A class for the \(M \to P l^+ l^-\) decay. More...

#include <MPll.h>

Detailed Description

A class for the \(M \to P l^+ l^-\) decay.

Author: HEPfit Collaboration

Copyright: GNU General Public License

This class is used to compute all the functions needed in order to build the observables relative to the \(M \to P l^+ l^-\) decays, where \(M\) is a generic meson and \(P\) is a pseudoscalar meson.

MPll parameters

The mandatory parameters of MPll are summarized below:

Label	LaTeX symbol	Description
r_1_fplus, r_2_fplus, m_fit2_fplus	\(r_1^{f_+}, r_2^{f_+}, m_{fit}^{2,f_+}\)	The fit parameters for the LCSR form factor \(f_+\) of the \(B\to K\).
r_1_fT, r_2_fT, m_fit2_fT	\(r_1^{f_T}, r_2^{f_T}, m_{fit}^{2,f_T}\)	The fit parameters for the LCSR form factor \(f_T\) of the \(B\to K\).
r_2_f0, m_fit2_f0	\(r_2^{f_0}, m_{fit}^{2,f_0}\)	The fit parameters for the LCSR form factor \(f_0\) of the \(B\to K\).
absh_0_MP, absh_0_1_MP	\(\mathrm{Abs}h_0^{(0)}, \mathrm{Abs}h_0^{(1)}\)	The constant and linear terms of the absolute value of the hadronic parameter \(h_0\) of the \(B\to K\).
argh_0_MP, argh_0_1_MP	\(\mathrm{Arg}h_0^{(0)}, \mathrm{Arg}h_0^{(1)}\)	The constant and linear terms of the argument of the hadronic parameter \(h_0\) of the \(B\to K\).

This kind of decays can be described by means of the \(\Delta B = 1 \) weak effective Hamiltonian

\[ \mathcal{H}_\mathrm{eff}^{\Delta B = 1} = \mathcal{H}_\mathrm{eff}^\mathrm{had} + \mathcal{H}_\mathrm{eff}^\mathrm{sl+\gamma}, \]

where the first term is the hadronic contribution

\[ \mathcal{H}_\mathrm{eff}^\mathrm{had} = \frac{4G_F}{\sqrt{2}}\Bigg[\sum_{p=u,c}\lambda_p\bigg(C_1 Q^{p}_1 + C_2 Q^{p}_2\bigg) -\lambda_t \bigg(\sum_{i=3}^{6} C_i P_i + C_{8}Q_{8g} \bigg)\Bigg] \,, \]

involving current-current, chromodynamic penguin and chromomagnetic dipole operators, while the second one, given by

\[ \mathcal{H}_\mathrm{eff}^\mathrm{sl+\gamma} = - \frac{4G_F}{\sqrt{2}}\lambda_t \bigg( C_7Q_{7\gamma} + C_9Q_{9V} + C_{10}Q_{10A} \bigg) \,, \]

includes the electromagnetic penguin plus the semileptonic operators.

Considering the matrix element of \(\mathcal{H}_\mathrm{eff}^{\Delta B = 1}\) between the initial state \(M\) and the final state \(P l^+ l^-\), only the contribution of \(\mathcal{H}_\mathrm{eff}^\mathrm{sl+\gamma}\) clearly factorizes into the product of hadronic form factors and leptonic tensors at all orders in strong interactions. Following [144], we implemented the amplitude in the helicity basis; hence we made use of the helicity form factors \( \tilde{V}_0(q^2), \tilde{T}_0(q^2)\) and \(\tilde{S}(q^2) \), which are related to the ones in the transverse basis through the following relations :

\[ \tilde{V}_0(q^2) = i \frac{\sqrt{\lambda(q^2)}}{2m_M\sqrt{q^2}}f_+(q^2)\,,\\ \tilde{T}_0(q^2) = i \frac{\sqrt{\lambda(q^2)q^2}}{2m_M^2(m_M+m_P)}f_T(q^2)\,,\\ \tilde{S}(q^2) = -\frac{m_M^2-m_P^2}{2m_M(m_b+m_s)}\frac{1+m_s/m_b}{1-m_s/m_b}f_0(q^2)\,, \]

where \(\lambda(q^2) = 4m_M^2|\vec{k}|^2\), with \(\vec{k}\) as the 3-momentum of the meson \(P\) in the \(M\) rest frame.

The effect of the operators of \(\mathcal{H}_\mathrm{eff}^\mathrm{had}\) due to exchange of soft gluon can be reabsorbed in the following parameterization,

\[ h_0(q^2) = \frac{\epsilon^*_\mu(\lambda)}{m_M^2} \int d^4x e^{iqx} \langle \bar P \vert T\{j^{\mu}_\mathrm{em} (x) \mathcal{H}_\mathrm{eff}^\mathrm{had} (0)\} \vert \bar M \rangle = h_0^{(0)} + \frac{q^2}{1\,\mathrm{GeV}^2} h_0^{(1)}\,. \]

The amplitude can be therefore parametrized in terms of the following helicity amplitudes:

\[ H_V = -i\, N \Big\{C_{9} \tilde{V}_{L,0} +C_{9}' \tilde{V}_{R,0} + \frac{m_M^2}{q^2} \Big[\frac{2\, m_b}{m_M} (C_{7} \tilde{T}_{L,0} + C_{7}' \tilde{T}_{R,0}) - 16 \pi^2 h_0 \Big] \Big\} \,, \\ H_A = -i\, N (C_{10} \tilde{V}_{L,0} + C_{10}'\tilde{V}_{R,0}) \,, \\ H_S = i\, N \frac{ m_b}{m_W} (C_S \tilde{S}_L + C_S' \tilde{S}_R)\,, \\ H_P = i\, N \Big\{ \frac{ m_b}{m_W} (C_P \tilde{S}_L + C_P' \tilde{S}_R) + \frac{2\,m_\ell m_b}{q^2} \left[C_{10} \Big(\tilde{S}_L - \frac{m_s}{m_b} \tilde{S}_R \Big) + C_{10}' \Big(\tilde{S}_R - \frac{m_s}{m_b} \tilde{S}_L\Big) \right] \Big\} \,, \]

where \( N = - \frac{4 G_F m_M}{\sqrt{2}}\frac{e^2}{16\pi^2}\lambda_t\) and we have defined

\[ \tilde{V}_{L,0}(q^2) = -\tilde{V}_{R,0}(q^2)=\tilde{V}_0(q^2)\,,\\ \tilde{T}_{L,0}(q^2) = -\tilde{T}_{R,0}(q^2)=\tilde{V}_0(q^2)\,,\\ \tilde{S}_L(q^2) = -\tilde{S}_R(q^2)=\tilde{S}(q^2)\,. \]

Squaring the amplitude and summing over the spins it is possible to obtain the fully differential decay rate, which is

\[ \frac{d^{(4)} \Gamma}{dq^2\,d(\cos\theta_l)} = \frac{9}{32\,\pi} \Big( I^c_1 +I^c_2\cos2\theta_l + I_6^c \cos\theta_l \Big) \]

The angular coefficients involved in the differential decay rate are related to the helicity amplitudes according to the following relations:

\[ I_1^c = F \left\{ \frac{1}{2}\left(|H_V^0|^2+|H_A^0|^2\right)+ |H_P|^2+\frac{2m_\ell^2}{q^2}\left(|H_V^0|^2-|H_A^0|^2\right) + \beta^2 |H_S|^2 \right\}\,,\\ I_2^c = -F\, \frac{\beta^2}{2}\left(|H_V^0|^2+|H_A^0|^2\right)\,,\\ I_6^c = 2 F \frac{\beta\, m_\ell}{\sqrt{q^2}} {\rm Re} \left[ H_S^* H_V^0 \right]\,,\\ \]

where

\[ F=\frac{ \lambda^{1/2}\beta\, q^2}{3 \times 2^{5} \,\pi^3\, m_M^3}\,, \qquad \beta = \sqrt{1 - \frac{4 m_\ell^2}{q^2} }\,. \]

The final observables are hence build employing CP-averages \(\Sigma_i\) or CP-asymmetries \(\Delta_i\) of such angular coefficients; however, since on the experimental side the observables are averaged over \( q^2 \) bins, an integration of the coeffiecients over such bins has to be performed before they are combined in order to build the observables.

The class is organized as follows: after the parameters are updated in updateParameters() and the cache is checked in checkCache(), the form factor are build in the transverse basis in the functions f_plus(), f_0() and f_T() [31]. They are consequentely translated in the helicity basis through the functions V_L(), V_R(), T_L(), T_R(), S_L() and S_R(). Form factors and parameters are combined together in the functions H_V(), H_A(), H_S() and H_P() in order to build the helicity amplitudes, which are consequentely combined to create the angular coefficients in the function I(). Those coefficients are used to create the CP averaged coefficients in the function Sigma() ad the CP asymmetric coefficients in the function Delta(). Form factors, CP averaged and asymmetric coefficients and hadronic contributions are integrated in the functions integrateSigma() and integrateDelta() in order to be further used to build the observables.

Definition at line 172 of file MPll.h.

Public Member Functions
gslpp::complex	DeltaC9_KD (double q2)

gslpp::complex	funct_g (double q2)

double	getSigma (int i, double q_2)
	The value of \( \Sigma_{i} \) from \(q_{min}\) to \(q_{max}\). More...

double	getwidth ()
	The width of the meson M. More...

gslpp::complex	H_A (double q2)
	The helicity amplitude \( H_A^{\lambda} \) . More...

gslpp::complex	h_lambda (double q2)
	The non-pertubative ccbar contributions to the helicity amplitudes. More...

gslpp::complex	H_P (double q2)
	The helicity amplitude \( H_P^{\lambda} \) . More...

gslpp::complex	H_S (double q2)
	The helicity amplitude \( H_S^{\lambda} \) . More...

gslpp::complex	H_V (double q2)
	The helicity amplitude \( H_V^{\lambda} \) . More...

std::vector< std::string >	initializeMPllParameters ()
	A method for initializing the parameters necessary for MPll. More...

double	integrateDelta (int i, double q_min, double q_max)
	The integral of \( \Delta_{i} \) from \(q_{min}\) to \(q_{max}\). More...

double	integrateSigma (int i, double q_min, double q_max)
	The integral of \( \Sigma_{i} \) from \(q_{min}\) to \(q_{max}\). More...

	MPll (const StandardModel &SM_i, QCD::meson meson_i, QCD::meson pseudoscalar_i, QCD::lepton lep_i)
	Constructor. More...

virtual	~MPll ()
	Destructor. More...

Private Attributes
double	ale

bool	dispersion

bool	FixedWCbtos

double	GF

QCD::lepton	lep

double	Mb

double	mb_pole

double	Mc

double	mc_pole

QCD::meson	meson

double	mJ2

double	Mlep

double	MM

double	MP

std::vector< std::string >	mpllParameters

double	Ms

double	mu_b

double	mu_h

std::unique_ptr< F_1 >	myF_1

std::unique_ptr< F_2 >	myF_2

const StandardModel &	mySM

QCD::meson	pseudoscalar

double	spectator_charge

double	width

Constructor & Destructor Documentation

◆ MPll()

MPll::MPll	(	const StandardModel &	SM_i,
		QCD::meson	meson_i,
		QCD::meson	pseudoscalar_i,
		QCD::lepton	lep_i
	)

Constructor.

Parameters

[in]	SM_i	a reference to an object of type StandardModel
[in]	meson_i	initial meson of the decay
[in]	pseudoscalar_i	final pseudoscalar meson of the decay
[in]	lep_i	final leptons of the decay

Definition at line 19 of file MPll.cpp.

 : mySM(SM_i), myF_1(new F_1()), myF_2(new F_2()),
 #if LATTICE        
 fplus_lat_cache(3, 0.),
 fT_lat_cache(3, 0.),
 f0_lat_cache(3, 0.),
 #else        
 fplus_cache(2, 0.),
 fT_cache(2, 0.),
 f0_cache(2, 0.),
 #endif        
 k2_cache(2, 0.),
 SL_cache(2, 0.),
 N_cache(3, 0.),
 Ycache(2, 0.),
 H_V0cache(2, 0.),
 H_Scache(2, 0.),
 H_P_cache(4, 0.),
 T_cache(5, 0.)
 {
     lep = lep_i;
     meson = meson_i;
     pseudoscalar = pseudoscalar_i;
     dispersion = true;
     FixedWCbtos = false;
     mJ2 = 3.096 * 3.096;
  
     I0_updated = 0;
     I2_updated = 0;
     I8_updated = 0;
  
     VL_updated = 0;
     TL_updated = 0;
     SL_updated = 0;
  
     deltaTparpupdated = 0;
     deltaTparmupdated = 0;
  
     w_sigma = gsl_integration_cquad_workspace_alloc(100);
     w_delta = gsl_integration_cquad_workspace_alloc(100);
     w_DTPPR = gsl_integration_cquad_workspace_alloc(100);
  
     acc_Re_deltaC7_QCDF = gsl_interp_accel_alloc();
     acc_Im_deltaC7_QCDF = gsl_interp_accel_alloc();
     acc_Re_deltaC9_QCDF = gsl_interp_accel_alloc();
     acc_Im_deltaC9_QCDF = gsl_interp_accel_alloc();
  
     spline_Re_deltaC7_QCDF = gsl_spline_alloc(gsl_interp_cspline, GSL_INTERP_DIM_DC);
     spline_Im_deltaC7_QCDF = gsl_spline_alloc(gsl_interp_cspline, GSL_INTERP_DIM_DC);
     spline_Re_deltaC9_QCDF = gsl_spline_alloc(gsl_interp_cspline, GSL_INTERP_DIM_DC);
     spline_Im_deltaC9_QCDF = gsl_spline_alloc(gsl_interp_cspline, GSL_INTERP_DIM_DC);
 }

◆ ~MPll()

MPll::~MPll ( )

virtual

Destructor.

Definition at line 72 of file MPll.cpp.

73 {

74 }

Member Function Documentation

◆ DeltaC9_KD()

gslpp::complex MPll::DeltaC9_KD ( double q2 )

Definition at line 1090 of file MPll.cpp.

1094 {

◆ funct_g()

gslpp::complex MPll::funct_g ( double q2 )

Definition at line 1082 of file MPll.cpp.

 {
     if (q2 < 4. * Mc * Mc)
         return -8. / 9. * log(Mc / Mb) + 8. / 27. + 16. / 9. * Mc * Mc / q2 - 4. / 9. * (2. + 4. * Mc * Mc / q2) * (sqrt(4. * Mc * Mc / q2 - 1.) * atan(1. / sqrt(4. * Mc * Mc / q2 - 1.)));

◆ getSigma()

double MPll::getSigma	(	int	i,
		double	q_2
	)

The value of \( \Sigma_{i} \) from \(q_{min}\) to \(q_{max}\).

Parameters

[in]	i	index of the angular coefficient \( I_{i} \)
[in]

Definition at line 1211 of file MPll.cpp.

 {
     updateParameters();
  
     switch (i) {
         case 0:
             return getSigma1c(q_2);
             break;
         case 2:
             return getSigma2c(q_2);
             break;
         case 8:
             return getSigma6c(q_2);
             break;
         default:
             std::stringstream out;

◆ getwidth()

double MPll::getwidth ( )

inline

The width of the meson M.

Returns: \( \Gamma_M \)

Definition at line 262 of file MPll.h.

                      {
         updateParameters();
         return width;
     }

◆ H_A()

gslpp::complex MPll::H_A ( double q2 )

The helicity amplitude \( H_A^{\lambda} \) .

Parameters

[in] q2 \(q^2\) of the decay

Returns: \( H_A^{\lambda} \)

Definition at line 1110 of file MPll.cpp.

1114 {

◆ h_lambda()

gslpp::complex MPll::h_lambda ( double q2 )

The non-pertubative ccbar contributions to the helicity amplitudes.

Parameters

hel	helicity
q2	\(q^2\)

Returns: \(h_{hel}(q^2)\)

Definition at line 1096 of file MPll.cpp.

 {
     if (!dispersion) {
         return (twoMboMM * h_0 * T_L(q2) + h_1 * q2 / MM2 * V_L(q2)) / sixteenM_PI2 + h_2 * q2 * q2;
     } else {

◆ H_P()

gslpp::complex MPll::H_P ( double q2 )

The helicity amplitude \( H_P^{\lambda} \) .

Parameters

[in] q2 \(q^2\) of the decay

Returns: \( H_P^{\lambda} \)

Definition at line 1120 of file MPll.cpp.

1124 {

◆ H_S()

gslpp::complex MPll::H_S ( double q2 )

The helicity amplitude \( H_S^{\lambda} \) .

Parameters

[in] q2 \(q^2\) of the decay

Returns: \( H_S^{\lambda} \)

Definition at line 1115 of file MPll.cpp.

1119 {

◆ H_V()

gslpp::complex MPll::H_V ( double q2 )

The helicity amplitude \( H_V^{\lambda} \) .

Parameters

[in] q2 \(q^2\) of the decay

Returns: \( H_V^{\lambda} \)

Definition at line 1105 of file MPll.cpp.

1109 {

◆ initializeMPllParameters()

std::vector< std::string > MPll::initializeMPllParameters ( )

A method for initializing the parameters necessary for MPll.

Returns: the vector of MPll specific parameters

Definition at line 76 of file MPll.cpp.

 {
     dispersion = mySM.getFlavour().getFlagUseDispersionRelation();
     FixedWCbtos = mySM.getFlavour().getFlagFixedWCbtos();
  
 #if NFPOLARBASIS_MPLL
     if (pseudoscalar == StandardModel::K_P || pseudoscalar == StandardModel::K_0) mpllParameters = make_vector<std::string>()
 #if LATTICE
         << "b_0_fplus" << "b_1_fplus" << "b_2_fplus" << "m_fit_fplus_lat"
         << "b_0_fT" << "b_1_fT" << "b_2_fT" << "m_fit_fT_lat"
         << "b_0_f0" << "b_1_f0" << "b_2_f0" << "m_fit_f0_lat"
 #else
         << "r_1_fplus" << "r_2_fplus" << "m_fit2_fplus" << "r_1_fT" << "r_2_fT" << "m_fit2_fT" << "r_2_f0" << "m_fit2_f0"
 #endif            
         << "absh_0_MP" << "argh_0_MP" << "absh_1_MP" << "argh_1_MP" << "absh_2_MP" << "argh_2_MP";
 #else
     if (pseudoscalar == StandardModel::K_P || pseudoscalar == StandardModel::K_0) mpllParameters = make_vector<std::string>()
 #if LATTICE            
         << "b_0_fplus" << "b_1_fplus" << "b_2_fplus" << "m_fit_fplus_lat"
         << "b_0_fT" << "b_1_fT" << "b_2_fT" << "m_fit_fT_lat"
         << "b_0_f0" << "b_1_f0" << "b_2_f0" << "m_fit_f0_lat"
 #else            
         << "r_1_fplus" << "r_2_fplus" << "m_fit2_fplus" << "r_1_fT" << "r_2_fT" << "m_fit2_fT" << "r_2_f0" << "m_fit2_f0"
 #endif            
         << "reh_0_MP" << "imh_0_MP" << "reh_1_MP" << "imh_1_MP" << "reh_2_MP" << "imh_2_MP";
 #endif
     else {
         std::stringstream out;
         out << pseudoscalar;
         throw std::runtime_error("MPll: pseudoscalar " + out.str() + " not implemented");
     }
  
     if (dispersion) {
         mpllParameters.clear();
         if (pseudoscalar == StandardModel::K_P || pseudoscalar == StandardModel::K_0) mpllParameters = make_vector<std::string>()
 #if LATTICE
             << "b_0_fplus" << "b_1_fplus" << "b_2_fplus" << "m_fit_fplus_lat"
             << "b_0_fT" << "b_1_fT" << "b_2_fT" << "m_fit_fT_lat"
             << "b_0_f0" << "b_1_f0" << "b_2_f0" << "m_fit_f0_lat"
 #else                
             << "r_1_fplus" << "r_2_fplus" << "m_fit2_fplus" << "r_1_fT" << "r_2_fT" << "m_fit2_fT" << "r_2_f0" << "m_fit2_f0"
 #endif                
             << "r1_BK" << "r2_BK" << "deltaC9_BK" << "phDC9_BK";
     }
  
     if (FixedWCbtos) mpllParameters.insert(mpllParameters.end(), { "C7_SM", "C9_SM", "C10_SM" });
     mySM.initializeMeson(meson);
     mySM.initializeMeson(pseudoscalar);
     return mpllParameters;
 }

◆ integrateDelta()

double MPll::integrateDelta	(	int	i,
		double	q_min,
		double	q_max
	)

The integral of \( \Delta_{i} \) from \(q_{min}\) to \(q_{max}\).

Parameters

[in]	i	index of the angular coefficient \( I_{i} \)
[in]	q_min	minimum q^2 of the integral
[in]	q_max	maximum q^2 of the integral

Returns: \( <\Delta_{i}> \)

Definition at line 1232 of file MPll.cpp.

                                                 : index " + out.str() + " not implemented");
     }
 }
  
 double MPll::integrateDelta(int i, double q_min, double q_max)
 {
     updateParameters();
  
     std::pair<double, double > qbin = std::make_pair(q_min, q_max);
  
     old_handler = gsl_set_error_handler_off();
  
     switch (i) {
         case 0:
             if (delta0Cached[qbin] == 0) {
                 FD = convertToGslFunction(boost::bind(&MPll::getDelta1c, &(*this), _1));
                 if (gsl_integration_cquad(&FD, q_min, q_max, 1.e-2, 1.e-1, w_delta, &avaDelta, &errDelta, NULL) != 0) return std::numeric_limits<double>::quiet_NaN();
                 cacheDelta0[qbin] = NN*avaDelta;
                 delta0Cached[qbin] = 1;
             }
             return cacheDelta0[qbin];
             break;
         case 2:
             if (delta2Cached[qbin] == 0) {
                 FD = convertToGslFunction(boost::bind(&MPll::getDelta2c, &(*this), _1));
                 if (gsl_integration_cquad(&FD, q_min, q_max, 1.e-2, 1.e-1, w_delta, &avaDelta, &errDelta, NULL) != 0) return std::numeric_limits<double>::quiet_NaN();
                 cacheDelta2[qbin] = NN*avaDelta;
                 delta2Cached[qbin] = 1;
             }
             return cacheDelta2[qbin];
             break;
         default:
             std::stringstream out;
             out << i;
             throw std::runtime_error("MPll::integrateDelta: index " + out.str() + " not implemented");
     }

◆ integrateSigma()

double MPll::integrateSigma	(	int	i,
		double	q_min,
		double	q_max
	)

The integral of \( \Sigma_{i} \) from \(q_{min}\) to \(q_{max}\).

Parameters

[in]	i	index of the angular coefficient \( I_{i} \)
[in]	q_min	minimum q^2 of the integral
[in]	q_max	maximum q^2 of the integral

Returns: \( <\Sigma_{i}> \)

Definition at line 1174 of file MPll.cpp.

 {
     updateParameters();
  
     std::pair<double, double > qbin = std::make_pair(q_min, q_max);
  
     old_handler = gsl_set_error_handler_off();
  
     switch (i) {
         case 0:
             if (sigma0Cached[qbin] == 0) {
                 FS = convertToGslFunction(boost::bind(&MPll::getSigma1c, &(*this), _1));
                 if (gsl_integration_cquad(&FS, q_min, q_max, 1.e-2, 1.e-1, w_sigma, &avaSigma, &errSigma, NULL) != 0) return std::numeric_limits<double>::quiet_NaN();
                 cacheSigma0[qbin] = NN*avaSigma;
                 sigma0Cached[qbin] = 1;
             }
             return cacheSigma0[qbin];
             break;
         case 2:
             if (sigma2Cached[qbin] == 0) {
                 FS = convertToGslFunction(boost::bind(&MPll::getSigma2c, &(*this), _1));
                 if (gsl_integration_cquad(&FS, q_min, q_max, 1.e-2, 1.e-1, w_sigma, &avaSigma, &errSigma, NULL) != 0) return std::numeric_limits<double>::quiet_NaN();
                 cacheSigma2[qbin] = NN*avaSigma;
                 sigma2Cached[qbin] = 1;
             }
             return cacheSigma2[qbin];
             break;
         default:
             std::stringstream out;
             out << i;
             throw std::runtime_error("MPll::integrateSigma: index " + out.str() + " not implemented");
     }

Member Data Documentation

◆ ale

double MPll::ale

private

alpha electromagnetic

Definition at line 287 of file MPll.h.

◆ dispersion

bool MPll::dispersion

private

Definition at line 282 of file MPll.h.

◆ FixedWCbtos

bool MPll::FixedWCbtos

private

Definition at line 283 of file MPll.h.

◆ GF

double MPll::GF

private

Fermi constant

Definition at line 286 of file MPll.h.

◆ lep

QCD::lepton MPll::lep

private

Final leptons type

Definition at line 276 of file MPll.h.

◆ Mb

double MPll::Mb

private

b quark mass

Definition at line 291 of file MPll.h.

◆ mb_pole

double MPll::mb_pole

private

b quark pole mass

Definition at line 295 of file MPll.h.

◆ Mc

double MPll::Mc

private

c quark mass

Definition at line 294 of file MPll.h.

◆ mc_pole

double MPll::mc_pole

private

c quark pole mass

Definition at line 296 of file MPll.h.

◆ meson

QCD::meson MPll::meson

private

Initial meson type

Definition at line 277 of file MPll.h.

◆ mJ2

double MPll::mJ2

private

Definition at line 284 of file MPll.h.

◆ Mlep

double MPll::Mlep

private

muon mass

Definition at line 288 of file MPll.h.

◆ MM

double MPll::MM

private

initial meson mass

Definition at line 289 of file MPll.h.

◆ MP

double MPll::MP

private

final pseudoscalar meson mass

Definition at line 290 of file MPll.h.

◆ mpllParameters

std::vector<std::string> MPll::mpllParameters

private

The string of mandatory MPll parameters

Definition at line 279 of file MPll.h.

◆ Ms

double MPll::Ms

private

s quark mass

Definition at line 297 of file MPll.h.

◆ mu_b

double MPll::mu_b

private

b mass scale

Definition at line 292 of file MPll.h.

◆ mu_h

double MPll::mu_h

private

\(\sqrt{\mu_b*\lambda_{QCD}}\)

Definition at line 293 of file MPll.h.

◆ myF_1

std::unique_ptr<F_1> MPll::myF_1

private

Definition at line 280 of file MPll.h.

◆ myF_2

std::unique_ptr<F_2> MPll::myF_2

private

Definition at line 281 of file MPll.h.

◆ mySM

const StandardModel& MPll::mySM

private

Model type

Definition at line 275 of file MPll.h.

◆ pseudoscalar

QCD::meson MPll::pseudoscalar

private

Final pseudoscalar meson type

Definition at line 278 of file MPll.h.

◆ spectator_charge

double MPll::spectator_charge

private

spectator quark charge

Definition at line 298 of file MPll.h.

◆ width

double MPll::width

private

initial meson width

Definition at line 299 of file MPll.h.

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

Detailed Description

MPll parameters

Public Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ MPll()

◆ ~MPll()

Member Function Documentation

◆ DeltaC9_KD()

◆ funct_g()

◆ getSigma()

◆ getwidth()

◆ H_A()

◆ h_lambda()

◆ H_P()

◆ H_S()

◆ H_V()

◆ initializeMPllParameters()

◆ integrateDelta()

◆ integrateSigma()

Member Data Documentation

◆ ale

◆ dispersion

◆ FixedWCbtos

◆ GF

◆ lep

◆ Mb

◆ mb_pole

◆ Mc

◆ mc_pole

◆ meson

◆ mJ2

◆ Mlep

◆ MM

◆ MP

◆ mpllParameters

◆ Ms

◆ mu_b

◆ mu_h

◆ myF_1

◆ myF_2

◆ mySM

◆ pseudoscalar

◆ spectator_charge

◆ width