Bsgamma Class Reference

A class for the \(b \to s \gamma\) decay. More...

#include <bsgamma.h>

Inheritance diagram for Bsgamma:

Collaboration diagram for Bsgamma:

Detailed Description

A class for the \(b \to s \gamma\) decay.

Author

HEPfit Collaboration

Copyright

GNU General Public License

This class is used to compute all the functions needed in order to compute the observables relative to the \(b \to s \gamma\) decay, following the prescriptions of [108] and [107]. After the Wilson coefficients are computed in computeCoeff() and the cache is checked in checkCache(), the parameters are updated in updateParameters(), in which part of the parameters are taken from the fit in [9] and used to compute the ratio \(C = | \frac{V_{ub}}{V_{cb}} |^2 \frac{\Gamma[\bar{B} \to X_c e \bar{\nu}]} {\Gamma[\bar{B} \to X_u e \bar{\nu}]} \) 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 \(C_7\) [109] and the subleading term due to the 4-body contribution, computed in P0_4body() [94] ;

• at Next to Leading Order it is computed in P11() and P21(), where the latter is build from the Kij_1() function [109], 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() [46], [81], [113] . The subleading terms due to the 4-body contributions [92] 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() [94], while at NLO are computed in the function Vub_NLO() [81], [92] , 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(), which follows the prescription of [41]. The observables are finally computed in the computeThValue() function.

Definition at line 61 of file Flavour/src/bsgamma.h.

Public Member Functions
gslpp::complex	a (double z)
	The funcion \( a(z) \) as defined in [46] . More...
gslpp::complex	b (double z)
	The funcion \( b(z) \) as defined in [46] . More...
	Bsgamma (const StandardModel &SM_i, int obsFlag)
	Constructor. More...
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 [82] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino). More...
void	computeCoeff (double mu)
	Compute the Wilson Coefficient. More...
double	computeThValue ()
	Computes the Branching Ratio for the \(b \to s \gamma\) decay. More...
double	delta (double E0)
	The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \). More...
double	ff7_dMP (double E0)
	The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [92] . More...
double	ff7_sMP (double E0)
	The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [92] . More...
double	ff8_dMP (double E0)
	The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [92] . More...
double	ff8_sMP (double E0)
	The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [92] . More...
gslpp::complex	Gamma_t (double t)
	The function \( \Gamma \) as defined in [81] . More...
double	getKb_abs2_1mt (double t)
	The function \(|k_b(t)|^2(1 - t)\). More...
double	getKb_abs2_1mt2 (double t)
	The function \(|k_b(t)|^2(1 - t)^2\). More...
double	getKb_abs2_t2_1mt (double t)
	The function \(|k_b(t)|^2t^2(1 - t)\). More...
double	getKb_abs2_t2_1mt2 (double t)
	The function \(|k_b(t)|^2t^2(1 - t)^2\). More...
double	getKb_abs2_t_1mt (double t)
	The function \(|k_b(t)|^2t(1 - t)\). More...
double	getKb_abs2_t_1mt2 (double t)
	The function \(|k_b(t)|^2t(1 - t)^2\). More...
double	getKb_re_1mt (double t)
	The function \(Re(k_b(t))(1-t)\). More...
double	getKb_re_1mt2 (double t)
	The function \(Re(k_b(t))(1-t)^2\). More...
double	getKb_re_t (double t)
	The function \(Re(k_b(t))t\). More...
double	getKb_re_t2_1mt (double t)
	The function \(Re(k_b(t))t^2(1-t)\). More...
double	getKb_re_t2_1mt2 (double t)
	The function \(Re(k_b(t))t^2(1-t)^2\). More...
double	getKb_re_t_1mt (double t)
	The function \(Re(k_b(t))t(1-t)\). More...
double	getKb_re_t_1mt2 (double t)
	The function \(Re(k_b(t))t(1-t)^2\). More...
double	getKc_abs2_1mt (double t)
	The function \(|k_c(t)|^2(1 - t)\). More...
double	getKc_abs2_1mt2 (double t)
	The function \(t|k_c(t)|^2(1 - t)^2\). More...
double	getKc_abs2_t (double t)
	The function \(|k_c(t)|^2 t\). More...
double	getKc_abs2_t_1mt (double t)
	The function \(|k_c(t)|^2t(1 - t)\). More...
double	getKc_im_1mt (double t)
	The function \(Im(k_c(t))(1-t)\). More...
double	getKc_im_1mt2 (double t)
	The function \(Im(k_c(t))(1-t)^2\). More...
double	getKc_re_1mt (double t)
	The function \(Re(k_c(t))(1-t)\). More...
double	getKc_re_1mt2 (double t)
	The function \(Re(k_c(t))(1-t)^2\). More...
double	getKc_re_Kb_1mt (double t)
	The function \(Re(k_b(t))Re(k_c(t))(1-t)\). More...
double	getKc_re_Kb_1mt2 (double t)
	The function \(Re(k_b(t))Re(k_c(t))(1-t)^2\). More...
double	getKc_re_Kb_t_1mt (double t)
	The function \(Re(k_b(t))Re(k_c(t)t(1-t)\). More...
double	getKc_re_Kb_t_1mt2 (double t)
	The function \(Re(k_b(t))Re(k_c(t)t(1-t)^2\). More...
double	getKc_re_t (double t)
	The function \(Re(k_c(t))t\). More...
double	getKc_re_t_1mt (double t)
	The function \(Re(k_c(t))t(1-t)\). More...
double	getKc_re_t_1mt2 (double t)
	The function \(Re(k_c(t))t(1-t)^2\). More...
double	Int_b1 (double E0)
	Integral of the functions getKb_re_1mt() and getKb_re_1mt2(). More...
double	Int_b2 (double E0)
	Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2(). More...
double	Int_b3 (double E0)
	Integral of the functions getKb_re_t() and getKb_re_t_1mt(). More...
double	Int_b4 (double E0)
	Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2(). More...
double	Int_bb1 (double E0)
	Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2(). More...
double	Int_bb2 (double E0)
	Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2(). More...
double	Int_bb4 (double E0)
	Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2(). More...
double	Int_bc1 (double E0)
	Integral of the functions getKc_re_Kb_1mt() and getKc_re_Kb_1mt2(). More...
double	Int_bc2 (double E0)
	Integral of the functions getKc_re_Kb_t_1mt() and getKc_re_Kb_t_1mt2(). More...
double	Int_c1 (double E0)
	Integral of the functions getKc_re_1mt() and getKc_re_1mt2(). More...
double	Int_c1_im (double E0)
	Integral of the functions getKc_im_1mt() and getKc_im_1mt2(). More...
double	Int_c2 (double E0)
	Integral of the functions getKc_re_t_1mt() and getKc_re_t_1mt2(). More...
double	Int_c3 (double E0)
	Integral of the functions getKc_re_t() and getKc_re_t_1mt(). More...
double	Int_cc (double E0)
	Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt(). More...
double	Int_cc1 (double E0)
	Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^(). More...
double	Int_cc1_part1 (double E0)
	Integral of the functions getKc_abs2_1mt(). More...
gslpp::complex	kappa (double Mq, double t)
	The function \( k \) as defined in [113] . More...
double	Kij_1 (int i, int j, double E0, double mu)
	The \( K_{ij}^{(1)} \) function from [109] . More...
double	N (double E0, double mu)
	The non perturbative part of the \(BR\) as defined in [41] , \(N\). More...
double	N_27 ()
	The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [81] , \(N_{27}\). More...
double	N_77 (double E0, double mu)
	The non perturbative part of the \(BR\) due to \(Q_7-Q_7\) interference as defined in [73] , \(N_{77}\). More...
double	omega (double E0)
	The cutoff energy function \( \omega \) as defined in [94] . More...
double	P (double E0, double mu_b, double mu_c, orders order, bool CPodd)
	The perturbative part of the \(BR\) as defined in [109] , \(P\). More...
double	P0 (double E0)
	The perturbative part \( P^{(0)} \) of the BR as defined in [109] . More...
double	P0_4body (double E0, double t)
	The 4-body LO contribution as defined in [94] . More...
double	P11 ()
	The perturbative part \( P_1^{(1)} \) of the BR as defined in [109] . More...
double	P12 ()
	The perturbative part \( P_1^{(2)} \) of the BR as defined in [109] . More...
double	P21 (double E0, double mu)
	The perturbative part \( P_2^{(1)} \) of the BR as defined in [109] . More...
double	P22 (double E0, double mu_b, double mu_c)
	The perturbative part \( P_2^{(2)} \) of the BR as defined in [109] . More...
double	P32 (double E0, double mu)
	The perturbative part \( P_3^{(2)} \) of the BR as defined in [109] . More...
double	Phi11_1 (double E0)
	The \( \Phi_{11}^{(1)} \) function from [81] . More...
double	Phi12_1 (double E0)
	The \( \Phi_{12}^{(1)} \) function from [81] . More...
double	Phi13_1 (double E0)
	The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi14_1 (double E0)
	The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi15_1 (double E0)
	The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi16_1 (double E0)
	The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi17_1 (double E0, double z)
	The \( \Phi_{17}^{(1)} \) function from [81] . More...
double	Phi18_1 (double E0, double z)
	The \( \Phi_{18}^{(1)} \) function from [81] . More...
double	Phi22_1 (double E0)
	The \( \Phi_{22}^{(1)} \) function from [81] . More...
double	Phi23_1 (double E0)
	The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi23_1_4body (double E0)
	The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [92] . More...
double	Phi24_1 (double E0)
	The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi24_1_4body (double E0)
	The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [92] . More...
double	Phi25_1 (double E0)
	The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi25_1_4body (double E0)
	The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [92] . More...
double	Phi26_1 (double E0)
	The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi26_1_4body (double E0)
	The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [92] . More...
double	Phi27_1 (double E0, double z)
	The \( \Re \Phi_{27}^{(1)} \) function from [81] . More...
double	Phi27_1_im (double E0, double z)
	The \( \Im\Phi_{27}^{(1)} \) function from [81] . More...
double	Phi28_1 (double E0, double z)
	The \( \Phi_{28}^{(1)} \) function from [81] . More...
double	Phi33_1 (double E0)
	The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi34_1 (double E0)
	The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi35_1 (double E0)
	The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi36_1 (double E0)
	The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi37_1 (double E0)
	The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi38_1 (double E0)
	The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi44_1 (double E0)
	The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi45_1 (double E0)
	The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi46_1 (double E0)
	The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi47_1 (double E0)
	The \( \Phi_{47}^{(1)} \) function from [81] and adding the 4-body contribution from [92] . More...
double	Phi48_1 (double E0)
	The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi55_1 (double E0)
	The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi56_1 (double E0)
	The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi57_1 (double E0)
	The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi58_1 (double E0)
	The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi66_1 (double E0)
	The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [50] . More...
double	Phi67_1 (double E0)
	The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi68_1 (double E0)
	The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] . More...
double	Phi77_1 (double E0)
	The \( \Phi_{77}^{(1)} \) function from [81] . More...
double	Phi78_1 (double E0)
	The \( \Phi_{78}^{(1)} \) function from [81] . More...
double	Phi88_1 (double E0)
	The \( \Phi_{88}^{(1)} \) function from [81] . More...
gslpp::complex	r1 (int i, double z)
	The funcion \( r_i^{(1)}(z) \) as defined in [46] . More...
double	rho (double E0)
	The cutoff energy function \( \rho \) as defined in [94] . More...
double	T1 (double E0, double t)
	The cutoff energy function \( T_1 \) as defined in [94] . More...
double	T2 (double E0, double t)
	The cutoff energy function \( T_2 \) as defined in [94] . More...
double	T3 (double E0, double t)
	The cutoff energy function \( T_3 \) as defined in [94] . More...
void	updateParameters ()
	The update parameter method for bsgamma. More...
double	Vub_NLO (double E0, bool CPodd)
	The total NLO Vub part of the \(BR\), \(Vub^{NLO}\). More...
double	Vub_NLO_2body (bool CPodd)
	The 2 body NLO Vub part of the \(BR\) as defined in [81] , \(Vub^{NLO}_{2b}\). More...
double	Vub_NLO_3body (double E0, bool CPodd)
	The 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b}\). More...
double	Vub_NLO_4body (double E0, bool CPodd)
	The 4 body NLO Vub part of the \(BR\) obtained from [92] , \(Vub^{NLO}_{4b}\). More...
double	zeta ()
	The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \). More...
Public Member Functions inherited from ThObservable
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...
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...
	ThObservable (const StandardModel &SM_i)
	Constructor. More...
	ThObservable (const ThObservable &orig)
	The copy constructor. More...
virtual	~ThObservable ()
	The default destructor. More...

Private Member Functions
void	checkCache ()
	The caching method for bsgamma. More...

Private Attributes
double	ale
gslpp::vector< gslpp::complex > **	allcoeff
gslpp::vector< gslpp::complex > **	allcoeffprime
double	Alstilde
double	alsUps
double	avaINT
double	BLNPcorr
double	BR
double	BR_CPodd
double	BRsl
double	C
gslpp::complex	C1_0
gslpp::complex	C1_1
gslpp::complex	C2_0
gslpp::complex	C2_1
gslpp::complex	C3_0
gslpp::complex	C3_1
gslpp::complex	C4_0
gslpp::complex	C4_1
gslpp::complex	C5_0
gslpp::complex	C5_1
gslpp::complex	C6_0
gslpp::complex	C6_1
gslpp::complex	C7_0
gslpp::complex	C7_1
gslpp::complex	C7_2
gslpp::complex	C7p_0
gslpp::complex	C7p_1
gslpp::complex	C8_0
gslpp::complex	C8_1
double	CacheIntb1
double	CacheIntb2
double	CacheIntb3
double	CacheIntb4
double	CacheIntbb1
double	CacheIntbb2
double	CacheIntbb4
double	CacheIntbc1
double	CacheIntbc2
double	CacheIntc1
double	CacheIntc1im
double	CacheIntc2
double	CacheIntc3
double	CacheIntcc
double	CacheIntcc1
double	CacheIntcc1p1
double	CacheIntPhi772r
gslpp::complex	CKMu
double	E0
double	errINT
gsl_function	INT
unsigned int	Intb1Cached
unsigned int	Intb2Cached
unsigned int	Intb3Cached
unsigned int	Intb4Cached
double	Intb_cache
unsigned int	Intb_updated
unsigned int	Intbb1Cached
unsigned int	Intbb2Cached
unsigned int	Intbb4Cached
unsigned int	Intbc1Cached
unsigned int	Intbc2Cached
gslpp::vector< double >	Intbc_cache
unsigned int	Intbc_updated
unsigned int	Intc1Cached
unsigned int	Intc1imCached
unsigned int	Intc2Cached
unsigned int	Intc3Cached
unsigned int	Intcc1Cached
unsigned int	Intcc1p1Cached
unsigned int	IntccCached
unsigned int	IntPhi772rCached
gslpp::complex	lambda_t
double	Mb_kin
double	Mc
double	Ms
double	mu_b
double	mu_c
double	mu_G2
double	mu_kin
double	mu_pi2
int	obs
double	overall
double	rho_D3
double	rho_LS3
gslpp::complex	V_cb
gsl_integration_cquad_workspace *	w_INT

Additional Inherited Members
Protected Attributes inherited from ThObservable
double	max
	the bin maximum. More...
double	min
	The bin minimum. More...
const StandardModel &	SM
	A reference to an object of StandardMode class. More...

Constructor & Destructor Documentation

Bsgamma::Bsgamma	(	const StandardModel &	SM_i,
		int	obsFlag
	)

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 16 of file Flavour/src/bsgamma.cpp.

: ThObservable(SM_i),
Intbc_cache(2, 0.)
{
    if (SM.ModelName().compare("StandardModel") != 0 && SM.ModelName().compare("FlavourWilsonCoefficient") != 0) std::cout << "\nWARNING: b to s gamma not implemented in: " + SM.ModelName() + " model, returning Standard Model value.\n" << std::endl;
    
    if (obsFlag > 0 and obsFlag < 3) obs = obsFlag;
    else throw std::runtime_error("obsFlag in bsgamma can only be 1 (BR) or 2 (BR_CPodd)");
    
    Intb1Cached = 0;
    Intb2Cached = 0;
    Intb3Cached = 0;
    Intb4Cached = 0;
    Intbb1Cached = 0;
    Intbb2Cached = 0;
    Intbb4Cached = 0;
    Intbc1Cached = 0;
    Intbc2Cached = 0;
    Intc1Cached = 0;
    Intc2Cached = 0;
    Intc3Cached = 0;
    Intcc1Cached = 0;
    
    w_INT = gsl_integration_cquad_workspace_alloc (100);
}

Member Function Documentation

gslpp::complex Bsgamma::a

(

double

z

)

The funcion \( a(z) \) as defined in [46] .

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( a(z) \)

Definition at line 153 of file Flavour/src/bsgamma.cpp.

{
    double zeta3 = gsl_sf_zeta_int(3);
    
    double z2=z*z;
    double z3=z2*z;
    double z4=z3*z;
    double z5=z4*z;
    double z6=z5*z;
    
    double L=log(z);
    double L2=L*L;
    double L3=L2*L;
    
    double pi2=M_PI*M_PI;
    
    if (z == 1.) return 4.0859 + 4./9. * M_PI * gslpp::complex::i();
    else return 16./9. * ( ( 5./2. - pi2/3. - 3.*zeta3 
            + ( 5./2. - 3./4.*pi2 )*L + L2/4. + L3/12. )*z 
            + ( 7./4. + 2./3.*pi2 - pi2*L/2. - L2/4. + L3/12. )*z2 
            + ( -7./6. - pi2/4. + 2*L - 3./4.*L2 )*z3 
            + ( 457./216. - 5./18*pi2 - L/72. - 5./6.*L2 )*z4 
            + ( 35101./8640. - 35./72.*pi2 - 185./144.*L - 35./24.*L2 )*z5
            + ( 67801./8000. - 21./20.*pi2 - 3303./800.*L - 63./20.*L2 )*z6 + 
            gslpp::complex::i()*M_PI*( ( 2. - pi2/6. + L/2. + L2/2. )*z 
            + ( 1./2. - pi2/6. - L + L2/2. )*z2
            + z3 + 5./9.*z4 + 49./72.*z5 + 231./200.*z6) );
}

gslpp::complex Bsgamma::b

(

double

z

)

The funcion \( b(z) \) as defined in [46] .

Parameters

[in]

z

squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( b(z) \)

Definition at line 182 of file Flavour/src/bsgamma.cpp.

{
    double z2=z*z;
    double z3=z2*z;
    double z4=z3*z;
    double z5=z4*z;
    double z6=z5*z;
    
    double L=log(z);
    double L2=L*L;
    
    double pi2=M_PI*M_PI;
    
    if (z == 1.) return 0.0316 + 4./81. * M_PI * gslpp::complex::i();
    else return -8./9. * ( ( -3. + pi2/6. - L )*z - 2./3.*pi2*pow(z,3./2.) 
            + ( 1./2. + pi2 -2.*L - L2/2. )*z2 
            + ( -25./12. - pi2/9. - 19./18.*L + 2.*L2 )*z3 
            + ( -1376./225. + 137./30.*L + 2.*L2 + 2./3.*pi2 )*z4 
            + ( -131317./11760. + 887./84.*L + 5.*L2 + 5./3.*pi2 )*z5 
            + ( -2807617./97200. + 16597./540.*L + 14.*L2 + 14./3.*pi2 )*z6 + 
            gslpp::complex::i()*M_PI*( -z + ( 1 - 2.*L )*z2 
            + ( -10./9. + 4./3.*L )*z3 + z4 + 2./3.*z5 + 7./9.*z6) );
}

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 [82] , but with coefficients slightly modified due to different imput parameters (obtained by private conversation with Paolo Gambino).

Returns

\(C\)

Definition at line 1221 of file Flavour/src/bsgamma.cpp.

{
    double z=zeta();
    return (1. - 8. * z + 8. * z*z*z - z*z*z*z - 12. * z*z * log(z)) * ( 0.903 
            - 0.588 * (SM.Alstilde5(4.6)*4*M_PI - 0.22) + 0.0650 * (Mb_kin - 4.55) 
            - 0.1080 * (Mc - 1.05) - 0.0122  * mu_G2 - 0.199 * rho_D3 + 0.004 * rho_LS3);
}

void Bsgamma::checkCache ( )

private

The caching method for bsgamma.

Definition at line 42 of file Flavour/src/bsgamma.cpp.

{
    if (Mb_kin == Intb_cache)
        Intb_updated = 1;
    else {
        Intb_cache = Mb_kin;
        Intb_updated = 0;
    }
    
    if (Mb_kin == Intbc_cache(0) && Mc == Intbc_cache(1)) 
        Intbc_updated = 1;
    else {
        Intbc_cache(0) = Mb_kin;
        Intbc_cache(1) = Mc;
        Intbc_updated = 0;
    }
}

void Bsgamma::computeCoeff

(

double

mu

)

Compute the Wilson Coefficient.

Parameters

[in]

mu

low scale of the decay

Definition at line 1028 of file Flavour/src/bsgamma.cpp.

{
    allcoeff = SM.getMyFlavour()->ComputeCoeffsgamma(mu);
    allcoeffprime = SM.getMyFlavour()->ComputeCoeffprimesgamma(mu);
    
    C1_0 = (*(allcoeff[LO]))(0);
    C2_0 = (*(allcoeff[LO]))(1);
    C3_0 = (*(allcoeff[LO]))(2);
    C4_0 = (*(allcoeff[LO]))(3);
    C5_0 = (*(allcoeff[LO]))(4);
    C6_0 = (*(allcoeff[LO]))(5);
    C7_0 = (*(allcoeff[LO]))(6);
    C8_0 = (*(allcoeff[LO]))(7);
    
    C1_1 = (*(allcoeff[NLO]))(0)/Alstilde;
    C2_1 = (*(allcoeff[NLO]))(1)/Alstilde;
    C3_1 = (*(allcoeff[NLO]))(2)/Alstilde;
    C4_1 = (*(allcoeff[NLO]))(3)/Alstilde;
    C5_1 = (*(allcoeff[NLO]))(4)/Alstilde;
    C6_1 = (*(allcoeff[NLO]))(5)/Alstilde;
    C7_1 = (*(allcoeff[NLO]))(6)/Alstilde;
    C8_1 = (*(allcoeff[NLO]))(7)/Alstilde;
    
    C7p_0 = (*(allcoeffprime[LO]))(6);
    C7p_1 = (*(allcoeffprime[NLO]))(6)/Alstilde;

}

double Bsgamma::computeThValue ( )

virtual

Computes the Branching Ratio for the \(b \to s \gamma\) decay.

Returns

\(BR\)

Implements ThObservable.

Definition at line 1282 of file Flavour/src/bsgamma.cpp.

{
    updateParameters();
    
    if (obs == 1) 
        return overall *  ( P(E0, mu_b, mu_c, NLO, false) + N(E0,mu_b) );
    if (obs == 2) 
        return overall *  ( P(E0, mu_b, mu_c, NLO, true) + N(E0,mu_b) );
    
    throw std::runtime_error("Bsgamma::computeThValue(): Observable type not defined. Can be only 1 or 2");
}

double Bsgamma::delta

(

double

E0

)

The cutoff energy function \( \delta = 1 - \frac{2 E_0}{M_b^{\rm kin}} \).

Parameters

[in]

E0

cutoff energy

Returns

\( \delta(E0) \)

Definition at line 60 of file Flavour/src/bsgamma.cpp.

{
    return 1. - 2.*E0/Mb_kin;
}

double Bsgamma::ff7_dMP

(

double

E0

)

The 4-body NLO correction due to \(Q_7\) and d, \(ff^7_{d,MP}\), from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^7_{d,MP}\)

Definition at line 562 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;

        return 4. * d * (18. - 33.*d + 2.*d2 + 13.*d3 - 6.* d2 * (2. + d) * log(d)) 
                / (81. * (d - 1.));   
    }
    else 
        return 0.;
}

double Bsgamma::ff7_sMP

(

double

E0

)

The 4-body NLO correction due to \(Q_7\) and s, \(ff^7_{s,MP}\), from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^7_{s,MP}\)

Definition at line 576 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;

        return (-2. * d * (72. + 39.*d - 76.*d2 - 35.*d3 
                + 6.*d*(18. + 13.*d + 2.*d2)*log(d))) / (243.*(d - 1.));
    }
    else 
        return 0.;
}

double Bsgamma::ff8_dMP

(

double

E0

)

The 4-body NLO correction due to \(Q_8\) and d, \(ff^8_{d,MP}\), from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^8_{d,MP}\)

Definition at line 590 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
        double ld = log(d);
        double l1d = log(1. - d);
        double Li2 = gsl_sf_dilog(d);

        return -136./27. * d - 724./81. * d2 + 20./27. * d3 
                + (-8./9. + 16./9. * d - 8./9. * d2) * l1d* l1d 
                + (32./27. * d + 76./27. * d2 - 16./81. * d3) * ld 
                + (-104./27. - 80./9. * d + 40./9. * d2 + (32./27. 
                + 32./9. * d - 16./9. * d2) * ld) * l1d 
                + (-64./27. * d - 152./27. * d2 + 32./81. * d3 
                + (-64./27. - 64./9. * d + 32./9. * d2) * l1d) * log(Ms/Mb_kin) 
                + (32./27. + 32./9. * d - 16./9. * d2) * Li2;
    }
    else 
        return 0.;
}

double Bsgamma::ff8_sMP

(

double

E0

)

The 4-body NLO correction due to \(Q_8\) and s, \(ff^8_{s,MP}\), from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\(ff^8_{s,MP}\)

Definition at line 613 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY){
        double d=delta(E0);
        double d2=d*d;
        double d3=d2*d;
        double ld = log(d);
        double l1d = log(1. - d);
        double Li2 = gsl_sf_dilog(d);

        return -340./243. * d - 104./81. * d2 + 16./729. * d3 
                + (-4./27. + 8./27. * d - 4./27. * d2) * l1d* l1d 
                + (8./27. * d + 4./9. * d2) * ld 
                + (-16./27. * d - 8./9. * d2) * log(Ms/Mb_kin)
                + (-268./243. - 40./27. * d + 20./27. * d2 + (8./27. 
                + 16./27. * d - 8./27. * d2) * ld
                + (-16./27. - 32./27. * d + 16./27. * d2) * log(Ms/Mb_kin)) * l1d 
                + (8./27. + 16./27. * d - 8./27. * d2) * Li2;
    }
    else 
        return 0.;
}

gslpp::complex Bsgamma::Gamma_t

(

double

t

)

The function \( \Gamma \) as defined in [81] .

Parameters

[in]

t

dummy variable to be integrated out

Returns

\( \Gamma \)

Definition at line 233 of file Flavour/src/bsgamma.cpp.

{
    if (t<4) return -2. * atan( sqrt(t/(4.-t)) ) * atan( sqrt(t/(4.-t)) );
    else return -M_PI*M_PI/2. + 2.*log( ( sqrt(t) + sqrt(t-4.) ) / 2. )*log( ( sqrt(t) + sqrt(t-4.) ) / 2. )
            - 2.*gslpp::complex::i()*M_PI*log( ( sqrt(t) + sqrt(t-4.) ) / 2. );
}

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 306 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * (1. - t);
    };

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 317 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * (1. - t) * (1. - t);
    };

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 350 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * t * (1. - t);
    };

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 361 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * t * (1. - t) * (1. - t);
    };

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 328 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * (1. - t);
    };

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 339 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).abs2() * t * (1. - t) * (1. - t);
    };

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 427 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * (1. - t);
    };

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 438 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * (1. - t) * (1. - 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 372 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t ;
    };

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 394 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * t * (1. - t);
    };

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 405 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * t * (1. - t) * (1. - t);
    };

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 383 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * (1. - t);
    };

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 416 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mb_kin,t).real() * t * (1. - t) * (1. - t);
    };

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 196 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).abs2() * (1. - t);
    };

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 218 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).abs2() * (1. - t) * (1. - 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 185 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).abs2() * t;
    };

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 207 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).abs2() * t * (1. - t);
    };

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 273 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).imag() * (1. - t);
    };

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 295 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).imag() * (1. - t) * (1. - t);
    };

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 262 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * (1. - t);
    };

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 284 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * (1. - t) * (1. - t);
    };

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 449 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * (1. - t);
    };

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 460 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * (1. - t) * (1. - t);
    };

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 471 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * t * (1. - t);
    };

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 482 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * kappa(Mb_kin,t).real() * t * (1. - t) * (1. - 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 229 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * t ;
    };

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 240 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * t * (1. - t);
    };

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 251 of file Flavour/src/bsgamma.h.

    {
        return kappa(Mc,t).real() * t * (1. - t) * (1. - t);
    };

double Bsgamma::Int_b1

(

double

E0

)

Integral of the functions getKb_re_1mt() and getKb_re_1mt2().

Parameters

[in]

E0

energy cutoff

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 247 of file Flavour/src/bsgamma.cpp.

{
    if (Intb1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntb1 = delta(E0)*mt + mt2;
        Intb1Cached = 1;
    }

    return CacheIntb1;
}

double Bsgamma::Int_b2

(

double

E0

)

Integral of the functions getKb_re_t_1mt() and getKb_re_t_1mt2().

Parameters

[in]

E0

energy cutoff

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 267 of file Flavour/src/bsgamma.cpp.

{
    if (Intb2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntb2 = delta(E0)*mt + mt2;
        Intb2Cached = 1;
    }

    return CacheIntb2;
}

double Bsgamma::Int_b3

(

double

E0

)

Integral of the functions getKb_re_t() and getKb_re_t_1mt().

Parameters

[in]

E0

energy cutoff

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 287 of file Flavour/src/bsgamma.cpp.

{
    if (Intb3Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t, &(*this), _1));
        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();
        double t = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        CacheIntb3 = delta(E0)*t + mt;
        Intb3Cached = 1;
    }

    return CacheIntb3;
}

double Bsgamma::Int_b4

(

double

E0

)

Integral of the functions getKb_re_t2_1mt() and getKb_re_t2_1mt2().

Parameters

[in]

E0

energy cutoff

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 307 of file Flavour/src/bsgamma.cpp.

{
    if (Intb4Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t2_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_re_t2_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntb4 = delta(E0)*mt + mt2;
        Intb4Cached = 1;
    }

    return CacheIntb4;
}

double Bsgamma::Int_bb1

(

double

E0

)

Integral of the functions getKb_abs2_1mt() and getKb_abs2_1mt2().

Parameters

[in]

E0

energy cutoff

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 327 of file Flavour/src/bsgamma.cpp.

{
    if (Intbb1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntbb1 = delta(E0)*mt + mt2;
        Intbb1Cached = 1;
    }

    return CacheIntbb1;
}

double Bsgamma::Int_bb2

(

double

E0

)

Integral of the functions getKb_abs2_t_1mt() and getKb_abs2_t_1mt2().

Parameters

[in]

E0

energy cutoff

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 347 of file Flavour/src/bsgamma.cpp.

{
    if (Intbb2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_t_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntbb2 = delta(E0)*mt + mt2;
        Intbb2Cached = 1;
    }

    return CacheIntbb2;
}

double Bsgamma::Int_bb4

(

double

E0

)

Integral of the functions getKb_abs2_t2_1mt() and getKb_abs2_t2_1mt2().

Parameters

[in]

E0

energy cutoff

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 367 of file Flavour/src/bsgamma.cpp.

{
    if (Intbb4Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_t2_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKb_abs2_t2_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntbb4 = delta(E0)*mt + mt2;
        Intbb4Cached = 1;
    }

    return CacheIntbb4;
}

double Bsgamma::Int_bc1

(

double

E0

)

Integral of the functions getKc_re_Kb_1mt() and getKc_re_Kb_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))Re(k_c(t))(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))Re(k_c(t))(1-t)^2\)

Definition at line 387 of file Flavour/src/bsgamma.cpp.

{
    if (Intbc1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_Kb_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_Kb_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntbc1 = delta(E0)*mt + mt2;
        Intbc1Cached = 1;
    }

    return CacheIntbc1;
}

double Bsgamma::Int_bc2

(

double

E0

)

Integral of the functions getKc_re_Kb_t_1mt() and getKc_re_Kb_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_b(t))Re(k_c(t))t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_b(t))Re(k_c(t))t(1-t)^2\)

Definition at line 407 of file Flavour/src/bsgamma.cpp.

{
    if (Intbc2Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_Kb_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_Kb_t_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntbc2 = delta(E0)*mt + mt2;
        Intbc2Cached = 1;
    }

    return CacheIntbc2;
}

double Bsgamma::Int_c1

(

double

E0

)

Integral of the functions getKc_re_1mt() and getKc_re_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_c(t))(1-t) + \int_{1-\delta(E_0)}^1 Re(k_c(t))(1-t)^2\)

Definition at line 427 of file Flavour/src/bsgamma.cpp.

{
    if (Intc1Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntc1 = delta(E0)*mt + mt2;
        Intc1Cached = 1;
    }

    return CacheIntc1;
}

double Bsgamma::Int_c1_im

(

double

E0

)

Integral of the functions getKc_im_1mt() and getKc_im_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Im(k_c(t))(1-t) + \int_{1-\delta(E_0)}^1 Im(k_c(t))(1-t)^2\)

Definition at line 447 of file Flavour/src/bsgamma.cpp.

{
    if (Intc1imCached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_im_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_im_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntc1im = delta(E0)*mt + mt2;
        Intc1imCached = 1;
    }

    return CacheIntc1im;
}

double Bsgamma::Int_c2

(

double

E0

)

Integral of the functions getKc_re_t_1mt() and getKc_re_t_1mt2().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_c(t))t(1-t) + \int_{1-\delta(E_0)}^1 Re(k_c(t))t(1-t)^2\)

Definition at line 467 of file Flavour/src/bsgamma.cpp.

{
    if (Intc2Cached == 0) {
        double t1 = (1. - delta(E0));

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_t_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;

        CacheIntc2 = delta(E0)*mt + mt2;
        Intc2Cached = 1;
    }

    return CacheIntc2;
}

double Bsgamma::Int_c3

(

double

E0

)

Integral of the functions getKc_re_t() and getKc_re_t_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} Re(k_c(t))t + \int_{1-\delta(E_0)}^1 Re(k_c(t))t(1-t)\)

Definition at line 487 of file Flavour/src/bsgamma.cpp.

{
    if (Intc3Cached == 0) {
        double t1 = (1. - delta(E0));
    
        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_t, &(*this), _1));
        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();
        double t = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_re_t_1mt, &(*this), _1));
        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();
        double mt = avaINT;
        
        CacheIntc3 = delta(E0)*t + mt;
        Intc3Cached = 1;
    }

    return CacheIntc3;
}

double Bsgamma::Int_cc

(

double

E0

)

Integral of the functions getKc_abs2_t() and getKc_abs2_t_1mt().

Parameters

[in]

E0

energy cutoff

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 507 of file Flavour/src/bsgamma.cpp.

{
    if (IntccCached == 0) {
        double t1 = (1. - delta(E0));

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_abs2_t, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_abs2_t_1mt, &(*this), _1));
        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();
        double mt2 = avaINT;
        
        CacheIntcc = delta(E0)*mt + 2. * mt2;
        IntccCached = 1;
    }
    
    return CacheIntcc;
}

double Bsgamma::Int_cc1

(

double

E0

)

Integral of the functions getKc_abs2_1mt() and getKc_abs2_1mt^().

Parameters

[in]

E0

energy cutoff

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 527 of file Flavour/src/bsgamma.cpp.

{
    if (Intcc1Cached == 0) {
        double t1 = (1. - delta(E0));

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_abs2_1mt, &(*this), _1));
        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();
        double mt = avaINT;

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_abs2_1mt2, &(*this), _1));
        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();
        double mt2 = avaINT;
        
        CacheIntcc1 = delta(E0)*mt + mt2;
        Intcc1Cached = 1;
    }
    
    return CacheIntcc1;
}

double Bsgamma::Int_cc1_part1

(

double

E0

)

Integral of the functions getKc_abs2_1mt().

Parameters

[in]

E0

energy cutoff

Returns

\(\delta(E_0)\int_0^{1-\delta(E_0)} |k_c(t)|^2(1-t)\)

Definition at line 547 of file Flavour/src/bsgamma.cpp.

{
    if (Intcc1p1Cached == 0) {
        double t1 = (1. - delta(E0));

        INT = convertToGslFunction(boost::bind(&Bsgamma::getKc_abs2_1mt, &(*this), _1));
        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();
        
        CacheIntcc1p1 = delta(E0)*avaINT;
        Intcc1p1Cached = 1;
    }
    
    return CacheIntcc1p1;
}

gslpp::complex Bsgamma::kappa	(	double	Mq,
		double	t
	)

The function \( k \) as defined in [113] .

Parameters

[in]	Mq	quark mass
[in]	t	dummy variable to be integrated out

Returns

\( k \)

Definition at line 241 of file Flavour/src/bsgamma.cpp.

{
    double s = t * Mb_kin*Mb_kin/Mq/Mq;
    return 1./2. + Gamma_t(s)/s;
}

double Bsgamma::Kij_1	(	int	i,
		int	j,
		double	E0,
		double	mu
	)

The \( K_{ij}^{(1)} \) function from [109] .

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 969 of file Flavour/src/bsgamma.cpp.

{
    if (i > 8 || j>8 || i<1 || j<1) throw std::runtime_error("Bsgamma::Kij_1(): indexes (i,j) must be included in (1,..,8)");
    
    int temp;
    
    if (i > j) {temp=i; i=j; j=temp;}
    
    double gamma_i7[8] = {-208./243., 416./81., -176./81., -152./243., -6272./81., 4624./243., 32./3., -32./9.};
    double K_ij[8][8];
    double Lb = log(mu/Mb_kin);
    
    K_ij[0][0] = 4.*Phi11_1(E0);
    K_ij[0][1] = 2.*Phi12_1(E0);
    K_ij[0][2] = 2.*Phi13_1(E0);
    K_ij[0][3] = 2.*Phi14_1(E0);
    K_ij[0][4] = 2.*Phi15_1(E0);
    K_ij[0][5] = 2.*Phi16_1(E0);
    K_ij[0][6] = r1(1,zeta()).real() - gamma_i7[0]*Lb + 2.*Phi17_1(E0, zeta());
    K_ij[0][7] = 2.*Phi18_1(E0, zeta());
    
    K_ij[1][1] = 4.*Phi22_1(E0);
    K_ij[1][2] = 2.*Phi23_1(E0);
    K_ij[1][3] = 2.*Phi24_1(E0);
    K_ij[1][4] = 2.*Phi25_1(E0);
    K_ij[1][5] = 2.*Phi26_1(E0);
    K_ij[1][6] = r1(2,zeta()).real() - gamma_i7[1]*Lb + 2.*Phi27_1(E0, zeta());
    K_ij[1][7] = 2.*Phi28_1(E0, zeta());
    
    K_ij[2][2] = 4.*Phi33_1(E0);
    K_ij[2][3] = 2.*Phi34_1(E0);
    K_ij[2][4] = 2.*Phi35_1(E0);
    K_ij[2][5] = 2.*Phi36_1(E0);
    K_ij[2][6] = r1(3,zeta()).real() - gamma_i7[2]*Lb + 2.*Phi37_1(E0);
    K_ij[2][7] = 2.*Phi38_1(E0);
    
    K_ij[3][3] = 4.*Phi44_1(E0);
    K_ij[3][4] = 2.*Phi45_1(E0);
    K_ij[3][5] = 2.*Phi46_1(E0);
    K_ij[3][6] = r1(4,zeta()).real() - gamma_i7[3]*Lb + 2.*Phi47_1(E0);
    K_ij[3][7] = 2.*Phi48_1(E0);
    
    K_ij[4][4] = 4.*Phi55_1(E0);
    K_ij[4][5] = 2.*Phi56_1(E0);
    K_ij[4][6] = r1(5,zeta()).real() - gamma_i7[4]*Lb + 2.*Phi57_1(E0);
    K_ij[4][7] = 2.*Phi58_1(E0);
    
    K_ij[5][5] = 4.*Phi66_1(E0);
    K_ij[5][6] = r1(6,zeta()).real() - gamma_i7[5]*Lb + 2.*Phi67_1(E0);
    K_ij[5][7] = 2.*Phi68_1(E0);
    
    K_ij[6][6] = -182./9. + 8./9.*M_PI*M_PI - gamma_i7[6]*2.*Lb + 4.*Phi77_1(E0);
    K_ij[6][7] =  r1(8,zeta()).real() - gamma_i7[7]*Lb + 2.*Phi78_1(E0);
    
    K_ij[7][7] = 4.*Phi88_1(E0);
    
    return K_ij[i-1][j-1];
}

double Bsgamma::N	(	double	E0,
		double	mu
	)

The non perturbative part of the \(BR\) as defined in [41] , \(N\).

Parameters

[in]	E0	energy cutoff
[in]	mu	b quark scale

Returns

\(N\)

Definition at line 1216 of file Flavour/src/bsgamma.cpp.

{
    return N_27() + N_77(E0,mu) + BLNPcorr * P0(E0);
}

double Bsgamma::N_27

(

)

The non perturbative part of the \(BR\) due to \(Q_2-Q_7\) interference as defined in [81] , \(N_{27}\).

Returns

\(N_{27}\)

Definition at line 1161 of file Flavour/src/bsgamma.cpp.

{
    double mcnorm = 1.131; // value fixed according to arXiv:1003.5012, in order to employ the remaining corrections given in that work
    double lambda2 = mu_G2/3.;
    
    return -1./18. * (C7_0 * ( 2.*C2_0 - C1_0/3. )).real() * lambda2/mcnorm/mcnorm;
}

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 [73] , \(N_{77}\).

Parameters

[in]	E0	energy cutoff
[in]	mu	b quark scale

Returns

\(N_{77}\)

Definition at line 1169 of file Flavour/src/bsgamma.cpp.

{
    double z = 1. - delta(E0);
    double z2 = z*z;
    double z3 = z2*z;
    double z4 = z3*z;
    double umz2 = (1.-z)*(1.-z);
    double Lz = log(1. - z);
    double Lz2 = Lz*Lz;
    double Lb = 2. * log(mu/Mb_kin);
    
    double corrLambda2_rad;
    double corrLambda2_sem;
    double corrLambda2_mix;
    double corrLambda2;
    double corrLambda3;
    
    double alsb = SM.Alstilde5(Mb_kin);
    double Lambda_pert = 64./9. * alsb * mu_kin * 
                (1. + 4. * alsb * (9./2. * (log(Mb_kin/2./mu_kin) + 8./3.)
                - 3. * (M_PI*M_PI/6. - 13./12.)) );
    double mu_pi2_pert = 3./4. * mu_kin * Lambda_pert - 48. * alsb*alsb * mu_kin*mu_kin;
    double rho_D3_pert = 1./2. * mu_kin*mu_kin * Lambda_pert - 128./3. * alsb*alsb * mu_kin*mu_kin*mu_kin;
    
    double lambda1 = -mu_pi2 + mu_pi2_pert;
    double lambda2 = mu_G2/3.;
    double rho1 = rho_D3 - rho_D3_pert;
    
    double f1EGN = 16./9. * ( 4. - M_PI*M_PI) - 8./3. * Lz2 - 
             ( 4. * z * ( 30. - 63. * z + 31. * z2 + 5. * z3))/(9. * umz2) -
             ( 4. * (30. - 72. * z + 51. * z2 - 2. * z3 - 3. * z4))/(9. * umz2) * Lz;
    double f2EGN = -2./9. * ( 87. + 32. * M_PI*M_PI) - 32./3. * Lz2 + 
             2. * ( 162. - 244. * z + 113. * z2 - 7. * z3)/(3. * (1. - z)) * Lz +
             2. * z * ( 54 - 49. * z + 15. * z2)/(1. - z);
    
    corrLambda2_rad = lambda1 * ( f1EGN/8.  - 4./3. * (Lb + 1.) ) 
            + lambda2 * (f2EGN/8.  + 12. * (Lb + 1.) );
    corrLambda2_sem = -3. * 4.98 * lambda2 + (25. - 4. * M_PI*M_PI)/12.*lambda1;
    corrLambda2_mix = 1./8. * (9. * lambda2 - lambda1) * Kij_1(7,7,E0,mu);
    
    corrLambda2 = corrLambda2_rad - corrLambda2_sem + corrLambda2_mix;
    
    corrLambda3 = (-88./6. + 16.*log(2.))* rho1 /Mb_kin/Mb_kin/Mb_kin;
    
    return (C7_0.abs2() + C7p_0.abs2()) * (4. * Alstilde / Mb_kin / Mb_kin * corrLambda2 + corrLambda3);
}

double Bsgamma::omega

(

double

E0

)

The cutoff energy function \( \omega \) as defined in [94] .

Parameters

[in]

E0

cutoff energy

Returns

\( \omega(E0) \)

Definition at line 73 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 3./2. * d2 - 2. * d3 + d4;
}

double Bsgamma::P	(	double	E0,
		double	mu_b,
		double	mu_c,
		orders	order,
		bool	CPodd
	)

The perturbative part of the \(BR\) as defined in [109] , \(P\).

Parameters

[in]	E0	energy cutoff
[in]	mu_b	b quark scale
[in]	mu_c	c quark scale
[in]	order	perturbation theory order
[in]	CPodd	switch to allow for CPodd terms

Returns

\(P\)

Definition at line 1145 of file Flavour/src/bsgamma.cpp.

{
    switch(order) {
        case NLO:
            return P0(E0) + Alstilde * (P11() + P21(E0,mu_b)) + Vub_NLO(E0, CPodd);
            break;
        case LO:
            return P0(E0);
            break;
        default:
            std::stringstream out;
            out << order;
            throw std::runtime_error("Bsgamma::P(): order " + out.str() + " not implemented");
    }
}

double Bsgamma::P0

(

double

E0

)

The perturbative part \( P^{(0)} \) of the BR as defined in [109] .

Parameters

[in]

E0

energy cutoff

Returns

\( P^{(0)} \)

Definition at line 1056 of file Flavour/src/bsgamma.cpp.

{
    return C7_0.abs2() + C7p_0.abs2() + P0_4body(E0,Mb_kin*Mb_kin/Ms/Ms);
}

double Bsgamma::P0_4body	(	double	E0,
		double	t
	)

The 4-body LO contribution as defined in [94] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( P_{tree}^{(0)} \)

Definition at line 127 of file Flavour/src/bsgamma.cpp.

{
    gslpp::complex A1 =-C1_0*CKMu;
    gslpp::complex A2 =-C2_0*CKMu;
    
    return (C3_0.abs2() + 20. * (C3_0*C5_0).real() + 2./9. * C4_0.abs2() 
            + 40./9. * (C4_0*C6_0).real() + 136. * C5_0.abs2() 
            + 272./9. * C6_0.abs2()) * T1(E0,t)
            + (2./9. * A1.abs2() + A2.abs2() 
            + (8./9. * C3_0.real() 
            - 4./27. * C4_0.real() + 128./9. * C5_0.real() 
            - 64./27. * C6_0.real()) * A1.real() 
            +(2./3. * C3_0.real() + 8./9. * C4_0.real() + 32./3. * C5_0.real() 
            + 128./9. * C6_0.real()) * A2.real()) * T2(E0,t)
            + (C3_0.abs2() + 8./3. * (C3_0*C4_0).real() + 32. * (C3_0*C5_0).real() 
            + 128./3. * (C3_0*C6_0).real() - 2./9. * C4_0.abs2() 
            + 128./3. * (C4_0*C5_0).real() - 64./9. * (C4_0*C6_0).real()
            + 256. * C5_0.abs2() + 2048./3 * (C5_0*C6_0).real() 
            - 512./9. * C6_0.abs2()) * T3(E0,t);
}

double Bsgamma::P11

(

)

The perturbative part \( P_1^{(1)} \) of the BR as defined in [109] .

Returns

\( P_1^{(1)} \)

Definition at line 1061 of file Flavour/src/bsgamma.cpp.

{
    return 2.*((C7_0*C7_1).real() + (C7p_0*C7p_1).real()); /*CHECK SIGN*/
}

double Bsgamma::P12

(

)

The perturbative part \( P_1^{(2)} \) of the BR as defined in [109] .

Returns

\( P_1^{(2)} \)

double Bsgamma::P21	(	double	E0,
		double	mu
	)

The perturbative part \( P_2^{(1)} \) of the BR as defined in [109] .

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( P_2^{(1)} \)

Definition at line 1066 of file Flavour/src/bsgamma.cpp.

{
    int i,j;
    gslpp::complex C0[8]={C1_0,C2_0,C3_0,C4_0,C5_0,C6_0,C7_0,C8_0};
    gslpp::complex C0p[8]={C7p_0}; /*IMPLEMENT OTHER WC*/
    double p21=0.;
    
    for(i=0;i<8;i++)
    {
        for(j=0;j<8;j++)
        {
            p21 += (C0[i]*C0[j]).real() * Kij_1(i+1,j+1,E0,mu);
        }
    }
    
    for(i=6;i<7;i++) /*CHECK ALGORITHM*/
    {
        for(j=6;j<7;j++)
        {
            p21 += (C0p[i]*C0p[j]).real() * Kij_1(i+1,j+1,E0,mu);
        }
    }
    
    return p21;
}

double Bsgamma::P22	(	double	E0,
		double	mu_b,
		double	mu_c
	)

The perturbative part \( P_2^{(2)} \) of the BR as defined in [109] .

Parameters

[in]	E0	energy cutoff
[in]	mu_b	b quark scale
[in]	mu_c	c quark scale

Returns

\( P_2^{(2)} \)

double Bsgamma::P32	(	double	E0,
		double	mu
	)

The perturbative part \( P_3^{(2)} \) of the BR as defined in [109] .

Parameters

[in]	E0	energy cutoff
[in]	mu	low scale of the decay

Returns

\( P_3^{(2)} \)

double Bsgamma::Phi11_1

(

double

E0

)

The \( \Phi_{11}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{11}^{(1)} \)

Definition at line 636 of file Flavour/src/bsgamma.cpp.

{
    return Phi22_1(E0)/36.;
}

double Bsgamma::Phi12_1

(

double

E0

)

The \( \Phi_{12}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{12}^{(1)} \)

Definition at line 641 of file Flavour/src/bsgamma.cpp.

{
    return -Phi22_1(E0)/3.;
}

double Bsgamma::Phi13_1

(

double

E0

)

The \( \Phi_{13}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{13}^{(1)} \)

Definition at line 646 of file Flavour/src/bsgamma.cpp.

{
    return -Phi23_1(E0)/6.;
}

double Bsgamma::Phi14_1

(

double

E0

)

The \( \Phi_{14}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{14}^{(1)} \)

Definition at line 651 of file Flavour/src/bsgamma.cpp.

{
    return -Phi24_1(E0)/6.;
}

double Bsgamma::Phi15_1

(

double

E0

)

The \( \Phi_{15}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{15}^{(1)} \)

Definition at line 656 of file Flavour/src/bsgamma.cpp.

{
    return -Phi25_1(E0)/6.;
}

double Bsgamma::Phi16_1

(

double

E0

)

The \( \Phi_{16}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{16}^{(1)} \)

Definition at line 661 of file Flavour/src/bsgamma.cpp.

{
    return -Phi26_1(E0)/6.;
}

double Bsgamma::Phi17_1	(	double	E0,
		double	z
	)

The \( \Phi_{17}^{(1)} \) function from [81] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{17}^{(1)} \)

Definition at line 666 of file Flavour/src/bsgamma.cpp.

{
    return -Phi27_1(E0,z)/6.;
}

double Bsgamma::Phi18_1	(	double	E0,
		double	z
	)

The \( \Phi_{18}^{(1)} \) function from [81] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{18}^{(1)} \)

Definition at line 671 of file Flavour/src/bsgamma.cpp.

{
    return Phi27_1(E0,z)/18.;
}

double Bsgamma::Phi22_1

(

double

E0

)

The \( \Phi_{22}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{22}^{(1)} \)

Definition at line 676 of file Flavour/src/bsgamma.cpp.

{
    return 16./27. * Int_cc1(E0);
}

double Bsgamma::Phi23_1

(

double

E0

)

The \( \Phi_{23}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{23}^{(1)} \)

Definition at line 689 of file Flavour/src/bsgamma.cpp.

{
    return -8./27. * (Int_c1(E0) + Int_c2(E0) + 2.*Int_bc1(E0) - 2.*Int_bc2(E0))
            - Phi23_1_4body(E0);
}

double Bsgamma::Phi23_1_4body

(

double

E0

)

The \( \Phi_{23}^{(1),{\rm 4-body}} \) function obtained from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{23}^{(1),{\rm 4-body}} \)

Definition at line 681 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.0039849625073434735;
    else
        return 0.;
}

double Bsgamma::Phi24_1

(

double

E0

)

The \( \Phi_{24}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{24}^{(1)} \)

Definition at line 703 of file Flavour/src/bsgamma.cpp.

{
    return -1./6. * (Phi23_1(E0) + Phi23_1_4body(E0))
            - Phi24_1_4body(E0);
}

double Bsgamma::Phi24_1_4body

(

double

E0

)

The \( \Phi_{24}^{(1),{\rm 4-body}} \) function obtained from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{24}^{(1),{\rm 4-body}} \)

Definition at line 695 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.012330977673588935;
    else
        return 0.;
}

double Bsgamma::Phi25_1

(

double

E0

)

The \( \Phi_{25}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{25}^{(1)} \)

Definition at line 717 of file Flavour/src/bsgamma.cpp.

{
    return -32./27. * (4.*Int_c1(E0) + Int_c2(E0) + 8.*Int_bc1(E0) - 2.*Int_bc2(E0))
            - Phi25_1_4body(E0);
}

double Bsgamma::Phi25_1_4body

(

double

E0

)

The \( \Phi_{25}^{(1),{\rm 4-body}} \) function obtained from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{25}^{(1),{\rm 4-body}} \)

Definition at line 709 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.06375940011749558;
    else
        return 0.;
}

double Bsgamma::Phi26_1

(

double

E0

)

The \( \Phi_{26}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{26}^{(1)} \)

Definition at line 731 of file Flavour/src/bsgamma.cpp.

{
    return 16./81. * (4.*Int_c1(E0) + Int_c2(E0) - 10.*Int_bc1(E0) - 2.*Int_bc2(E0) + 36.*Int_cc1(E0))
            - Phi26_1_4body(E0);
}

double Bsgamma::Phi26_1_4body

(

double

E0

)

The \( \Phi_{26}^{(1),{\rm 4-body}} \) function obtained from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{26}^{(1),{\rm 4-body}} \)

Definition at line 723 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY)
        return 0.11932481422855279;
    else
        return 0.;
}

double Bsgamma::Phi27_1	(	double	E0,
		double	z
	)

The \( \Re \Phi_{27}^{(1)} \) function from [81] .

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 737 of file Flavour/src/bsgamma.cpp.

{
    double d = delta(E0);
    double d2 = d*d;
    double Pi2 = M_PI*M_PI;
    double st0 = sqrt(1. - 4.*z);
    double std = sqrt( (1. - d - 4.*z) * (1. - d) );
    double L0 = log( ( 1. + st0 ) / ( 2.*sqrt(z) ) );
    double Ld = log( ( sqrt(1. - d) + sqrt(1. - d - 4.*z) ) / ( 2.*sqrt(z) ) );
    
    if (d == 1) {
        return -2./27. + (2.*Pi2 - 7.)/9. * z + 4.*(3. - 2.*Pi2)/9. * z * z
                + 4./3. * z * (1. - 2.*z) * st0 * L0
                - 8./9. * z * (6.*z*z - 4.*z + 1.) * L0*L0 + 4./3. * Pi2 * z * z *z;
    } else return -2./27. * d * (3. - 3.*d + d2) + (2.*Pi2 - 7.)/9. * z * d * (2. - d)
            + 4.*(3. - 2.*Pi2)/9. * z * z * d 
            + 4./3. * z * (1. - 2.*z) * ( st0 * L0 - std * Ld ) 
            + 4./3. * z * d * std * Ld 
            - 8./9. * z * (6.*z*z - 4.*z + 1.) * ( L0*L0 - Ld*Ld ) 
            - 8./9. * z * d * (2. - d - 4.*z) * Ld * Ld;
}

double Bsgamma::Phi27_1_im	(	double	E0,
		double	z
	)

The \( \Im\Phi_{27}^{(1)} \) function from [81] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Im\Phi_{27}^{(1)} \)

Definition at line 759 of file Flavour/src/bsgamma.cpp.

{
    if (z >= 1./4.) 
        throw std::runtime_error("Bsgamma::Phi27_1_im(): z can not be greater than 1/4");
    
    double d = delta(E0);
    double z2 = z*z;
    double st0 = sqrt(1. - 4.*z);
    double std = sqrt( (1. - d - 4.*z) * (1. - d) );
    double L0 = log( ( 1. + st0 ) / ( 2.*sqrt(z) ) );
    double Ld = log( ( sqrt(1. - d) + sqrt(1. - d - 4.*z) ) / ( 2.*sqrt(z) ) );
    
    if (z < (1. - d)/4.)
        return 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2)* (L0-Ld) - 3./4. * (1. - 2. * z) * (st0-std) 
                + d * (2. - d - 4. * z) * Ld - 3./4. * d * std );
    else
        return 8./9. * M_PI * z * ( (1. - 4. * z + 6. * z2) * L0 - 3./4. * (1. - 2. * z) * st0 );
}

double Bsgamma::Phi28_1	(	double	E0,
		double	z
	)

The \( \Phi_{28}^{(1)} \) function from [81] .

Parameters

[in]	E0	energy cutoff
[in]	z	squared ratio between \(m_c\) and \(m_b^{\rm kin}\)

Returns

\( \Phi_{28}^{(1)} \)

Definition at line 778 of file Flavour/src/bsgamma.cpp.

{
    return -Phi27_1(E0, z)/3.;
}

double Bsgamma::Phi33_1

(

double

E0

)

The \( \Phi_{33}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{33}^{(1)} \)

Definition at line 783 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 2./27. * (Int_b1(E0) + 8.*Int_b2(E0) - 4.*Int_b4(E0)
            + 33.*Int_bb1(E0) - 20.*Int_bb2(E0) + 4.*Int_bb4(E0))
            + 1./18. * d * ( 1./2. - 1./2.*d2 + 1./3.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi34_1

(

double

E0

)

The \( \Phi_{34}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{34}^{(1)} \)

Definition at line 795 of file Flavour/src/bsgamma.cpp.

{
    return -1./3.*Phi33_1(E0);
}

double Bsgamma::Phi35_1

(

double

E0

)

The \( \Phi_{35}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{35}^{(1)} \)

Definition at line 800 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 32./27. * (2.*Int_b1(E0) + 4.*Int_b2(E0) - 2.*Int_b4(E0)
            + 18.*Int_bb1(E0) - 13.*Int_bb2(E0) + 2.*Int_bb4(E0))
            + 4./9. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi36_1

(

double

E0

)

The \( \Phi_{36}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{36}^{(1)} \)

Definition at line 812 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 8./81. * (5.*Int_b1(E0) + Int_b2(E0) + 4.*Int_b4(E0)
            - 18.*Int_bb1(E0) + 8.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 6. * (Phi23_1(E0) + Phi23_1_4body(E0))
            - 2./27. * d * ( 4./3. - d2 + 1./2.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi37_1

(

double

E0

)

The \( \Phi_{37}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{37}^{(1)} \)

Definition at line 825 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return -4./3. * Int_b3(E0) + 1./9. * d * (1. - d + 1./3.*d2) + 1./4.*ff7_sMP(E0);
}

double Bsgamma::Phi38_1

(

double

E0

)

The \( \Phi_{38}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{38}^{(1)} \)

Definition at line 833 of file Flavour/src/bsgamma.cpp.

{
    return -1./3. * ( Phi37_1(E0) - 1./4.*ff7_sMP(E0) ) + 1./4.*ff8_sMP(E0);
}

double Bsgamma::Phi44_1

(

double

E0

)

The \( \Phi_{44}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{44}^{(1)} \)

Definition at line 838 of file Flavour/src/bsgamma.cpp.

{
    return 1./36. * Phi33_1(E0);
}

double Bsgamma::Phi45_1

(

double

E0

)

The \( \Phi_{45}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{45}^{(1)} \)

Definition at line 843 of file Flavour/src/bsgamma.cpp.

{
    return -1./6. * Phi35_1(E0);
}

double Bsgamma::Phi46_1

(

double

E0

)

The \( \Phi_{46}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{46}^{(1)} \)

Definition at line 848 of file Flavour/src/bsgamma.cpp.

{
    return -1./6. * Phi36_1(E0);
}

double Bsgamma::Phi47_1

(

double

E0

)

The \( \Phi_{47}^{(1)} \) function from [81] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{47}^{(1)} \)

Definition at line 853 of file Flavour/src/bsgamma.cpp.

{
    return -1./6. * ( Phi37_1(E0) - 1./4.*ff7_sMP(E0) ) 
            + 1./4. * (-1./6. * ff7_sMP(E0) + ff7_dMP(E0));
}

double Bsgamma::Phi48_1

(

double

E0

)

The \( \Phi_{48}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{48}^{(1)} \)

Definition at line 859 of file Flavour/src/bsgamma.cpp.

{
    return -1./3. * (Phi47_1(E0) - 1./4. * (-1./6. * ff7_sMP(E0) + ff7_dMP(E0)) ) 
            + 1./4. * (-1./6. * ff8_sMP(E0) + ff8_dMP(E0));
}

double Bsgamma::Phi55_1

(

double

E0

)

The \( \Phi_{55}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{55}^{(1)} \)

Definition at line 865 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 128./27. * (4.*Int_b1(E0) + 2.*Int_b2(E0) - Int_b4(E0)
            + 12.*Int_bb1(E0) - 8.*Int_bb2(E0) + Int_bb4(E0))
            + 8./9. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi56_1

(

double

E0

)

The \( \Phi_{56}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{56}^{(1)} \)

Definition at line 877 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return 32./81. * (20.*Int_b1(E0) + Int_b2(E0) + 4.*Int_b4(E0)
            + 24.*Int_bb1(E0) + 14.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 6. * (Phi25_1(E0) + Phi25_1_4body(E0))
            - 8./27. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi57_1

(

double

E0

)

The \( \Phi_{57}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{57}^{(1)} \)

Definition at line 890 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return 16./9. * d * ( 1. - d + 1./3.*d2) + 4. * ff7_sMP(E0);
}

double Bsgamma::Phi58_1

(

double

E0

)

The \( \Phi_{58}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{58}^{(1)} \)

Definition at line 898 of file Flavour/src/bsgamma.cpp.

{
    return -1./3. * (Phi57_1(E0) - 4. *  ff7_sMP(E0)) 
            + 4. * ff8_sMP(E0);
}

double Bsgamma::Phi66_1

(

double

E0

)

The \( \Phi_{66}^{(1)} \) function obtained using the prescription of [50] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{66}^{(1)} \)

Definition at line 904 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    return -8./243. * (56.*Int_b1(E0) + 10.*Int_b2(E0) + 4.*Int_b4(E0)
            + 15.*Int_bb1(E0) - 4.*Int_bb2(E0) - 4.*Int_bb4(E0))
            + 32./27. * (4.*Int_c1(E0) + Int_c2(E0) - Int_bc1(E0) 
            - 2.*Int_bc2(E0) + 9.*Int_cc1(E0))
            + 2./81. * d * ( 11./3. - 2.*d2 + 2./3.*d3 - 1./15.*d4 );
}

double Bsgamma::Phi67_1

(

double

E0

)

The \( \Phi_{67}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{67}^{(1)} \)

Definition at line 918 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    
    return 8./3. * (Int_b3(E0) - 2.*Int_c3(E0)) - 8./27. * d * ( 1. - d + 1./3.*d2) 
            + 1./4. * (-8./3. * ff7_sMP(E0) + 10. * ff7_dMP(E0));
}

double Bsgamma::Phi68_1

(

double

E0

)

The \( \Phi_{68}^{(1)} \) function obtained using the prescription of [50] and adding the 4-body contribution from [92] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{68}^{(1)} \)

Definition at line 927 of file Flavour/src/bsgamma.cpp.

{
    return -1./3. * (Phi67_1(E0) - 1./4. * (-8./3. * ff7_sMP(E0) + 10. * ff7_dMP(E0)) ) 
            + 1./4. * (-8./3. * ff8_sMP(E0) + 10. * ff8_dMP(E0));
}

double Bsgamma::Phi77_1

(

double

E0

)

The \( \Phi_{77}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{77}^{(1)} \)

Definition at line 933 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    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.;
}

double Bsgamma::Phi78_1

(

double

E0

)

The \( \Phi_{78}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{78}^{(1)} \)

Definition at line 942 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    double Li2 = gsl_sf_dilog(1. - d);
    
    double pi2=M_PI*M_PI;
    
    return 8./9.*( Li2 -  pi2/6. - d*log(d) + 9./4.*d - d2/4. + d3/12.);
}

double Bsgamma::Phi88_1

(

double

E0

)

The \( \Phi_{88}^{(1)} \) function from [81] .

Parameters

[in]

E0

energy cutoff

Returns

\( \Phi_{88}^{(1)} \)

Definition at line 955 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    
    double Li2 = gsl_sf_dilog(1. - d);
    
    double pi2=M_PI*M_PI;
    
    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) 
            + 8.*log(1. - d) -  2./3.*d3 + 3.*d2 +7*d);
}

gslpp::complex Bsgamma::r1	(	int	i,
		double	z
	)

The funcion \( r_i^{(1)}(z) \) as defined in [46] .

Parameters

[in]	i	function index
[in]	z	squared ratio between m_c and m_b^{ kin}

Returns

\( r_i(z)^{(1)} \)

Definition at line 206 of file Flavour/src/bsgamma.cpp.

{
    double Xb = -0.16844083981858157;
    
    switch(i){
        case 1:
            return 833./729. - (a(z) + b(z))/3. + 40./243.*gslpp::complex::i()*M_PI;
        case 2:
            return - 1666./243. + 2.*(a(z) + b(z)) - 80./81.*gslpp::complex::i()*M_PI;
        case 3:
            return 2392./243. + 8.*M_PI/3./sqrt(3.) + 32./9.*Xb - a(1.) + 2.*b(1.) + 56./81.*gslpp::complex::i()*M_PI;
        case 4:
            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;
        case 5:
            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;
        case 6:
            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) 
                    - 2296./243.*gslpp::complex::i()*M_PI;
        case 8:
            return 44./9. - 8./27.*M_PI*M_PI + 8./9.*gslpp::complex::i()*M_PI;
        default:
            std::stringstream out;
            out << i;
            throw std::runtime_error("Bsgamma::r1(): index " + out.str() + " not implemented");
    }
}

double Bsgamma::rho

(

double

E0

)

The cutoff energy function \( \rho \) as defined in [94] .

Parameters

[in]

E0

cutoff energy

Returns

\( \rho(E0) \)

Definition at line 65 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d4=d*d*d*d;
    
    return d + d4/6. + log(1. - d);
}

double Bsgamma::T1	(	double	E0,
		double	t
	)

The cutoff energy function \( T_1 \) as defined in [94] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_1(E0) \)

Definition at line 83 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 109./18. * d + 17./18. * d2 - 191./108. * d3 + 23./16. * d4 
            + 79./18. * log(1. - d) - 5./3. * Li2 
            - (5./3. * rho(E0) + 2./9. * omega(E0)) * log(t*d) 
            /* + rho(E0)/9.*log(ms^5/(mu^4*md)) */;
}

double Bsgamma::T2	(	double	E0,
		double	t
	)

The cutoff energy function \( T_2 \) as defined in [94] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_2(E0) \)

Definition at line 98 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 187./108. * d + 7./18. * d2 - 395./648. * d3 + 1181./2592. * d4 
            + 133./108. * log(1. - d) - Li2/2. 
            - (rho(E0)/2. + 2./27. * omega(E0)) * log(t*d) 
            /* + rho(E0)/9.*log(ms/mu) */;
}

double Bsgamma::T3	(	double	E0,
		double	t
	)

The cutoff energy function \( T_3 \) as defined in [94] .

Parameters

[in]	E0	cutoff energy
[in]	t	squared ratio between b quark and s quark masses

Returns

\( T_3(E0) \)

Definition at line 113 of file Flavour/src/bsgamma.cpp.

{
    double d=delta(E0);
    double d2=d*d;
    double d3=d2*d;
    double d4=d3*d;
    
    double Li2 = gsl_sf_dilog(d);
    
    return 35./162. * d + 1./72. * d2 - 89./1944. * d3 + 341./7776. * d4 
            + 13./81. * log(1. - d) - Li2/18. 
            - (rho(E0)/18. + omega(E0)/162.) * log(t*d);
}

void Bsgamma::updateParameters

(

)

The update parameter method for bsgamma.

Definition at line 1229 of file Flavour/src/bsgamma.cpp.

{
    mu_kin=SM.getGambino_mukin();
    BRsl=SM.getGambino_BRsem()/100.;
    Mb_kin=SM.getGambino_Mbkin();
    Mc=SM.getGambino_Mcatmuc();
    mu_pi2=SM.getGambino_mupi2();
    rho_D3=SM.getGambino_rhoD3();
    mu_G2=SM.getGambino_muG2();
    rho_LS3=SM.getGambino_rhoLS3();
    C=C_sem();
    
    ale=SM.getAle();
    E0=SM.getbsgamma_E0();
    mu_b=SM.getMub();
    mu_c=SM.getMuc();
    alsUps=8./M_PI * mu_kin/Mb_kin * ( 1. + 3./8. * mu_kin/Mb_kin );
    Alstilde = SM.Alstilde5(mu_b);
    Ms=SM.getQuarks(QCD::STRANGE).getMass();
    lambda_t=SM.computelamt_s();
    V_cb=SM.getCKM().getVcb();
    CKMu=SM.computelamu_s().conjugate() / SM.computelamt_s().conjugate();
    
    BLNPcorr=SM.getBLNPcorr();
    
    checkCache();
    
    if (Intb_updated == 0) {
        Intb1Cached = 0;
        Intb2Cached = 0;
        Intb3Cached = 0;
        Intb4Cached = 0;
        Intbb1Cached = 0;
        Intbb2Cached = 0;
        Intbb4Cached = 0;
    }
    if (Intbc_updated == 0) {
        Intbc1Cached = 0;
        Intbc2Cached = 0;
        Intc1Cached = 0;
        Intc1imCached = 0;
        Intc2Cached = 0;
        Intc3Cached = 0;
        IntccCached = 0;
        Intcc1Cached = 0;
        Intcc1p1Cached = 0;
    }
    
    computeCoeff(mu_b);
    
    overall = BRsl * (lambda_t/V_cb).abs2() * 6. * ale / (M_PI * C);
}

double Bsgamma::Vub_NLO	(	double	E0,
		bool	CPodd
	)

The total NLO Vub part of the \(BR\), \(Vub^{NLO}\).

Parameters

[in]	E0	energy cutoff
[in]	CPodd	switch to allow for CPodd terms

Returns

\(Vub^{NLO}\)

Definition at line 1140 of file Flavour/src/bsgamma.cpp.

{
    return Vub_NLO_2body(CPodd) + Vub_NLO_3body(E0,CPodd) + Vub_NLO_4body(E0,CPodd);
}

double Bsgamma::Vub_NLO_2body

(

bool

CPodd

)

The 2 body NLO Vub part of the \(BR\) as defined in [81] , \(Vub^{NLO}_{2b}\).

Parameters

[in]

CPodd

switch to allow for CPodd terms

Returns

\(Vub^{NLO}_{2b}\)

Definition at line 1092 of file Flavour/src/bsgamma.cpp.

{
    double z = zeta();
    
    return 4. * Alstilde * (C7_0 * ( C2_0 - C1_0/6. )).real() *
            (CKMu.real()*( a(z) + b(z) ).real() - CPodd * CKMu.imag()*( a(z) + b(z) ).imag());
}

double Bsgamma::Vub_NLO_3body	(	double	E0,
		bool	CPodd
	)

The 3 body NLO Vub part of the \(BR\), \(Vub^{NLO}_{3b}\).

Parameters

[in]	E0	energy cutoff
[in]	CPodd	switch to allow for CPodd terms

Returns

\(Vub^{NLO}_{3b}\)

Definition at line 1100 of file Flavour/src/bsgamma.cpp.

{
    double d = delta(E0);
    
    return 64./27. * Alstilde * ( C2_0 - C1_0/6. ).abs2() *
            ( CKMu.real() * ( 2. * Int_cc1(E0) - Int_c1(E0) )
            + CKMu.abs2() *  ( Int_cc1(E0) - Int_c1(E0) + 1./8. * d * ( 1. - 1./3. * d*d ) )
            - CPodd * CKMu.imag() * Int_c1_im(E0) )
            + 4. * Alstilde * (( C7_0 - C8_0/3. ) * ( C2_0 - C1_0/6. )).real() *
            ( CKMu.real() * ( Phi27_1(E0,zeta()) + 2./9. * d * ( 1. - d + 1./3. * d*d ) )
            - CPodd * CKMu.imag() * Phi27_1_im(E0,zeta()) );
}

double Bsgamma::Vub_NLO_4body	(	double	E0,
		bool	CPodd
	)

The 4 body NLO Vub part of the \(BR\) obtained from [92] , \(Vub^{NLO}_{4b}\).

Parameters

[in]	E0	energy cutoff
[in]	CPodd	switch to allow for CPodd terms

Returns

\(Vub^{NLO}_{4b}\)

Definition at line 1113 of file Flavour/src/bsgamma.cpp.

{
    if (FOUR_BODY) {
        double d = delta(E0);
        double d2 = d*d;
        double d3 = d2*d;
        double Ld = log(d);
        double Lumd = log(1. - d);
        double Lq = log(Ms/Mb_kin);

        double uphib427 = ( 2. * d * (-63. + 30. * d + 35. * d2 - 2. * d3 
                    + 3. * d * (-18. - 7. * d + d2) * Ld) ) / ( 243. * (d - 1.) );
        double uphib428 = ( 108. * (d - 1.) * (d - 1.) * Lumd*Lumd 
                    - 12. * Lumd * (- 25. - 18. * Lq - 18. * d * (5. + 4. * Lq) 
                    + 9. * d2 * (5. + 4. * Lq) + (9. + 36. * d - 18. * d2) * Ld) 
                    + d * (24. * (17. + 9. * Lq) + 27. * d * (43. + 26. * Lq) 
                    - d2 * (127. + 72. * Lq) + 9. * (-12. - 39. * d + 4. * d2) * Ld) 
                    + 108. * (-1. - 4. * d + 2. * d2) * gsl_sf_dilog(d) ) / 729.;

        return 4. * Alstilde * ( ( C2_0 - C1_0/6. ).abs2() * 
                ( CKMu.real() * 0.005025213076791178 + CPodd * CKMu.imag() * 0.013978889449487913)
                + ( C2_0 - C1_0/6. ).real() * CKMu.real() * (C7_0.real() * uphib427 + C8_0.real() * uphib428) );
    }
    
    else return 0.;
}

double Bsgamma::zeta

(

)

The squared ratio between \(m_c\) and \(m_b^{\rm kin}\), \( z \).

Returns

\( z \)

Definition at line 148 of file Flavour/src/bsgamma.cpp.

{
    return Mc*Mc/Mb_kin/Mb_kin;
}

Member Data Documentation

double Bsgamma::ale

private

alpha electromagnetic

Definition at line 1147 of file Flavour/src/bsgamma.h.

gslpp::vector<gslpp::complex>** Bsgamma::allcoeff

private

vector that contains the Wilson coeffients

Definition at line 1174 of file Flavour/src/bsgamma.h.

gslpp::vector<gslpp::complex>** Bsgamma::allcoeffprime

private

vector that contains the primed Wilson coeffients

Definition at line 1175 of file Flavour/src/bsgamma.h.

double Bsgamma::Alstilde

private

alpha strong divided by 4 pi

Definition at line 1149 of file Flavour/src/bsgamma.h.

double Bsgamma::alsUps

private

alpha strong Upsilon

Definition at line 1148 of file Flavour/src/bsgamma.h.

double Bsgamma::avaINT

private

Gsl integral variable

Definition at line 1202 of file Flavour/src/bsgamma.h.

double Bsgamma::BLNPcorr

private

non perturbative correction from [41]

Definition at line 1167 of file Flavour/src/bsgamma.h.

double Bsgamma::BR

private

BR of the decay

Definition at line 1171 of file Flavour/src/bsgamma.h.

double Bsgamma::BR_CPodd

private

BR of the decay

Definition at line 1172 of file Flavour/src/bsgamma.h.

double Bsgamma::BRsl

private

BR of the semileptonic decay \(B \to X_c e \nu\)

Definition at line 1157 of file Flavour/src/bsgamma.h.

double Bsgamma::C

private

The semileptonic phase space ratio

Definition at line 1158 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C1_0

private

LO term of the Wilson coeffients \(C_1\)

Definition at line 1177 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C1_1

private

NLO term of the Wilson coeffients \(C_1\)

Definition at line 1186 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C2_0

private

LO term of the Wilson coeffients \(C_2\)

Definition at line 1178 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C2_1

private

NLO term of the Wilson coeffients \(C_2\)

Definition at line 1187 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C3_0

private

LO term of the Wilson coeffients \(C_3\)

Definition at line 1179 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C3_1

private

NLO term of the Wilson coeffients \(C_3\)

Definition at line 1188 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C4_0

private

LO term of the Wilson coeffients \(C_4\)

Definition at line 1180 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C4_1

private

NLO term of the Wilson coeffients \(C_4\)

Definition at line 1189 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C5_0

private

LO term of the Wilson coeffients \(C_5\)

Definition at line 1181 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C5_1

private

NLO term of the Wilson coeffients \(C_5\)

Definition at line 1190 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C6_0

private

LO term of the Wilson coeffients \(C_6\)

Definition at line 1182 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C6_1

private

NLO term of the Wilson coeffients \(C_6\)

Definition at line 1191 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C7_0

private

LO term of the Wilson coeffients \(C_7\)

Definition at line 1183 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C7_1

private

NLO term of the Wilson coeffients \(C_7\)

Definition at line 1192 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C7_2

private

NNLO term of the Wilson coeffients \(C_7\)

Definition at line 1195 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C7p_0

private

LO term of the Wilson coeffients \(C'_7\)

Definition at line 1197 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C7p_1

private

NLO term of the Wilson coeffients \(C_7\)

Definition at line 1198 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C8_0

private

LO term of the Wilson coeffients \(C_8\)

Definition at line 1184 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::C8_1

private

NLO term of the Wilson coeffients \(C_8\)

Definition at line 1193 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntb1

private

Cache variable

Definition at line 1223 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntb2

private

Cache variable

Definition at line 1224 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntb3

private

Cache variable

Definition at line 1225 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntb4

private

Cache variable

Definition at line 1226 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntbb1

private

Cache variable

Definition at line 1227 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntbb2

private

Cache variable

Definition at line 1228 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntbb4

private

Cache variable

Definition at line 1229 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntbc1

private

Cache variable

Definition at line 1230 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntbc2

private

Cache variable

Definition at line 1231 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntc1

private

Cache variable

Definition at line 1232 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntc1im

private

Cache variable

Definition at line 1233 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntc2

private

Cache variable

Definition at line 1234 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntc3

private

Cache variable

Definition at line 1235 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntcc

private

Cache variable

Definition at line 1236 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntcc1

private

Cache variable

Definition at line 1237 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntcc1p1

private

Cache variable

Definition at line 1238 of file Flavour/src/bsgamma.h.

double Bsgamma::CacheIntPhi772r

private

Cache variable

Definition at line 1239 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::CKMu

private

Vckm factor

Definition at line 1160 of file Flavour/src/bsgamma.h.

double Bsgamma::E0

private

energy cutoff

Definition at line 1150 of file Flavour/src/bsgamma.h.

double Bsgamma::errINT

private

Gsl integral variable

Definition at line 1203 of file Flavour/src/bsgamma.h.

gsl_function Bsgamma::INT

private

Gsl integral variable

Definition at line 1200 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intb1Cached

private

Cache variable

Definition at line 1205 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intb2Cached

private

Cache variable

Definition at line 1206 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intb3Cached

private

Cache variable

Definition at line 1207 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intb4Cached

private

Cache variable

Definition at line 1208 of file Flavour/src/bsgamma.h.

double Bsgamma::Intb_cache

private

Cache variable

Definition at line 1244 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intb_updated

private

Cache variable

Definition at line 1241 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbb1Cached

private

Cache variable

Definition at line 1209 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbb2Cached

private

Cache variable

Definition at line 1210 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbb4Cached

private

Cache variable

Definition at line 1211 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbc1Cached

private

Cache variable

Definition at line 1212 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbc2Cached

private

Cache variable

Definition at line 1213 of file Flavour/src/bsgamma.h.

gslpp::vector<double> Bsgamma::Intbc_cache

private

Cache variable

Definition at line 1245 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intbc_updated

private

Cache variable

Definition at line 1242 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intc1Cached

private

Cache variable

Definition at line 1214 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intc1imCached

private

Cache variable

Definition at line 1215 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intc2Cached

private

Cache variable

Definition at line 1216 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intc3Cached

private

Cache variable

Definition at line 1217 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intcc1Cached

private

Cache variable

Definition at line 1219 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::Intcc1p1Cached

private

Cache variable

Definition at line 1220 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::IntccCached

private

Cache variable

Definition at line 1218 of file Flavour/src/bsgamma.h.

unsigned int Bsgamma::IntPhi772rCached

private

Cache variable

Definition at line 1221 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::lambda_t

private

Vckm factor

Definition at line 1159 of file Flavour/src/bsgamma.h.

double Bsgamma::Mb_kin

private

b quark mass in the kinetic scheme

Definition at line 1154 of file Flavour/src/bsgamma.h.

double Bsgamma::Mc

private

c quark mass scale

Definition at line 1155 of file Flavour/src/bsgamma.h.

double Bsgamma::Ms

private

s quark mass scale

Definition at line 1156 of file Flavour/src/bsgamma.h.

double Bsgamma::mu_b

private

b quark mass scale

Definition at line 1151 of file Flavour/src/bsgamma.h.

double Bsgamma::mu_c

private

c quark mass scale

Definition at line 1152 of file Flavour/src/bsgamma.h.

double Bsgamma::mu_G2

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1164 of file Flavour/src/bsgamma.h.

double Bsgamma::mu_kin

private

kinetic mass scale

Definition at line 1153 of file Flavour/src/bsgamma.h.

double Bsgamma::mu_pi2

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1163 of file Flavour/src/bsgamma.h.

int Bsgamma::obs

private

observable type

Definition at line 1169 of file Flavour/src/bsgamma.h.

double Bsgamma::overall

private

overall BR factor

Definition at line 1162 of file Flavour/src/bsgamma.h.

double Bsgamma::rho_D3

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1165 of file Flavour/src/bsgamma.h.

double Bsgamma::rho_LS3

private

B meson expectation value of one of the relevant dim. 5 and 6 local operators

Definition at line 1166 of file Flavour/src/bsgamma.h.

gslpp::complex Bsgamma::V_cb

private

Vckm factor

Definition at line 1161 of file Flavour/src/bsgamma.h.

gsl_integration_cquad_workspace* Bsgamma::w_INT

private

Gsl integral variable

Definition at line 1201 of file Flavour/src/bsgamma.h.

---

The documentation for this class was generated from the following files:

• Flavour/src/bsgamma.h
• Flavour/src/bsgamma.cpp