CKM Class Reference

A class for the CKM matrix elements. More...

#include <CKM.h>

Detailed Description

A class for the CKM matrix elements.

Author

HEPfit Collaboration

Copyright

GNU General Public License

This is the class for defining the CKM matrix and its elements with the Wolfenstein and Gilman parameterizations.

Definition at line 23 of file CKM.h.

Public Member Functions
	CKM ()
double	computeAlpha () const
	The CKM angle \(\alpha\). More...
double	computeBeta () const
	The CKM angle \(\beta\). More...
double	computeBetas () const
	The CKM angle \(\beta_s\). More...
void	computeCKM (double Vus_v, double Vcb_v, double Vub_v, double gamma_v)
	A set method to calculate the CKM matrix from CKM elements and \( \gamma \). More...
void	computeCKMwithWolfenstein (double Lambda_v, double A_v, double Rho_v, double Eta_v)
	A set method to calculate the CKM matrix from Wolfenstein parameters. More...
double	computeGamma () const
	The CKM angle \(\gamma\). More...
gslpp::complex	computelamc () const
	The product of the CKM elements \(V_{cd} V_{cs}^*\). More...
gslpp::complex	computelamc_d () const
	The product of the CKM elements \(V_{cd} V_{cb}^*\). More...
gslpp::complex	computelamc_s () const
	The product of the CKM elements \(V_{cs} V_{cb}^*\). More...
gslpp::complex	computelamt () const
	The product of the CKM elements \(V_{td} V_{ts}^*\). More...
gslpp::complex	computelamt_d () const
	The product of the CKM elements \(V_{td} V_{tb}^*\). More...
gslpp::complex	computelamt_s () const
	The product of the CKM elements \(V_{ts} V_{tb}^*\). More...
gslpp::complex	computelamu () const
	The product of the CKM elements \(V_{ud} V_{us}^*\). More...
gslpp::complex	computelamu_d () const
	The product of the CKM elements \(V_{ud} V_{ub}^*\). More...
gslpp::complex	computelamu_s () const
	The product of the CKM elements \(V_{us} V_{ub}^*\). More...
double	computeRb () const
	\(R_b=|(V_{ud}V_{ub}^*)/(V_{ud}V_{ub}^*)|\). More...
double	computeRt () const
	\(R_t=|(V_{td} V_{tb}^*)/(V_{cd}V_{cb}^*)|\). More...
double	computeRts () const
	\(R_{ts}=|(V_{ts}V_{tb}^*)/(V_{cs}V_{cb}^*)|\). More...
double	getA () const
	A member for returning the value of the Wolfenstein parameter \( A \). More...
double	getc12 () const
	A member for returning the value of the cosine of the CKM parameter \( \theta_{12} \). More...
double	getc13 () const
	A member for returning the value of the cosine of the CKM parameter \( \theta_{13} \). More...
double	getc23 () const
	A member for returning the value of the cosine of the CKM parameter \( \theta_{23} \). More...
gslpp::matrix< gslpp::complex >	getCKM () const
	A member for returning the CKM matrix. More...
double	getdelta () const
	A member for returning the value of the CKM parameter \( \delta \). More...
double	getEta () const
	A member for returning the value of the Wolfenstein parameter \( \eta \). More...
double	getEtaBar () const
	A member for returning the value of the Wolfenstein parameter \( \bar{\eta} \). More...
double	getJcp () const
	A member for returning the value of the Jarlskog determinant. More...
double	getLambda () const
	A member for returning the value of the Wolfenstein parameter \( \lambda \). More...
double	getRho () const
	A member for returning the value of the Wolfenstein parameter \( \rho \). More...
double	getRhoBar () const
	A member for returning the value of the Wolfenstein parameter \( \bar{\rho} \). More...
double	gets12 () const
	A member for returning the value of the sine of the CKM parameter \( \theta_{12} \). More...
double	gets13 () const
	A member for returning the value of the sine of the CKM parameter \( \theta_{13} \). More...
double	gets23 () const
	A member for returning the value of the sine of the CKM parameter \( \theta_{23} \). More...
gslpp::complex	getV_cb () const
	A member for returning the value of the CKM element \( V_{cb} \). More...
gslpp::complex	getV_cd () const
	A member for returning the value of the CKM element \( V_{cd} \). More...
gslpp::complex	getV_cs () const
	A member for returning the value of the CKM element \( V_{cs} \). More...
gslpp::complex	getV_tb () const
	A member for returning the value of the CKM element \( V_{tb} \). More...
gslpp::complex	getV_td () const
	A member for returning the value of the CKM element \( V_{td} \). More...
gslpp::complex	getV_ts () const
	A member for returning the value of the CKM element \( V_{ts} \). More...
gslpp::complex	getV_ub () const
	A member for returning the value of the CKM element \( V_{ub} \). More...
gslpp::complex	getV_ud () const
	A member for returning the value of the CKM element \( V_{ud} \). More...
gslpp::complex	getV_us () const
	A member for returning the value of the CKM element \( V_{us} \). More...

Private Member Functions
void	computeCKMfromAngles ()

Private Attributes
double	A
	The Wolfenstein parameters. More...
double	c12
double	c13
	The cosine of the three mixing angles. More...
double	c23
double	delta
	The CP violating phase in the CKM matrix. More...
double	Eta
double	Lambda
double	Rho
double	s12
double	s13
double	s23
	The sine of the three mixing angles. More...
gslpp::matrix< gslpp::complex >	V
	The CKM matrix. More...

Constructor & Destructor Documentation

CKM()

CKM::CKM

(

)

Definition at line 10 of file CKM.cpp.

         : V(3, 3)
{}

Member Function Documentation

computeAlpha()

double CKM::computeAlpha

(

)

const

The CKM angle \(\alpha\).

Returns

\(\alpha\) in radians

Definition at line 92 of file CKM.cpp.

{
    return (-V(2, 0)*V(2, 2).conjugate()/(V(0, 0)*V(0, 2).conjugate())).arg();
}

computeBeta()

double CKM::computeBeta

(

)

const

The CKM angle \(\beta\).

Returns

\(\beta\) in radians

Definition at line 82 of file CKM.cpp.

{
    return (-V(1, 0)*V(1, 2).conjugate()/(V(2, 0)*V(2, 2).conjugate())).arg();
}

computeBetas()

double CKM::computeBetas

(

)

const

The CKM angle \(\beta_s\).

Returns

\(\beta_s\) in radians

Definition at line 97 of file CKM.cpp.

{
    return (-V(2, 1)*V(2, 2).conjugate()/(V(1, 1)*V(1, 2).conjugate())).arg();
}

computeCKM()

void CKM::computeCKM	(	double	Vus_v,
		double	Vcb_v,
		double	Vub_v,
		double	gamma_v
	)

A set method to calculate the CKM matrix from CKM elements and \( \gamma \).

Parameters

[in]	Vus_v	the CKM element \( V_{us} \)
[in]	Vcb_v	the CKM element \( V_{cb} \)
[in]	Vub_v	the CKM element \( V_{ub} \)
[in]	gamma_v	the CKM element \( \gamma \)

Definition at line 55 of file CKM.cpp.

{
    s13 = Vub_v;
    c13 = sqrt(1.-s13*s13);
    s12 = Vus_v / c13;
    s23 = Vcb_v / c13;
 
    c12 = sqrt(1. - s12 * s12);
    c23 = sqrt(1. - s23 * s23);
    
    double a = c12 * s13 * s23 / s12 / c23;
    if ( fabs(gamma_v) < 1.e-10 )
        delta = 0.;
    else
        delta = 2. * atan((1. + sqrt(1. - (a * a - 1.) * pow(tan(gamma_v), 2.))*(cos(gamma_v) < 0. ? 1. : (-1.))) / (a - 1.) / tan(gamma_v));
 
    computeCKMfromAngles();
    
    // Wolfenstein to all orders
    Lambda = s12;
    A = s23 / Lambda / Lambda;
    gslpp::complex Rb = V(0, 0) * V(0, 2).conjugate() / (V(1, 0) * V(1, 2).conjugate());
    Rho = -Rb.real();
    Eta = -Rb.imag();
    return;
}

computeCKMfromAngles()

void CKM::computeCKMfromAngles ( )

private

Definition at line 40 of file CKM.cpp.

{   
    V.assign(0, 0, c12*c13);
    V.assign(0, 1, s12*c13);
    V.assign(0, 2, gslpp::complex(s13, -delta, true));
 
    V.assign(1, 0 , -s12 * c23 - gslpp::complex(c12 * s23*s13, delta, true));
    V.assign(1, 1, c12 * c23 - gslpp::complex(s12 * s23*s13, delta, true));
    V.assign(1, 2, s23*c13);
 
    V.assign(2, 0, s12 * s23 - gslpp::complex(c12 * c23*s13, delta, true));
    V.assign(2, 1, -c12 * s23 - gslpp::complex(s12 * c23*s13, delta, true));
    V.assign(2, 2, c23*c13);  
}

computeCKMwithWolfenstein()

void CKM::computeCKMwithWolfenstein	(	double	Lambda_v,
		double	A_v,
		double	Rho_v,
		double	Eta_v
	)

A set method to calculate the CKM matrix from Wolfenstein parameters.

Parameters

[in]	Lambda_v	the Wolfenstein parameter \( \lambda \)
[in]	A_v	the Wolfenstein parameter \( A \)
[in]	Rho_v	the Wolfenstein parameter \( \bar{\rho} \)
[in]	Rho_v	the Wolfenstein parameter \( \bar{\eta} \)

Definition at line 13 of file CKM.cpp.

{
    Rho = Rho_v;
    Eta = Eta_v;
    Lambda = Lambda_v;
    A = A_v;
 
    gslpp::complex num(Rho, Eta);
    num = num * sqrt(1. - pow(A, 2.) * pow(Lambda, 4.));
    gslpp::complex den = sqrt(1. - pow(Lambda, 2.)) * gslpp::complex(1. - pow(A, 2.) * pow(Lambda, 4.) * Rho, -pow(A, 2.) * pow(Lambda, 4.) * Eta);
    gslpp::complex ratio = num / den;
 
    double rho_nb = ratio.real();
    double eta_nb = ratio.imag();
 
    s12 = Lambda;
    s23 = A * pow(Lambda, 2.);
    s13 = (gslpp::complex(A * pow(Lambda, 3.) * rho_nb, -A * pow(Lambda, 3.) * eta_nb)).abs();
    delta = -(gslpp::complex(A * pow(Lambda, 3.) * rho_nb, -A * pow(Lambda, 3.) * eta_nb)).arg();
 
    c12 = sqrt(1. - s12 * s12);
    c13 = sqrt(1. - s13 * s13);
    c23 = sqrt(1. - s23 * s23);
    
    computeCKMfromAngles();
}

computeGamma()

double CKM::computeGamma

(

)

const

The CKM angle \(\gamma\).

Returns

\(\gamma\) in radians

Definition at line 87 of file CKM.cpp.

{
    return (-V(0, 0)*V(0, 2).conjugate()/(V(1, 0)*V(1, 2).conjugate())).arg();
}

computelamc()

gslpp::complex CKM::computelamc

(

)

const

The product of the CKM elements \(V_{cd} V_{cs}^*\).

Returns

\(V_{cd} V_{cs}^*\)

Definition at line 109 of file CKM.cpp.

{
    return V(1, 0)*V(1, 1).conjugate();
}

computelamc_d()

gslpp::complex CKM::computelamc_d

(

)

const

The product of the CKM elements \(V_{cd} V_{cb}^*\).

Returns

\(V_{cd} V_{cb}^*\)

Definition at line 125 of file CKM.cpp.

{
    return V(1, 0)*V(1, 2).conjugate();
}

computelamc_s()

gslpp::complex CKM::computelamc_s

(

)

const

The product of the CKM elements \(V_{cs} V_{cb}^*\).

Returns

\(V_{cs} V_{cb}^*\)

Definition at line 141 of file CKM.cpp.

{
    return V(1, 1)*V(1, 2).conjugate();
}

computelamt()

gslpp::complex CKM::computelamt

(

)

const

The product of the CKM elements \(V_{td} V_{ts}^*\).

Returns

\(V_{td} V_{ts}^*\)

Definition at line 104 of file CKM.cpp.

{
    return V(2, 0)*V(2, 1).conjugate();
}

computelamt_d()

gslpp::complex CKM::computelamt_d

(

)

const

The product of the CKM elements \(V_{td} V_{tb}^*\).

Returns

\(V_{td} V_{tb}^*\)

Definition at line 120 of file CKM.cpp.

{
    return V(2, 0)*V(2, 2).conjugate();
}

computelamt_s()

gslpp::complex CKM::computelamt_s

(

)

const

The product of the CKM elements \(V_{ts} V_{tb}^*\).

Returns

\(V_{ts} V_{tb}^*\)

Definition at line 136 of file CKM.cpp.

{
    return V(2, 1)*V(2, 2).conjugate();
}

computelamu()

gslpp::complex CKM::computelamu

(

)

const

The product of the CKM elements \(V_{ud} V_{us}^*\).

Returns

\(V_{ud} V_{us}^*\)

Definition at line 114 of file CKM.cpp.

{
    return V(0, 0)*V(0, 1).conjugate();
}

computelamu_d()

gslpp::complex CKM::computelamu_d

(

)

const

The product of the CKM elements \(V_{ud} V_{ub}^*\).

Returns

\(V_{ud} V_{ub}^*\)

Definition at line 130 of file CKM.cpp.

{
    return V(0, 0)*V(0, 2).conjugate();
}

computelamu_s()

gslpp::complex CKM::computelamu_s

(

)

const

The product of the CKM elements \(V_{us} V_{ub}^*\).

Returns

\(V_{us} V_{ub}^*\)

Definition at line 146 of file CKM.cpp.

{
    return V(0, 1)*V(0, 2).conjugate();
}

computeRb()

double CKM::computeRb

(

)

const

\(R_b=|(V_{ud}V_{ub}^*)/(V_{ud}V_{ub}^*)|\).

Returns

\(R_b\)

Definition at line 161 of file CKM.cpp.

{
    return (V(0, 0)*V(0, 2).conjugate()/(V(1, 0)*V(1, 2).conjugate())).abs();
}

computeRt()

double CKM::computeRt

(

)

const

\(R_t=|(V_{td} V_{tb}^*)/(V_{cd}V_{cb}^*)|\).

Returns

\(R_t\)

Definition at line 152 of file CKM.cpp.

{
    return (V(2, 0)*V(2, 2).conjugate()/(V(1, 0)*V(1, 2).conjugate())).abs();
}

computeRts()

double CKM::computeRts

(

)

const

\(R_{ts}=|(V_{ts}V_{tb}^*)/(V_{cs}V_{cb}^*)|\).

Returns

\(R_{ts}\)

Definition at line 156 of file CKM.cpp.

{
    return (V(2, 1)*V(2, 2).conjugate()/(V(1, 1)*V(1, 2).conjugate())).abs();
}

getA()

double CKM::getA ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( A \).

Returns

the value of \( A \)

Definition at line 87 of file CKM.h.

    {
        return A;
    }

getc12()

double CKM::getc12 ( ) const

inline

A member for returning the value of the cosine of the CKM parameter \( \theta_{12} \).

Returns

the value of \( \cos\theta_{12} \)

Definition at line 143 of file CKM.h.

    {
        return c12;
    }

getc13()

double CKM::getc13 ( ) const

inline

A member for returning the value of the cosine of the CKM parameter \( \theta_{13} \).

Returns

the value of \( \cos\theta_{13} \)

Definition at line 161 of file CKM.h.

    {
        return c13;
    }

getc23()

double CKM::getc23 ( ) const

inline

A member for returning the value of the cosine of the CKM parameter \( \theta_{23} \).

Returns

the value of \( \cos\theta_{23} \)

Definition at line 152 of file CKM.h.

    {
        return c23;
    }

getCKM()

gslpp::matrix<gslpp::complex> CKM::getCKM ( ) const

inline

A member for returning the CKM matrix.

Returns

the CKM matrix

Definition at line 49 of file CKM.h.

    {
        return V;
    }

getdelta()

double CKM::getdelta ( ) const

inline

A member for returning the value of the CKM parameter \( \delta \).

Returns

the value of \( \delta \)

Definition at line 170 of file CKM.h.

    {
        return delta;
    }

getEta()

double CKM::getEta ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( \eta \).

Returns

the value of \( \eta \)

Definition at line 105 of file CKM.h.

    {
        return (s13 * sin(delta) / s12 / s23);
    }

getEtaBar()

double CKM::getEtaBar ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( \bar{\eta} \).

Returns

the value of \( \bar{\eta} \)

Definition at line 69 of file CKM.h.

    {
        return Eta;
    }

getJcp()

double CKM::getJcp ( ) const

inline

A member for returning the value of the Jarlskog determinant.

Returns

the value of \( J \)

Definition at line 181 of file CKM.h.

    {
        return Eta * pow(A * pow(Lambda, 3), 2);
    }

getLambda()

double CKM::getLambda ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( \lambda \).

Returns

the value of \( \lambda \)

Definition at line 78 of file CKM.h.

    {
        return Lambda;
    }

getRho()

double CKM::getRho ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( \rho \).

Returns

the value of \( \rho \)

Definition at line 96 of file CKM.h.

    {
        return (s13 * cos(delta) / s12 / s23);
    }

getRhoBar()

double CKM::getRhoBar ( ) const

inline

A member for returning the value of the Wolfenstein parameter \( \bar{\rho} \).

Returns

the value of \( \bar{\rho} \)

Definition at line 60 of file CKM.h.

    {
        return Rho;
    }

gets12()

double CKM::gets12 ( ) const

inline

A member for returning the value of the sine of the CKM parameter \( \theta_{12} \).

Returns

the value of \( \sin\theta_{12} \)

Definition at line 116 of file CKM.h.

    {
        return s12;
    }

gets13()

double CKM::gets13 ( ) const

inline

A member for returning the value of the sine of the CKM parameter \( \theta_{13} \).

Returns

the value of \( \sin\theta_{13} \)

Definition at line 125 of file CKM.h.

    {
        return s13;
    }

gets23()

double CKM::gets23 ( ) const

inline

A member for returning the value of the sine of the CKM parameter \( \theta_{23} \).

Returns

the value of \( \sin\theta_{23} \)

Definition at line 134 of file CKM.h.

    {
        return s23;
    }

getV_cb()

gslpp::complex CKM::getV_cb ( ) const

inline

A member for returning the value of the CKM element \( V_{cb} \).

Returns

the value of \( V_{cb} \)

Definition at line 237 of file CKM.h.

    {
        return V(1, 2);
    }

getV_cd()

gslpp::complex CKM::getV_cd ( ) const

inline

A member for returning the value of the CKM element \( V_{cd} \).

Returns

the value of \( V_{cd} \)

Definition at line 219 of file CKM.h.

    {
        return V(1, 0);
    }

getV_cs()

gslpp::complex CKM::getV_cs ( ) const

inline

A member for returning the value of the CKM element \( V_{cs} \).

Returns

the value of \( V_{cs} \)

Definition at line 228 of file CKM.h.

    {
        return V(1, 1);
    }

getV_tb()

gslpp::complex CKM::getV_tb ( ) const

inline

A member for returning the value of the CKM element \( V_{tb} \).

Returns

the value of \( V_{tb} \)

Definition at line 264 of file CKM.h.

    {
        return V(2, 2);
    }

getV_td()

gslpp::complex CKM::getV_td ( ) const

inline

A member for returning the value of the CKM element \( V_{td} \).

Returns

the value of \( V_{td} \)

Definition at line 246 of file CKM.h.

    {
        return V(2, 0);
    }

getV_ts()

gslpp::complex CKM::getV_ts ( ) const

inline

A member for returning the value of the CKM element \( V_{ts} \).

Returns

the value of \( V_{ts} \)

Definition at line 255 of file CKM.h.

    {
        return V(2, 1);
    }

getV_ub()

gslpp::complex CKM::getV_ub ( ) const

inline

A member for returning the value of the CKM element \( V_{ub} \).

Returns

the value of \( V_{ub} \)

Definition at line 210 of file CKM.h.

    {
        return V(0, 2);
    }

getV_ud()

gslpp::complex CKM::getV_ud ( ) const

inline

A member for returning the value of the CKM element \( V_{ud} \).

Returns

the value of \( V_{ud} \)

Definition at line 192 of file CKM.h.

    {
        return V(0, 0);
    }

getV_us()

gslpp::complex CKM::getV_us ( ) const

inline

A member for returning the value of the CKM element \( V_{us} \).

Returns

the value of \( V_{us} \)

Definition at line 201 of file CKM.h.

    {
        return V(0, 1);
    }

Member Data Documentation

A

double CKM::A

private

The Wolfenstein parameters.

Definition at line 368 of file CKM.h.

c12

double CKM::c12

private

Definition at line 370 of file CKM.h.

c13

double CKM::c13

private

The cosine of the three mixing angles.

Definition at line 370 of file CKM.h.

c23

double CKM::c23

private

Definition at line 370 of file CKM.h.

delta

double CKM::delta

private

The CP violating phase in the CKM matrix.

Definition at line 371 of file CKM.h.

Eta

double CKM::Eta

private

Definition at line 368 of file CKM.h.

Lambda

double CKM::Lambda

private

Definition at line 368 of file CKM.h.

Rho

double CKM::Rho

private

Definition at line 368 of file CKM.h.

s12

double CKM::s12

private

Definition at line 369 of file CKM.h.

s13

double CKM::s13

private

Definition at line 369 of file CKM.h.

s23

double CKM::s23

private

The sine of the three mixing angles.

Definition at line 369 of file CKM.h.

V

gslpp::matrix<gslpp::complex> CKM::V

private

The CKM matrix.

Definition at line 373 of file CKM.h.

---

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

• CKM.h
• CKM.cpp