EvolDB1Mll Class Reference

#include <EvolDB1Mll.h>

Inheritance diagram for EvolDB1Mll:

Detailed Description

Definition at line 14 of file EvolDB1Mll.h.

Public Member Functions
gslpp::matrix< double >	AnomalousDimension_M (orders order, unsigned int n_u, unsigned int n_d) const
	a method returning the anomalous dimension matrix given in the Misiak basis More...
gslpp::matrix< double > &	Df1EvolMll (double mu, double M, orders order, schemes scheme=NDR)
	a method returning the evolutor related to the high scale \( M \) and the low scale \( \mu \) More...
	EvolDB1Mll (unsigned int dim, schemes scheme, orders order, const StandardModel &model)
	EvolDF1bsg constructor. More...
gslpp::matrix< double >	ToEffectiveBasis (gslpp::matrix< double > mat) const
	a method returning the anomalous dimension for the evolution of the effective Wilson coefficients More...
gslpp::matrix< double >	ToRescaleBasis (orders order, unsigned int n_u, unsigned int n_d) const
	a method returning the anomalous dimension in the Chetyrkin, Misiak and Munz operator basis More...
virtual	~EvolDB1Mll ()
	EvolDF1bsg destructor. More...
Public Member Functions inherited from RGEvolutor
gslpp::matrix< double > *	Evol (orders order)
	Evolution matrix set at a fixed order of QCD coupling. More...
gslpp::matrix< double > *	Evol (orders_qed order_qed)
	Evolution matrix set at a fixed order of Electroweak coupling. More...
gslpp::matrix< double > **	getEvol () const
double	getM () const
	Retrieve the upper scale of the Wilson Coefficients. More...
	RGEvolutor (unsigned int dim, schemes scheme, orders order)
	constructor More...
	RGEvolutor (unsigned int dim, schemes scheme, orders order, orders_qed order_qed)
	constructor More...
void	setEvol (const gslpp::matrix< double > &m, orders order_i)
void	setEvol (const gslpp::matrix< double > &m, orders_qed order_qed_i)
void	setEvol (unsigned int i, unsigned int j, double x, orders order_i)
void	setEvol (unsigned int i, unsigned int j, double x, orders order_i, orders_qed order_qed)
void	setM (double M)
	Sets the upper scale for the running of the Wilson Coefficients. More...
void	setMu (double mu)
	Sets the lower scale for the running of the Wilson Coefficients. More...
void	setScales (double mu, double M)
	Sets the upper and lower scale for the running of the Wilson Coefficients. More...
virtual	~RGEvolutor ()
	destructor More...
Public Member Functions inherited from WilsonTemplate< gslpp::matrix< double > >
double	getMu () const
orders	getOrder () const
orders_qed	getOrder_qed () const
schemes	getScheme () const
unsigned int	getSize () const
virtual void	resetCoefficient ()
void	setScheme (schemes scheme)
	WilsonTemplate (const WilsonTemplate< gslpp::matrix< double > > &orig)
	WilsonTemplate (unsigned int dim, schemes scheme_i, orders order_i, orders_qed order_qed_i=NO_QED)
virtual	~WilsonTemplate ()

Private Member Functions
void	Df1EvolMll (double mu, double M, double nf, schemes scheme)
	a void type method storing properly the magic numbers for the implementation of the evolutor More...

Private Attributes
double	a [4][13]
double	alsMZ_cache
double	b [4][13][13][13]
double	c [4][13][13][13]
double	d [4][13][13][13]
unsigned int	dim
gslpp::vector< gslpp::complex >	e
gslpp::matrix< gslpp::complex >	gg
gslpp::matrix< gslpp::complex >	h
gslpp::matrix< gslpp::complex >	js
gslpp::matrix< gslpp::complex >	jss
gslpp::matrix< gslpp::complex >	jssv
gslpp::matrix< gslpp::complex >	jv
const StandardModel &	model
double	Mz_cache
int	nd
int	nu
gslpp::matrix< gslpp::complex >	s_s
gslpp::matrix< gslpp::complex >	v
gslpp::matrix< gslpp::complex >	vi
gslpp::matrix< gslpp::complex >	vij

Additional Inherited Members
Protected Member Functions inherited from WilsonTemplate< gslpp::matrix< double > >
gslpp::matrix< double > *	Elem (orders order) const
gslpp::matrix< double > *	Elem (orders_qed order_qed) const
void	setElem (const gslpp::matrix< double > &v, orders order_i)
void	setElem (const gslpp::matrix< double > &v, orders_qed order_qed_i)
Protected Attributes inherited from RGEvolutor
double	M
Protected Attributes inherited from WilsonTemplate< gslpp::matrix< double > >
gslpp::matrix< double > *	elem [MAXORDER_QED+1]
double	mu
orders	order
orders_qed	order_qed
schemes	scheme
unsigned int	size

Constructor & Destructor Documentation

EvolDB1Mll()

EvolDB1Mll::EvolDB1Mll	(	unsigned int	dim,
		schemes	scheme,
		orders	order,
		const StandardModel &	model
	)

EvolDF1bsg constructor.

Parameters

dim	an unsigned integer for the dimension of the evolutor
scheme	an enum "schemes" for the regularization scheme of the evolutor
order	an enum "orders" for the order of perturbation theory of the evolutor
model	an object of StandardModel class

Definition at line 12 of file EvolDB1Mll.cpp.

:           RGEvolutor(dim_i, scheme, order), model(model),
            v(dim_i,0.), vi(dim_i,0.), js(dim_i,0.), h(dim_i,0.), gg(dim_i,0.), s_s(dim_i,0.),
            jssv(dim_i,0.), jss(dim_i,0.), jv(dim_i,0.), vij(dim_i,0.), e(dim_i,0.), dim(dim_i) 
{
    if (dim != 13 ) throw std::runtime_error("ERROR: EvolDB1Mll can only be of dimension 13"); 
    
    /* magic numbers a & b */ 
    
    for(int L=3; L>-1; L--){
        
    /* L=3 --> u,d,s (nf=3) L=2 --> u,d,s,c (nf=4)  L=1 --> u,d,s,c,b (nf=5) L=0 --> u,d,s,c,b,t (nf=6) */
        
    nu = L;  nd = L;
    if(L == 3){nd = 2; nu = 1;} 
    if(L == 1){nd = 3; nu = 2;} 
    if(L == 0){nd = 3; nu = 3;}
 
    // LO evolutor of the effective Wilson coefficients in the Chetyrkin, Misiak and Munz basis
    
    (ToEffectiveBasis(ToRescaleBasis(LO,nu,nd))).transpose().eigensystem(v,e);
    vi = v.inverse();
    for(unsigned int i = 0; i < dim; i++){
       a[L][i] = e(i).real();
       for (unsigned int j = 0; j < dim; j++) {
           for (unsigned int k = 0; k < dim; k++)  {
                b[L][i][j][k] = v(i, k).real() * vi(k, j).real();
               }
           }
       }
    
    // NLO evolutor of the effective Wilson coefficients in the Chetyrkin, Misiak and Munz basis
    
    gg = vi * (ToEffectiveBasis(ToRescaleBasis(NLO,nu,nd))).transpose() * v;
    double b0 = model.Beta0(nu+nd);
    double b1 = model.Beta1(nu+nd);
    for (unsigned int i = 0; i < dim; i++){
        for (unsigned int j = 0; j < dim; j++){
            s_s.assign( i, j, (b1 / b0) * (i==j) * e(i).real() - gg(i,j));    
            if(fabs(e(i).real() - e(j).real() + 2. * b0)>0.00000000001){
                h.assign( i, j, s_s(i,j) / (2. * b0 + e(i) - e(j)));
                }
            }
        }
    js = v * h * vi;
    jv = js * v;
    vij = vi * js;
    jss = v * s_s * vi;
    jssv = jss * v;        
    for (unsigned int i = 0; i < dim; i++){
        for (unsigned int j = 0; j < dim; j++){
            if(fabs(e(i).real() - e(j).real() + 2. * b0) > 0.00000000001){
                for(unsigned int k = 0; k < dim; k++){
                        c[L][i][j][k] = jv(i, k).real() * vi(k, j).real();
                        d[L][i][j][k] = -v(i, k).real() * vij(k, j).real();
                        }
                    }
            else{    
                for(unsigned int k = 0; k < dim; k++){
                   c[L][i][j][k] = (1./(2. * b0)) * jssv(i, k).real() * vi(k, j).real();
                   d[L][i][j][k] = 0.;
                   }   
                }
            }
        }
    }
}

~EvolDB1Mll()

EvolDB1Mll::~EvolDB1Mll ( )

virtual

EvolDF1bsg destructor.

Definition at line 80 of file EvolDB1Mll.cpp.

{}

Member Function Documentation

AnomalousDimension_M()

gslpp::matrix< double > EvolDB1Mll::AnomalousDimension_M	(	orders	order,
		unsigned int	n_u,
		unsigned int	n_d
	)		const

a method returning the anomalous dimension matrix given in the Misiak basis

Parameters

order	an enum "orders" for the order of perturbation theory of the ADM
n_u	an unsigned integer for the up-type number of d.o.f.
n_d	an unsigned integer for the down-type number of d.o.f.

Returns

the ADM at the order LO/NLO in the Misiak basis

Definition at line 83 of file EvolDB1Mll.cpp.

{
    
    /* Delta F = 1 anomalous dimension in Misiak basis, 
       ref.: M. Misiak, Nucl. Phys. B393 (1993) 23, B439 (1995) 461 (E),  
             A.J. Buras and M. Munz, Phys. Rev. D52 (1995) 186. */   
    
    /* gamma(row, coloumn) at the LO */
    
    unsigned int nf = n_u + n_d; /*n_u/d = active type up/down flavor d.o.f.*/
  
    gslpp::matrix<double> gammaDF1(dim, dim, 0.);
   
    switch(order){
        
    case LO:
        
    gammaDF1(0,0) = -4. ;
    gammaDF1(0,1) = 8./3. ;
    gammaDF1(0,3) = -2./9.;
    gammaDF1(0,8) = -32./27.;
    
    
    gammaDF1(1,0) = 12.;
    gammaDF1(1,3) = 4./3.;
    gammaDF1(1,8) = -8./9.;
    
    gammaDF1(2,3) = -52./3.;
    gammaDF1(2,5) = 2.;
    gammaDF1(2,8) = 8./9. + (8.*n_d)/3. - (16.*n_u)/3.;
    
    gammaDF1(3,2) = -40./9.;
    gammaDF1(3,3) = -160./9. + 4./3.*nf;
    gammaDF1(3,4) = 4./9.;
    gammaDF1(3,5) = 5./6.;
    gammaDF1(3,8) = 32./27.;
    
    gammaDF1(4,3) = -256./3.;
    gammaDF1(4,5) = 20.;
    gammaDF1(4,8) = 128./9.+(80.*n_d)/3. - (160.*n_u)/3.;
    
    gammaDF1(5,2) = -256./9.;
    gammaDF1(5,3) = -544./9. + (40./3.)*nf;
    gammaDF1(5,4) = 40./9.;
    gammaDF1(5,5) = -2./3.;
    gammaDF1(5,8) = 512./27.;
    
    gammaDF1(6,6) = 32./3. - 2.*model.Beta0(nf);   
    
    gammaDF1(7,6) = -32./9.;
    gammaDF1(7,7) = 28./3. - 2.*model.Beta0(nf);
    
    gammaDF1(8,8) = -2.*model.Beta0(nf); 
    
    gammaDF1(9,9) = -2.*model.Beta0(nf); 
    
    gammaDF1(10,10)= -2.*model.Beta0(nf);
    
    gammaDF1(11,11)= -2.*model.Beta0(nf);
    
    gammaDF1(12,12)= -2.*model.Beta0(nf);
    
    break;    
    case NLO:
        
    if (!(nf == 3 || nf == 4 || nf == 5 || nf == 6)){ 
                throw std::runtime_error("EvolDF1::AnomalousDimension_M(): wrong number of flavours"); 
       }
    
    /* gamma(row, coloumn) at the NLO */
    
    gammaDF1(0,0) = -145./3. + (16./9.)*nf;
    gammaDF1(0,1) = -26. + (40./27.)*nf;
    gammaDF1(0,2) = -1412./243.;
    gammaDF1(0,3) = -1369./243.;
    gammaDF1(0,4) = 134./243.;
    gammaDF1(0,5) = -35./162.;
    gammaDF1(0,6) = -232./243.;
    gammaDF1(0,7) = +167./162.;
    gammaDF1(0,8) = -2272./729.;
            
    gammaDF1(1,0) = -45. + (20./3.)*nf; 
    gammaDF1(1,1) = -28./3.;
    gammaDF1(1,2) = -416./81.;
    gammaDF1(1,3) = 1280./81.;
    gammaDF1(1,4) = 56./81.;
    gammaDF1(1,5) = 35./27.;
    gammaDF1(1,6) = 464./81.;
    gammaDF1(1,7) = 76./27.;
    gammaDF1(1,8) = 1952./243.;
    
    gammaDF1(2,2) = -4468./81.;
    gammaDF1(2,3) = -29129./81. - (52./9.)*nf;
    gammaDF1(2,4) = 400./81.;
    gammaDF1(2,5) = 3493./108. - (2./9.)*nf;
    gammaDF1(2,6) = 64./81.;
    gammaDF1(2,7) = 368./27.;
    gammaDF1(2,8) = -4160./243. + (32.*n_d)/3. - (64.*n_u)/3.;
    
    gammaDF1(3,2) = -13678./243. + (368.*nf)/81.;       
    gammaDF1(3,3) = -79409./243. + (1334.*nf)/81.;
    gammaDF1(3,4) = 509./486. - (8.*nf)/81.;
    gammaDF1(3,5) = 13499./648. - (5.*nf)/27.;
    gammaDF1(3,6) = -680./243. + (32.*nf)/81;
    gammaDF1(3,7) = -427./81. - (37.*nf)/54.; 
    gammaDF1(3,8) = 784./729. - (2272.*n_d)/243. + (2912.*n_u)/243.;
            
    gammaDF1(4,2) = -244480./81. - (160./9.)*nf;
    gammaDF1(4,3) = -29648./81. - (2200./9.)*nf;
    gammaDF1(4,4) = 23116./81. + (16./9.)*nf;
    gammaDF1(4,5) = 3886./27. + (148./9.)*nf;
    gammaDF1(4,6) = -6464./81.;
    gammaDF1(4,7) = 8192./27. + 36.*nf;
    gammaDF1(4,8) = -58112./243. + (320.*n_d)/3. - (640.*n_u)/3.;
            
    gammaDF1(5,2) = 77600./243. - (1264./81.)*nf;
    gammaDF1(5,3) = -28808./243. + (164./81.)*nf;
    gammaDF1(5,4) = -20324./243. + (400./81.)*nf;
    gammaDF1(5,5) = -21211./162.+ (622./27.)*nf;
    gammaDF1(5,6) = -20096./243. - (976.*n_d)/81. + (2912.*n_u)/81.;
    gammaDF1(5,7) = -6040./81. + (220./27.)*nf;
    gammaDF1(5,8) = -22784./729. - (20704.*n_d)/243. + (28544.*n_u)/243.;
           
    gammaDF1(6,6) = 1936./9.-224./27.*nf-2*model.Beta1(nf); 
    
    gammaDF1(7,6) = -368./9.+224./81.*nf;
    gammaDF1(7,7) = 1456./9.-61./27.*nf-2*model.Beta1(nf);  
    
    gammaDF1(8,8) = -2.*model.Beta1(nf); 
    
    gammaDF1(9,9) = -2.*model.Beta1(nf); 
    
    gammaDF1(10,10)= -2.*model.Beta1(nf);
    
    gammaDF1(11,11)= -2.*model.Beta1(nf);
    
    gammaDF1(12,12)= -2.*model.Beta1(nf);
   
    break;
    default:
            throw std::runtime_error("EvolDF1bsg::AnomalousDimension_M(): order not implemented"); 
    }
    return (gammaDF1);
}

Df1EvolMll() [1/2]

void EvolDB1Mll::Df1EvolMll ( double  mu, double  M, double  nf, schemes  scheme  )

private

a void type method storing properly the magic numbers for the implementation of the evolutor

Parameters

mu	a double for the low scale of the evolution
M	a double for the high scale of the evolution
nf	a double for the active number of flavors
scheme	an enum "schemes" for the regularization scheme of the evolutor

Definition at line 393 of file EvolDB1Mll.cpp.

 {
 
    gslpp::matrix<double> resLO(dim, 0.), resNLO(dim, 0.), resNNLO(dim, 0.);
 
    int L = 6 - (int) nf;
    double alsM = model.Als(M) / 4. / M_PI;
    double alsmu = model.Als(mu) / 4. / M_PI;
    
    double eta = alsM / alsmu;
    
    for (unsigned int k = 0; k < dim; k++) {
        double etap = pow(eta, a[L][k] / 2. / model.Beta0(nf));
        for (unsigned int i = 0; i < dim; i++){
            for (unsigned int j = 0; j < dim; j++) {
                resNNLO(i, j) += 0.;
                
                if(fabs(e(i).real() - e(j).real() + 2. * model.Beta0(nf))>0.000000000001)  {
                    resNLO(i, j) += c[L][i][j][k] * etap * alsmu;
                    resNLO(i, j) += d[L][i][j][k] * etap * alsM;
                }
                else{
                    resNLO(i, j) += - c[L][i][j][k] * etap * alsmu * log(eta);    
                }        
                resLO(i, j) += b[L][i][j][k] * etap;
                if (fabs(resLO(i, j)) < 1.e-12) {resLO(i, j) = 0.;}
                if (fabs(resNLO(i, j)) < 1.e-12) {resNLO(i, j) = 0.;}
            }
        }
    }
    
    switch(order) {
        case NNLO:
            *elem[NNLO] = 0.;
        case NLO:
            *elem[NLO] = (*elem[LO]) * resNLO + (*elem[NLO]) * resLO;
        case LO:
            *elem[LO] = (*elem[LO]) * resLO;
            break;
        case FULLNNLO:
        case FULLNLO:
        default:
            throw std::runtime_error("Error in EvolDF1bsg::Df1Evolbsg()");
    } 
    
  }

Df1EvolMll() [2/2]

gslpp::matrix< double > & EvolDB1Mll::Df1EvolMll	(	double	mu,
		double	M,
		orders	order,
		schemes	scheme = NDR
	)

a method returning the evolutor related to the high scale \( M \) and the low scale \( \mu \)

Parameters

mu	a double for the low scale of the evolution
M	a double for the high scale of the evolution
order	an enum "orders" for the order of perturbation theory of the evolutor
scheme	an enum "schemes" for the regularization scheme of the evolutor

Returns

the evolutor \( U (\mu , M) \)

Definition at line 344 of file EvolDB1Mll.cpp.

{
 
    switch (scheme) {
        case NDR:
            break;
        case LRI:
        case HV:
        default:
            std::stringstream out;
            out << scheme;
            throw std::runtime_error("EvolDF1bsg::Df1Evolbsg(): scheme " + out.str() + " not implemented ");
    }
 
    double alsMZ = model.getAlsMz();
    double Mz = model.getMz();
    if (alsMZ == alsMZ_cache && Mz == Mz_cache) {
        if (mu == this->mu && M == this->M && scheme == this->scheme)
            return (*Evol(order));
    }
    alsMZ_cache = alsMZ;
    Mz_cache = Mz;
 
    if (M < mu) {
        std::stringstream out;
        out << "M = " << M << " < mu = " << mu;
        throw out.str();
    }
 
    setScales(mu, M); // also assign evol to identity
 
    if (M != mu) {
        double m_down = mu;
        double m_up = model.AboveTh(m_down);
        double nf = model.Nf(m_down);
 
        while (m_up < M) {
            Df1EvolMll(m_down, m_up, nf, scheme);
            m_down = m_up;
            m_up = model.AboveTh(m_down);
            nf += 1.;
        }
        Df1EvolMll(m_down, M, nf, scheme);
    }
 
    return (*Evol(order));
 
}

ToEffectiveBasis()

gslpp::matrix< double > EvolDB1Mll::ToEffectiveBasis

(

gslpp::matrix< double >

mat

)

const

a method returning the anomalous dimension for the evolution of the effective Wilson coefficients

Parameters

mat	a temporary variable of gslpp::matrix type

Returns

the ADM at the order LO/NLO for the effective Wilson coefficients

Definition at line 307 of file EvolDB1Mll.cpp.

{
    
    gslpp::matrix<double> y(dim, 0.);
    
    y(0,0) = 1.;
    y(1,1) = 1.;
    y(2,2) = 1.;
    y(3,3) = 1.;
    y(4,4) = 1.;
    y(5,5) = 1.;
    y(6,6) = 1.;
    y(7,7) = 1.;
    y(8,8) = 1.;
    y(9,9) = 1.;
    y(10,10) = 1.;
    y(11,11) = 1.;
    y(12,12) = 1.;
    
    y(6,2) = -1./3.;
    y(6,3) = -4./9.;
    y(6,4) = -20./3.;
    y(6,5) = -80./9.;
    
    y(7,2) = 1.;
    y(7,3) = -1./6.;
    y(7,4) = 20.;
    y(7,5) = -10./3.;
    
    y(8,2) = 4./3.;
    y(8,4) = 64./9.;
    y(8,5) = 64./27.; // Add terms proportional to Log(mb/mub))
    
    return( (y.inverse()).transpose() * mat * y.transpose() );
    
}

ToRescaleBasis()

gslpp::matrix< double > EvolDB1Mll::ToRescaleBasis	(	orders	order,
		unsigned int	n_u,
		unsigned int	n_d
	)		const

a method returning the anomalous dimension in the Chetyrkin, Misiak and Munz operator basis

Parameters

order	an enum "orders" for the order of perturbation theory of the evolutor
n_u	an unsigned integer for the up-type number of d.o.f.
n_d	an unsigned integer for the down-type number of d.o.f.

Returns

the ADM at the order LO/NLO in the Chetyrkin, Misiak and Munz basis

Definition at line 228 of file EvolDB1Mll.cpp.

{
    
    /* matrix entries for the anomalous dimension in the Chetyrkin, Misiak and Munz basis,
       ref. hep-ph/9711280v1, hep-ph/0504194 */
    
    gslpp::matrix<double> mat(dim, 0.);
    gslpp::matrix<double> mat1(dim, 0.);
    unsigned int nf = n_u + n_d;
    double z3 = gsl_sf_zeta_int(3);
    
    mat1(0,6) = - 13454./2187. + 44./2187.*nf;
    mat1(1,6) = 20644./729. - 88./729.*nf;
    mat1(2,6) = 119456./729. + 5440./729.*n_d -21776./729.*n_u;
    mat1(3,6) = - 202990./2187. + 32./729.*n_d*n_d + n_d*(16888./2187. + 64./729.*n_u)
                - 17132./2187.*n_u + 32./729.*n_u*n_u;
    mat1(4,6) = 530240./243. + 300928./729.*n_d - 461120./729.*n_u;
    mat1(5,6) = - 1112344./729. + 5432./729.*n_d*n_d + n_d*(419440./2187. - 
                2744./729.*n_u) + 143392./2187.*n_u - 8176./729.*n_u*n_u;
    
    mat1(0,7) = 25759./5832. + 431./5832.*nf;
    mat1(1,7) = 9733./486. - 917./972.*nf;
    mat1(2,7) = 82873./243. - 3361./243.*nf;
    mat1(3,7) = - 570773./2916. - 253./486.*n_d*n_d +n_d*(-40091./5832. - 
                253./243.*n_u) - 40091./5832.*n_u - 253./486.*n_u*n_u;
    mat1(4,7) = 838684./81. - 14.*n_d*n_d + n_d*(129074./243. - 28.*n_u) + 
                129074./243.*n_u - 14.*n_u*n_u;
    mat1(5,7) = - 923522./243. - 6031./486.*n_d*n_d + n_d*(-13247./1458. - 6031./243.*n_u)
                -13247./1458.*n_u - 6031./486.*n_u*n_u;
    
    mat1(0,8) = - 2357278./19683. + 14440./6561.*n_d + 144688./6561.*n_u + 6976./243.*z3;
    mat1(1,8) = - 200848./6561. - 23696./2187.*n_d + 30736./2187.*n_u - 3584./81.*z3;
    mat1(2,8) = - 1524104./6561. - 176./27.*n_d*n_d + 352./27.*n_u*n_u +
                n_d*(257564./2187. + 176./27.*n_u - 128./3.*z3) - 256./81.*z3 + 
                n_u*(-382984./2187. + 256./3.*z3); 
    mat1(3,8) = 1535926./19683. + 1984./2187.*n_d*n_d - 5792./2187.*n_u*n_u +
                n_d*(-256901./6561. - 3808./2187.*n_u - 2720./81.*z3) - 
                5056./243.*z3 + n_u*(34942./6561. + 1600./81.*z3);
    mat1(4,8) = - 31433600./6561. - 2912./27.*n_d*n_d + 5824./27.*n_u*n_u +
                n_d*(- 3786616./2187. + 2912./27.*n_u - 1280./3.*z3) -
                4096./81.*z3 + n_u*(7525520./2187. + 2560./3.*z3);
    mat1(5,8) = 48510784./19683. -51296./2187.*n_d*n_d + 54976./2187.*n_u*n_u +
                n_u*(-11231648./6561. - 22016./81.*z3) + n_d*(340984./6561. + 
                3680./2187.*n_u - 8192./81.*z3) - 80896./243.*z3;
     
    
    switch(order){
        case(NLO): 
            mat = AnomalousDimension_M(NLO, n_u, n_d);
            for (unsigned int i=0; i<6; i++){
                for (unsigned int j=6; j<dim; j++){
                    mat(i,j) = mat1(i,j);
                }
            }
            for (unsigned int i=6; i<dim; i++){
                for (unsigned int j=6; j<dim; j++){
                    mat(i,j) = mat(i,j) + 2. * (i==j) * model.Beta1(nf);
                }
            }
            return (mat);
        case(LO):
            mat = AnomalousDimension_M(LO, n_u, n_d);
            for (unsigned int i=0; i<6; i++){
                for (unsigned int j=6; j<dim; j++){
                    mat(i,j) = AnomalousDimension_M(NLO, n_u, n_d)(i,j);
                }
            }
            for (unsigned int i=6; i<dim; i++){
                for (unsigned int j=6; j<dim; j++){
                    mat(i,j) = mat(i,j) + 2. * (i==j) * model.Beta0(nf);
                }
            }
            return (mat);
        default:
            throw std::runtime_error("change to rescaled operator basis: order not implemented"); 
    }
    
}

Member Data Documentation

a

double EvolDB1Mll::a[4][13]

private

Parameters

a	array of double for the magic numbers of the evolutor ( LO evolution )
b	array of double for the magic numbers of the evolutor ( LO evolution )
c	array of double for the magic numbers of the evolutor ( NLO evolution, associated to \( \alpha_{strong}(\mu) \) )
d	array of double for the magic numbers of the evolutor ( NLO evolution, associated to \( \alpha_{strong}(M) \) )

Definition at line 82 of file EvolDB1Mll.h.

alsMZ_cache

double EvolDB1Mll::alsMZ_cache

private

Definition at line 95 of file EvolDB1Mll.h.

b

double EvolDB1Mll::b[4][13][13][13]

private

Definition at line 82 of file EvolDB1Mll.h.

c

double EvolDB1Mll::c[4][13][13][13]

private

Definition at line 82 of file EvolDB1Mll.h.

d

double EvolDB1Mll::d[4][13][13][13]

private

Definition at line 82 of file EvolDB1Mll.h.

dim

unsigned int EvolDB1Mll::dim

private

Definition at line 94 of file EvolDB1Mll.h.

e

gslpp::vector<gslpp::complex> EvolDB1Mll::e

private

Definition at line 93 of file EvolDB1Mll.h.

gg

gslpp::matrix<gslpp::complex> EvolDB1Mll::gg

private

Definition at line 92 of file EvolDB1Mll.h.

h

gslpp::matrix<gslpp::complex> EvolDB1Mll::h

private

Definition at line 92 of file EvolDB1Mll.h.

js

gslpp::matrix<gslpp::complex> EvolDB1Mll::js

private

Definition at line 92 of file EvolDB1Mll.h.

jss

gslpp::matrix<gslpp::complex> EvolDB1Mll::jss

private

Definition at line 92 of file EvolDB1Mll.h.

jssv

gslpp::matrix<gslpp::complex> EvolDB1Mll::jssv

private

Definition at line 92 of file EvolDB1Mll.h.

jv

gslpp::matrix<gslpp::complex> EvolDB1Mll::jv

private

Definition at line 92 of file EvolDB1Mll.h.

model

const StandardModel& EvolDB1Mll::model

private

Definition at line 83 of file EvolDB1Mll.h.

Mz_cache

double EvolDB1Mll::Mz_cache

private

Definition at line 96 of file EvolDB1Mll.h.

nd

int EvolDB1Mll::nd

private

Definition at line 75 of file EvolDB1Mll.h.

nu

int EvolDB1Mll::nu

private

Parameters

nu	an unsigned integer for the up-type number of d.o.f.
nu	an unsigned integer for the down-type number of d.o.f.

Definition at line 75 of file EvolDB1Mll.h.

s_s

gslpp::matrix<gslpp::complex> EvolDB1Mll::s_s

private

Definition at line 92 of file EvolDB1Mll.h.

v

gslpp::matrix<gslpp::complex> EvolDB1Mll::v

private

Definition at line 92 of file EvolDB1Mll.h.

vi

gslpp::matrix<gslpp::complex> EvolDB1Mll::vi

private

Definition at line 92 of file EvolDB1Mll.h.

vij

gslpp::matrix<gslpp::complex> EvolDB1Mll::vij

private

Definition at line 92 of file EvolDB1Mll.h.

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

• EvolDB1Mll.h
• EvolDB1Mll.cpp