of file bsgamma.h.
◆ C7p_1
NLO term of the Wilson coeffients \(C_7\)
Definition at line 1803 of file bsgamma.h.
◆ C8_0
LO term of the Wilson coeffients \(C_8\)
Definition at line 1787 of file bsgamma.h.
◆ C8_1
NLO term of the Wilson coeffients \(C_8\)
Definition at line 1796 of file bsgamma.h.
◆ C_7_NP
◆ C_7p_NP
◆ CacheIntb1
| double Bsgamma::CacheIntb1 |
|
private |
◆ CacheIntb2
| double Bsgamma::CacheIntb2 |
|
private |
◆ CacheIntb3
| double Bsgamma::CacheIntb3 |
|
private |
◆ CacheIntb4
| double Bsgamma::CacheIntb4 |
|
private |
◆ CacheIntbb1
| double Bsgamma::CacheIntbb1 |
|
private |
◆ CacheIntbb2
| double Bsgamma::CacheIntbb2 |
|
private |
◆ CacheIntbb4
| double Bsgamma::CacheIntbb4 |
|
private |
◆ CacheIntbc1
◆ CacheIntbc2
◆ CacheIntc1
◆ CacheIntc2
◆ CacheIntc3
◆ CacheIntcc
| double Bsgamma::CacheIntcc |
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private |
◆ CacheIntcc1
| double Bsgamma::CacheIntcc1 |
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private |
◆ CacheIntcc1p1
| double Bsgamma::CacheIntcc1p1 |
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private |
◆ CacheIntPhi772r
| double Bsgamma::CacheIntPhi772r |
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private |
◆ CKMratio
◆ CKMu
◆ CKMusq
◆ errINT
◆ EWflag
Flag to include EW NLO corrections (currently partialy hard-coded)
Definition at line 1741 of file bsgamma.h.
◆ FOUR_BODY
Flag to include NLO 4_body corrections (currently partialy hard-coded)
Definition at line 1742 of file bsgamma.h.
◆ INT
| gsl_function Bsgamma::INT |
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private |
◆ Intb1Cached
| unsigned int Bsgamma::Intb1Cached |
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private |
◆ Intb2Cached
| unsigned int Bsgamma::Intb2Cached |
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private |
◆ Intb3Cached
| unsigned int Bsgamma::Intb3Cached |
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private |
◆ Intb4Cached
| unsigned int Bsgamma::Intb4Cached |
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private |
◆ Intb_cache
| double Bsgamma::Intb_cache |
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private |
◆ Intb_updated
| unsigned int Bsgamma::Intb_updated |
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private |
◆ Intbb1Cached
| unsigned int Bsgamma::Intbb1Cached |
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private |
◆ Intbb2Cached
| unsigned int Bsgamma::Intbb2Cached |
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private |
◆ Intbb4Cached
| unsigned int Bsgamma::Intbb4Cached |
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private |
◆ Intbc1Cached
| unsigned int Bsgamma::Intbc1Cached |
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private |
◆ Intbc2Cached
| unsigned int Bsgamma::Intbc2Cached |
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private |
◆ Intbc_cache
◆ Intbc_updated
| unsigned int Bsgamma::Intbc_updated |
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private |
◆ Intc1Cached
| unsigned int Bsgamma::Intc1Cached |
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private |
◆ Intc1imCached
| unsigned int Bsgamma::Intc1imCached |
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private |
◆ Intc2Cached
| unsigned int Bsgamma::Intc2Cached |
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private |
◆ Intc3Cached
| unsigned int Bsgamma::Intc3Cached |
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private |
◆ Intcc1Cached
| unsigned int Bsgamma::Intcc1Cached |
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private |
◆ Intcc1p1Cached
| unsigned int Bsgamma::Intcc1p1Cached |
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private |
◆ IntccCached
| unsigned int Bsgamma::IntccCached |
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private |
◆ IntPhi772rCached
| unsigned int Bsgamma::IntPhi772rCached |
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private |
◆ Mb
◆ Mb_kin
b quark mass in the kinetic scheme
Definition at line 1752 of file bsgamma.h.
◆ Mc
◆ Ms
◆ mu_b
◆ mu_c
◆ mu_G2
B meson expectation value of one of the relevant dim. 5 and 6 local operators
Definition at line 1767 of file bsgamma.h.
◆ mu_kin
◆ mu_pi2
B meson expectation value of one of the relevant dim. 5 and 6 local operators
Definition at line 1766 of file bsgamma.h.
◆ Mz
◆ obs
◆ overall
◆ quark
◆ rho_D3
B meson expectation value of one of the relevant dim. 5 and 6 local operators
Definition at line 1768 of file bsgamma.h.
◆ rho_LS3
B meson expectation value of one of the relevant dim. 5 and 6 local operators
Definition at line 1769 of file bsgamma.h.
◆ SMEFT_NP_btos
| bool Bsgamma::SMEFT_NP_btos = false |
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private |
◆ SUM
Flag to choose whether the BR will be relative to a single quark (s or d) or their sum
Definition at line 1740 of file bsgamma.h.
◆ V_cb
◆ V_tb
◆ V_ub
◆ w_INT
| gsl_integration_cquad_workspace* Bsgamma::w_INT |
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private |
◆ WET_NP_btos
| bool Bsgamma::WET_NP_btos = false |
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private |
The documentation for this class was generated from the following files:
double getKc_re_t_1mt2(double t)
The function .
double getKc_im_Kb_1mt2(double t)
The function .
unsigned int Intcc1Cached
gslpp::vector< gslpp::complex > ** allcoeff
gslpp::complex a(double z)
The funcion as defined in .
double Int_b4(double E0)
Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2().
double Int_b3(double E0)
Integral of the functions getKb_re_t() and getKb_re_t_1mt().
gslpp::complex Int_c1(double E0)
Integral of the functions getKc_re_1mt(), getKc_im_1mt() and getKc_re_1mt2(), getKc_im_1mt2().
double Phi12_1(double E0)
The function from .
double Phi34_1(double E0)
The function obtained using the prescription of .
unsigned int Intbc_updated
double Phi26_1_4body(double E0)
The function obtained from .
double getKc_im_t_1mt(double t)
The function .
double P32(double E0, double mu)
The perturbative part of the BR as defined in .
double Y2NV_PHI3(double rho)
The function from arXiv:0805.3911v2.
double getKc_re_t_1mt(double t)
The function .
gslpp::complex CacheIntc3
virtual double v() const
The Higgs vacuum expectation value.
double getKb_re_t2_1mt2(double t)
The function .
double Int_Phi77_2rem(double E0)
The integral of omega77()
gslpp::complex computelamu_d() const
The product of the CKM elements .
double getKc_im_Kb_t_1mt(double t)
The function .
double T2(double E0, double t)
The cutoff energy function as defined in .
double Vub_NLO_2body_CPodd()
The CP odd part of the 2 body NLO Vub part of the as defined in , .
gslpp::complex kappa(double Mq, double t)
The function as defined in .
double F_1(double z)
The interpolated function from arXiv:1503.01791.
double Phi78_1(double E0)
The function from .
gslpp::complex getV_tb() const
A member for returning the value of the CKM element .
double Phi58_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
void setParametersForObservable(std::vector< std::string > parametersForObservable_i)
A set method to get the parameters for the specific observable.
double getKc_im_1mt2(double t)
The function .
double getKb_abs2_t2_1mt(double t)
The function .
gslpp::complex Phi24_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double getKb_abs2_t_1mt2(double t)
The function .
double getKc_im_Kb_1mt(double t)
The function .
double Phi24_1_4body(double E0)
The function obtained from .
double P0_4body(double E0, double t)
The 4-body LO contribution as defined in .
double Phi45_1(double E0)
The function obtained using the prescription of .
double Rer22(double z)
The function from .
gslpp::complex Phi66_1(double E0)
The function obtained using the prescription of .
double Vub_NLO_3body_A(double E0)
The first piece of the 3 body NLO Vub part of the , .
gslpp::vector< gslpp::complex > ** allcoeffprime
gslpp::complex Gamma_t(double t)
The function as defined in .
gslpp::complex Phi56_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double getKc_abs2_t_1mt(double t)
The function .
gslpp::complex Int_c2(double E0)
Integral of the functions getKc_re_t_1mt(), getKc_im_t_1mt() and getKc_re_t_1mt2(),...
double Phi57_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double getKb_abs2_1mt2(double t)
The function .
double Phi77_2beta0(double E0, double mu)
The function from ..
double Phi25_1_4body(double E0)
The function obtained from .
double P22(double E0, double mu_b, double mu_c)
The perturbative part of the BR as defined in .
double P0(double E0)
The perturbative part of the BR as defined in .
double Y2(double E0, double mu)
The function from arXiv:0805.3911v2 and arXiv:1005.5587v1.
gslpp::complex computelamt_s() const
The product of the CKM elements .
double Y2NL(double E0, double mu)
The function from arXiv:0805.3911v2.
unsigned int Intbb4Cached
gslpp::complex Phi13_1(double E0)
The function obtained using the prescription of .
double mddel_f_NLO(double z, double E0)
The function from arXiv:1503.01791.
void updateParameters()
The update parameter method for bsgamma.
double delddel_Phi28_1(double z, double E0)
Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.
double zdz_Phi22_1(double E0)
Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.
double f_b(double z)
The function from arXiv:1503.01791.
double Y1(double E0, double mu)
The function from arXiv:0805.3911v2.
double Li3(const double x) const
The trilogarithm .
double K77_2_z1(double E0, double mu)
The function computed in the limit .
double f_c(double z)
The function from arXiv:1503.01791.
double delta(double E0)
The cutoff energy function .
gslpp::complex Phi68_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
gslpp::complex CacheIntc2
A class for defining operations on and functions of complex numbers.
gslpp::complex r1(int i, double z)
The funcion as defined in .
gslpp::complex getV_cb() const
A member for returning the value of the CKM element .
complex log(const complex &z)
gslpp::complex Phi27_1(double E0, double z)
The function from .
double getKc_im_Kb_t_1mt2(double t)
The function .
double N_27()
The non perturbative part of the due to interference as defined in , .
double Vub_NLO_CPodd(double E0)
The CP odd part of the total NLO Vub part of the , .
double Int_cc1(double E0)
Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^().
double Delta(double r)
The function from Z. Phys. C 48, 673 (1990).
gslpp::complex Phi28_1(double E0, double z)
The function from .
double getKc_re_1mt(double t)
The function .
unsigned int Intbc1Cached
double omega(double E0)
The cutoff energy function as defined in .
double getKb_abs2_1mt(double t)
The function .
gslpp::complex b(double z)
The funcion as defined in .
double Int_cc(double E0)
Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt().
ThObservable(const StandardModel &SM_i)
Constructor.
double Phi22_1(double E0)
The function from .
gslpp::complex Phi26_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double Phi48_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double Phi88_1(double E0)
The function from .
gslpp::vector< double > Intbc_cache
double Alstilde5(const double mu) const
The value of at any scale with the number of flavours and full EW corrections.
double getKb_re_t_1mt(double t)
The function .
double P21(double E0, double mu)
The perturbative part of the BR as defined in .
double dY1(double E0)
The function from arXiv:0805.3911v2.
double Beta0(const double nf) const
The coefficient for a certain number of flavours .
An observable class for the quartic Higgs potential coupling .
double getKc_im_t(double t)
The function .
void computeCoeff(double mu)
Compute the Wilson Coefficient.
gslpp::complex r1_ew(int i, double z)
The funcion as defined in .
gslpp::complex computelamu_s() const
The product of the CKM elements .
gslpp::complex Kij_1(int i, int j, double E0, double mu)
The function from .
double Y2NV(double E0, double mu)
The function from arXiv:0805.3911v2.
double Cl3(const double phi) const
The Clausen function of index 3, .
double Vub_NLO_2body()
The 2 body NLO Vub part of the as defined in , .
double Y2NV_PHI1(double rho)
The function from arXiv:0805.3911v2.
double Phi28_2beta0(double E0, double mu)
The function from arXiv:1009.5685.
double Kij_2(int i, int j, double E0, double mu_b, double mu_c)
The function from arXiv:1503.01791.
const double & imag() const
double Y2NH(double E0, double mu)
The function from arXiv:0805.3911v2.
unsigned int Intbb1Cached
double getKc_abs2_1mt2(double t)
The function .
double ale_OS(const double mu, orders order=FULLNLO) const
The running electromagnetic coupling in the on-shell scheme.
complex conjugate() const
const double & getMass() const
A get method to access the particle mass.
double C_sem()
The ratio as defined in , but with coefficients slightly modified due to different imput parameters...
unsigned int Intcc1p1Cached
double delddel_Phi22_1(double E0)
Derivative of the function Phi22_1() used to compute effects of massive quark loops on gluon lines.
unsigned int Intbb2Cached
double h27_2(double z, double E0)
The function from arXiv:1009.5685 and arXiv:1503.01791.
double Phi44_1(double E0)
The function obtained using the prescription of .
gslpp::complex Int_bc1(double E0)
Integral of the functions getKc_re_Kb_1mt(), getKc_im_Kb_1mt() and getKc_re_Kb_1mt2(),...
double getKc_abs2_1mt(double t)
The function .
unsigned int IntPhi772rCached
unsigned int Intc1imCached
gsl_integration_cquad_workspace * w_INT
gslpp::complex Int_bc2(double E0)
Integral of the functions getKc_re_Kb_t_1mt(), getKc_im_Kb_t_1mt() and getKc_re_Kb_t_1mt2(),...
double P(double E0, double mu_b, double mu_c, orders order)
The perturbative part of the as defined in , .
double getKb_re_1mt2(double t)
The function .
complex pow(const complex &z1, const complex &z2)
double ff7_sMP(double E0)
The 4-body NLO correction due to and s, , from .
complex sqrt(const complex &z)
static const complex & i()
double Int_cc1_part1(double E0)
Integral of the functions getKc_abs2_1mt().
double rho(double E0)
The cutoff energy function as defined in .
double getKc_abs2_t(double t)
The function .
gslpp::complex CacheIntbc1
double zeta()
The squared ratio between and , .
double ff7_dMP(double E0)
The 4-body NLO correction due to and d, , from .
double omega77(double z)
The function, linear combination of the functions , and from hep-ph/0505097.
double Phi47_1(double E0)
The function from and adding the 4-body contribution from .
double getKb_abs2_t2_1mt2(double t)
The function .
double Y2NV_PHI2(double rho)
The function from arXiv:0805.3911v2.
gslpp::complex computelamt_d() const
The product of the CKM elements .
An observable class for the quartic Higgs potential coupling .
Particle getQuarks(const QCD::quark q) const
A get method to access a quark as an object of the type Particle.
double Phi77_2rem(double E0)
The part of the function with no dependance, as defined in .
unsigned int Intbc2Cached
double Phi38_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double Phi22_2beta0(double E0, double mu)
The function from arXiv:1009.5685.
const StandardModel & SM
A reference to an object of StandardMode class.
double Vub_NLO_4body_CPodd(double E0)
The CP odd part of the 4 body NLO Vub part of the obtained from , .
double N(double E0, double mu)
The non perturbative part of the as defined in , .
double getKc_im_1mt(double t)
The function .
double P11()
The perturbative part of the BR as defined in .
double Int_b1(double E0)
Integral of the functions getKb_re_1mt() and getKb_re_1mt2().
double Vub_NLO_3body_B(double E0)
The second piece of the 3 body NLO Vub part of the , .
const Flavour & getFlavour() const
double Phi55_1(double E0)
The function obtained using the prescription of .
double Phi33_1(double E0)
The function obtained using the prescription of .
gslpp::complex Phi23_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double Phi77_1(double E0)
The function from .
double T1(double E0, double t)
The cutoff energy function as defined in .
double Phi35_1(double E0)
The function obtained using the prescription of .
double T3(double E0, double t)
The cutoff energy function as defined in .
gslpp::complex Phi46_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
gslpp::complex Phi67_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double getKb_abs2_t_1mt(double t)
The function .
double Phi37_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
gslpp::complex Int_c3(double E0)
Integral of the functions getKc_re_t(), getKc_im_t() and getKc_re_t_1mt(), getKc_im_t_1mt().
double Int_bb4(double E0)
Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2().
double f(double r)
The function from hep-ph/0611123.
double ff8_dMP(double E0)
The 4-body NLO correction due to and d, , from .
double getMz() const
A get method to access the mass of the boson .
double f_NLO_1(double z)
The function from arXiv:1503.01791.
double Vub_NLO_3body_A_CPodd(double E0)
The CP odd part of the first piece of the 3 body NLO Vub part of the , .
double Phi23_1_4body(double E0)
The function obtained from .
double EW_NLO(double mu)
The NLO electroweak correction to the BR as defined in .
unsigned int Intb_updated
gslpp::complex Phi14_1(double E0)
The function obtained using the prescription of .
double F_2(double z)
The interpolated function from arXiv:1503.01791.
A class for the Clausen functions.
const double & real() const
gslpp::complex CacheIntc1
double getKb_re_1mt(double t)
The function .
gslpp::complex getV_ub() const
A member for returning the value of the CKM element .
gslpp::complex CacheIntbc2
double getKc_re_Kb_1mt2(double t)
The function .
double getBinMin()
A get method to get the minimum value of the bin.
double getKc_re_t(double t)
The function .
double getOptionalParameter(std::string name) const
A method to get parameters that are specific to only one set of observables.
gslpp::vector< gslpp::complex > ** ComputeCoeffsgamma(double mu, bool noSM=false, schemes scheme=NDR) const
Computes the Wilson coefficient for the process .
double Int_bb1(double E0)
Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2().
double Phi88_2beta0(double E0, double mu)
The function from arXiv:1009.5685.
double getKb_re_t_1mt2(double t)
The function .
double getKc_re_Kb_1mt(double t)
The function .
gslpp::vector< gslpp::complex > ** ComputeCoeffprimesgamma(double mu, schemes scheme=NDR) const
Computes the chirality flipped Wilson coefficient for the process .
double Y2CA(double E0, double mu)
The function from arXiv:1005.5587v1.
double getKc_re_Kb_t_1mt(double t)
The function .
gslpp::complex Phi18_1(double E0, double z)
The function from .
gslpp::complex Phi17_1(double E0, double z)
The function from .
double ff8_sMP(double E0)
The 4-body NLO correction due to and s, , from .
gslpp::complex Phi25_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
gsl_function convertToGslFunction(const F &f)
double zdz_Phi28_1(double z, double E0)
Derivative of the function Phi28_1() used to compute effects of massive quark loops on gluon lines.
double P21_CPodd(double E0, double mu)
The CP odd part of the perturbative part of the BR as defined in .
double Vub_NNLO(double E0)
The NNLO Vub part of the as defined in xxxxxxxxx, .
A class for the polylogarithms.
double f_q(double z, double E0)
The function from arXiv:1503.01791.
double Y2CF(double E0, double mu)
The function from arXiv:1005.5587v1.
double Int_b2(double E0)
Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2().
gslpp::complex Phi16_1(double E0)
The function obtained using the prescription of .
double N_77(double E0, double mu)
The non perturbative part of the due to interference as defined in arXiv:0911.2175,...
double getKc_im_t_1mt2(double t)
The function .
double Vub_NLO_4body(double E0)
The 4 body NLO Vub part of the obtained from , .
gslpp::complex Phi15_1(double E0)
The function obtained using the prescription of .
double zdz_f_NLO(double z, double E0)
The function from arXiv:1503.01791.
double delddel_Phi88_1(double E0)
Derivative of the function Phi88_1() used to compute effects of massive quark loops on gluon lines.
double getKb_re_t2_1mt(double t)
The function .
double getAle() const
A get method to retrieve the fine-structure constant .
void checkCache()
The caching method for bsgamma.
double getKc_re_1mt2(double t)
The function .
double Vub_NLO(double E0)
The total NLO Vub part of the , .
double Int_bb2(double E0)
Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2().
double Phi11_1(double E0)
The function from .
gslpp::complex Phi36_1(double E0)
The function obtained using the prescription of and adding the 4-body contribution from .
double P12()
The perturbative part of the BR as defined in .
double Y2NV_PHI4(double rho)
The function from arXiv:0805.3911v2.
double Vub_NLO_3body_B_CPodd(double E0)
The CP odd part of the second piece of the 3 body NLO Vub part of the , .
CKM getCKM() const
A get method to retrieve the member object of type CKM.
double f_u(double r)
The function obtained after multiplying the fitted function of arXiv:0803.0960 for and subtracting...
double getKc_re_Kb_t_1mt2(double t)
The function .
double getKb_re_t(double t)
The function .
Inheritance diagram for Bsgamma:
1.8.16 