A class for the \(M \to V \gamma\) decay. More...

#include <MVgamma.h>

Inheritance diagram for MVgamma:

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Collaboration diagram for MVgamma:

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Detailed Description

A class for the \(M \to V \gamma\) 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 \(M \to V \gamma\) decay. After the parameters are updated in updateParameters() and the form factor \( T_1 \) is computed in T_1() following [42], the QCDF corrections to the Wilson coefficient \( C_7 \) is computed in the functions G1(), G8(), H1() and H8() [43]. The helicity amplitudes \(H_V^{(+,-)},\overline{H}_V^{(+,-)}\) are build in H_V_p(), H_V_m(), H_V_p_bar() and H_V_m_bar() following [93], in order to be further used to build the observables.

Definition at line 30 of file MVgamma.h.

Public Member Functions
gslpp::complex	G1 (double s)
	Correction in eq. (42) of [43]. More...

gslpp::complex	G8 ()
	Correction in eq. (42) of [43]. More...

gslpp::complex	H1 (double s)
	Correction in eq. (42) of [43]. More...

gslpp::complex	H8 ()
	Correction in eq. (42) of [43]. More...

gslpp::complex	H_V_m ()
	The helicity amplitude \( H_V^- \). More...

gslpp::complex	H_V_m_bar ()
	The helicity amplitude \( \bar{H}_V^- \). More...

gslpp::complex	H_V_p ()
	The helicity amplitude \( H_V^+ \). More...

gslpp::complex	H_V_p_bar ()
	The helicity amplitude \( \bar{H}_V^+ \). More...

	MVgamma (const StandardModel &SM_i, StandardModel::meson meson_i, StandardModel::meson vector_i)
	Constructor. More...

double	T_1 ()
	The transverse form factor \( T_1 \). More...

void	updateParameters ()
	The update parameter method for MVgamma. More...

virtual	~MVgamma ()
	Destructor. More...

Public Member Functions inherited from ThObservable
virtual double	computeThValue ()=0
	A member to be overloaded by the respective theory observable. class that calculates the value of the observable. More...

double	getBinMax ()
	A get method to get the maximum value of the bin. More...

double	getBinMin ()
	A get method to get the minimum value of the bin. More...

const StandardModel &	getModel ()
	A get method to get the model. More...

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...

Public Attributes
double	a_0T1

double	a_1T1

double	a_2T1

double	ale

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

gslpp::vector< gslpp::complex > **	allcoeffh

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

gslpp::complex	C_2

gslpp::complex	C_2h

gslpp::complex	C_7

gslpp::complex	C_7p

gslpp::complex	C_8

gslpp::complex	C_8h

double	GF

gslpp::complex	h [2]

double	lambda

gslpp::complex	lambda_t

double	Mb

double	Mc

double	MM

double	MM2

double	MRT1_2

double	Ms

double	mu_b

double	mu_h

double	MV

double	MW

double	width

Private Attributes
StandardModel::meson	meson

StandardModel::meson	vectorM

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

MVgamma::MVgamma	(	const StandardModel &	SM_i,
		StandardModel::meson	meson_i,
		StandardModel::meson	vector_i
	)

Constructor.

Parameters

[in]	SM_i	a reference to an object of type StandardModel
[in]	meson_i	initial meson of the decay
[in]	vector_i	final vector meson of the decay

Definition at line 12 of file MVgamma.cpp.

                                                                                                    : ThObservable(SM_i)
 {
     if (SM.ModelName().compare("StandardModel") != 0 && SM.ModelName().compare("FlavourWilsonCoefficient") != 0) std::cout << "\nWARNING: B to V gamma not implemented in: " + SM.ModelName() + " model, returning Standard Model value.\n" << std::endl;
     meson = meson_i;
     vectorM = vector_i;
 }

MVgamma::~MVgamma ( )

virtual

Destructor.

Definition at line 19 of file MVgamma.cpp.

20 {

21 }

Member Function Documentation

gslpp::complex MVgamma::G1 ( double s )

Correction in eq. (42) of [43].

Parameters

s	\( m_c^2/m_b^2 \)

Returns: \( G_1(s) \)

Definition at line 85 of file MVgamma.cpp.

 {
     double logs = log(s);
     double M2 = M_PI*M_PI;
     double M3 = M_PI * M_PI*M_PI;
 
     return -104. / 27. * log(mu_b / Mb) - 833. / 162. - 20. * gslpp::complex::i() * M_PI / 27. +
             8. * M2 / 9. * pow(s, 1.5) + 2. / 9. * (48. + 30. * gslpp::complex::i() * M_PI -
             5. * M2 - 2. * gslpp::complex::i() * M3 - 36. * gsl_sf_zeta(3.)+
             (36. + 6. * gslpp::complex::i() * M_PI - 9. * M2) * logs + (3. + 6. *
             gslpp::complex::i() * M_PI) * logs * logs + logs * logs * logs) * s + 2. / 9. * (
             18. + 2. * M2 - 2. * gslpp::complex::i() * M3 + (12. - 6. * M2) * logs + 6. *
             gslpp::complex::i() * M_PI * logs * logs + logs * logs * logs) * s * s + 1. / 27. * (-9. + 112. *
             gslpp::complex::i() * M_PI - 14. * M2 + (182. - 48. * gslpp::complex::i() * M_PI) * logs -
             126. * logs * logs) * s * s*s;
 }

gslpp::complex MVgamma::G8 ( )

Correction in eq. (42) of [43].

Returns: \( G_8 \)

Definition at line 102 of file MVgamma.cpp.

 {
     return 8. / 3. * log(mu_b / Mb) + 11. / 3. - 2. / 9. * M_PI * M_PI + 2. / 3. * gslpp::complex::i() * M_PI;
 }

gslpp::complex MVgamma::H1 ( double s )

Correction in eq. (42) of [43].

Parameters

s	\( m_c^2/m_b^2 \)

Returns: \( H_1(s) \)

Definition at line 107 of file MVgamma.cpp.

 {
     gslpp::complex c0, c1, c2;
 
     c0 = 1.05171 + 1.02281 + gslpp::complex::i()*2.75305;
     c1 = 1.41919 + 0.413974 - gslpp::complex::i()*1.85404;
     c2 = 0.269769 - 1.73577 - gslpp::complex::i()*1.50017;
 
     return -2. * M_PI * M_PI / 9. * SM.getMesons(meson).getDecayconst() *
             SM.getMesons(vectorM).getDecayconst() / T_1() / MM / SM.getMesons(meson).getLambdaM()*
             (c0 + c1 * SM.getMesons(vectorM).getGegenalpha(0) + c2 * SM.getMesons(vectorM).getGegenalpha(1));
 }

gslpp::complex MVgamma::H8 ( )

Correction in eq. (42) of [43].

Returns: \( H_8 \)

Definition at line 120 of file MVgamma.cpp.

 {
     return 4. * M_PI * M_PI / 9. * SM.getMesons(meson).getDecayconst() *
             SM.getMesons(vectorM).getDecayconst() / T_1() / MM / SM.getMesons(meson).getLambdaM()*
             (3. - 3. * SM.getMesons(vectorM).getGegenalpha(0) + 3. * SM.getMesons(vectorM).getGegenalpha(1));
 }

gslpp::complex MVgamma::H_V_m ( )

The helicity amplitude \( H_V^- \).

Returns: \( H_V^- \)

Definition at line 130 of file MVgamma.cpp.

 {
     double s = Mc * Mc / Mb / Mb;
     return lambda_t * ((C_7 + SM.Als(mu_b) / 3. / M_PI * (C_2 * G1(s) + C_8 * G8())
             + SM.Als(mu_h) / 3. / M_PI * (C_2h * H1(s) + C_8h * H8())) * T_1()
             * lambda / MM2 - MM / (2 * Mb)*16 * M_PI * M_PI * h[1]);
 }

gslpp::complex MVgamma::H_V_m_bar ( )

The helicity amplitude \( \bar{H}_V^- \).

Returns: \( \bar{H}_V^- \)

Definition at line 143 of file MVgamma.cpp.

 {
     double s = Mc * Mc / Mb / Mb;
     return lambda_t.conjugate() * ((C_7 + SM.Als(mu_b) / 3. / M_PI * (C_2 * G1(s) + C_8 * G8())
             + SM.Als(mu_h) / 3. / M_PI * (C_2h * H1(s) + C_8h * H8())) * T_1() * lambda / MM2 - MM / (2 * Mb)*16 * M_PI * M_PI * h[1]);
 }

gslpp::complex MVgamma::H_V_p ( )

The helicity amplitude \( H_V^+ \).

Returns: \( H_V^+ \)

Definition at line 138 of file MVgamma.cpp.

 {
     return lambda_t * (-C_7p * T_1() * lambda / MM2 - MM / (2 * Mb)*16 * M_PI * M_PI * h[0]);
 }

gslpp::complex MVgamma::H_V_p_bar ( )

The helicity amplitude \( \bar{H}_V^+ \).

Returns: \( \bar{H}_V^+ \)

Definition at line 150 of file MVgamma.cpp.

 {
     return lambda_t.conjugate() * (-C_7p * T_1() * lambda / MM2 - MM / (2 * Mb)*16 * M_PI * M_PI * h[0]);
 }

double MVgamma::T_1 ( )

The transverse form factor \( T_1 \).

Returns: \( T_1 \)

Definition at line 77 of file MVgamma.cpp.

 {
     return ( a_0T1);
 }

void MVgamma::updateParameters ( )

The update parameter method for MVgamma.

Definition at line 23 of file MVgamma.cpp.

 {
     GF = SM.getGF();
     ale = SM.getAle();
     MM = SM.getMesons(meson).getMass();
     MM2 = MM * MM;
     MV = SM.getMesons(vectorM).getMass();
     Mb = SM.getQuarks(QCD::BOTTOM).getMass(); // add the PS b mass
     Mc = SM.getQuarks(QCD::CHARM).getMass();
     Ms = SM.getQuarks(QCD::STRANGE).getMass();
     MW = SM.Mw();
     lambda_t = SM.computelamt_s();
     mu_b = SM.getMub();
     mu_h = sqrt(mu_b * .5); // From Beneke Neubert
     width = SM.getMesons(meson).computeWidth();
     lambda = MM2 - pow(MV, 2.);
 
     switch (vectorM) {
         case StandardModel::K_star:
             a_0T1 = SM.geta_0T1();
 
             break;
         case StandardModel::PHI:
             a_0T1 = SM.geta_0T1phi();
 
             break;
         default:
             std::stringstream out;
             out << vectorM;
             throw std::runtime_error("MVgamma: vector " + out.str() + " not implemented");
     }
 
 
     h[0] = SM.geth_p(); //h_plus
     h[1] = SM.geth_m(); //h_minus
 
     allcoeff = SM.getMyFlavour()->ComputeCoeffBMll(mu_b); //check the mass scale, scheme fixed to NDR
     allcoeffprime = SM.getMyFlavour()->ComputeCoeffprimeBMll(mu_b); //check the mass scale, scheme fixed to NDR
 
     C_7 = (*(allcoeff[LO]))(6) + (*(allcoeff[NLO]))(6);
     C_7p = (*(allcoeffprime[LO]))(6) + (*(allcoeffprime[NLO]))(6);
     C_2 = (*(allcoeff[LO]))(1);
     C_8 = (*(allcoeff[LO]))(7);
 
     allcoeffh = SM.getMyFlavour()->ComputeCoeffBMll(mu_h); //check the mass scale, scheme fixed to NDR
 
     C_2h = (*(allcoeffh[LO]))(1);
     C_8h = (*(allcoeffh[LO]))(7);
     
 }

Member Data Documentation

double MVgamma::a_0T1

LCSR fit parameter

Definition at line 66 of file MVgamma.h.

double MVgamma::a_1T1

LCSR fit parameter

Definition at line 67 of file MVgamma.h.

double MVgamma::a_2T1

LCSR fit parameter

Definition at line 68 of file MVgamma.h.

double MVgamma::ale

alpha electromagnetic

Definition at line 51 of file MVgamma.h.

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

vector that contains the Wilson coeffients at mub

Definition at line 71 of file MVgamma.h.

gslpp::vector<gslpp::complex>** MVgamma::allcoeffh

vector that contains the Wilson coeffients at muh

Definition at line 72 of file MVgamma.h.

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

vector that contains the primed Wilson coeffients at mub

Definition at line 73 of file MVgamma.h.

gslpp::complex MVgamma::C_2

Wilson coeffients \(C_2(mu_b)\)

Definition at line 77 of file MVgamma.h.

gslpp::complex MVgamma::C_2h

Wilson coeffients \(C_2(mu_h)\)

Definition at line 79 of file MVgamma.h.

gslpp::complex MVgamma::C_7

Wilson coeffients \(C_7\)

Definition at line 75 of file MVgamma.h.

gslpp::complex MVgamma::C_7p

Wilson coeffients \(C_7'\)

Definition at line 76 of file MVgamma.h.

gslpp::complex MVgamma::C_8

Wilson coeffients \(C_8(mu_b)\)

Definition at line 78 of file MVgamma.h.

gslpp::complex MVgamma::C_8h

Wilson coeffients \(C_8(mu_h)\)

Definition at line 80 of file MVgamma.h.

double MVgamma::GF

Fermi constant

Definition at line 50 of file MVgamma.h.

gslpp::complex MVgamma::h[2]

parameter that contains the contribution from the hadronic hamiltonian

Definition at line 63 of file MVgamma.h.

double MVgamma::lambda

cinematic parameter

Definition at line 64 of file MVgamma.h.

gslpp::complex MVgamma::lambda_t

Vckm factor

Definition at line 62 of file MVgamma.h.

double MVgamma::Mb

b quark mass

Definition at line 55 of file MVgamma.h.

double MVgamma::Mc

c quark mass

Definition at line 56 of file MVgamma.h.

StandardModel::meson MVgamma::meson

private

Definition at line 140 of file MVgamma.h.

double MVgamma::MM

initial meson mass

Definition at line 52 of file MVgamma.h.

double MVgamma::MM2

square of the initial meson mass

Definition at line 53 of file MVgamma.h.

double MVgamma::MRT1_2

LCSR fit parameter

Definition at line 69 of file MVgamma.h.

double MVgamma::Ms

s quark mass

Definition at line 60 of file MVgamma.h.

double MVgamma::mu_b

b mass scale

Definition at line 57 of file MVgamma.h.

double MVgamma::mu_h

sqrt(mu_b*lambda_QCD)

Definition at line 58 of file MVgamma.h.

double MVgamma::MV

final vector meson mass

Definition at line 54 of file MVgamma.h.

double MVgamma::MW

W boson mass

Definition at line 61 of file MVgamma.h.

StandardModel::meson MVgamma::vectorM

private

Definition at line 141 of file MVgamma.h.

double MVgamma::width

initial meson width

Definition at line 59 of file MVgamma.h.

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

Detailed Description

Public Member Functions

Public Attributes

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation