EvtVubdGamma Class Reference

#include <EvtVubdGamma.hh>

Public Member Functions
	EvtVubdGamma (const double &alphas)
virtual	~EvtVubdGamma ()
double	getdGdxdzdp (const double &x, const double &z, const double &p2)

Protected Member Functions
double	delta (const double &x, const double &xmin, const double &xmax)
double	getW1nodelta (const double &x, const double &z, const double &p2)
double	getW2nodelta (const double &x, const double &z, const double &p2)
double	getW3nodelta (const double &x, const double &z, const double &p2)
double	getW4nodelta (const double &x, const double &z, const double &p2)
double	getW5nodelta (const double &x, const double &z, const double &p2)
double	getW1delta (const double &x, const double &z)
double	getW4plus5delta (const double &x, const double &z)

Detailed Description

Definition at line 38 of file EvtVubdGamma.hh.

Constructor & Destructor Documentation

EvtVubdGamma()

EvtVubdGamma::EvtVubdGamma

(

const double &

alphas

)

Definition at line 52 of file EvtVubdGamma.cc.

                                                 {
  _alphas = alphas;
 
  // the range for the delta distribution in p2 is from _epsilon1 to
  // _epsilon2. It was checked with the single differential formulae
  // in the paper that these values are small enough to imitate p2 = 0
  // for the regular terms.
  // The ()* distributions, however need further treatment. In order to
  // generate the correct spectrum in z a threshold need to be computed
  // from the desired value of the coupling alphas. The idea is that
  // for z=1 p2=0 is not allowed and therefore the part of dGamma proportional
  // to delta(p2) should go to 0 for z->1.
  // Using equation (3.1) and (3.2) it is possible to find the correct value
  // for log(_epsilon3) from this requirement.
 
  _epsilon1 = 1e-10;
  _epsilon2 = 1e-5;
  if ( alphas > 0 )
  {
    double lne3 = 9. / 16. - 2 * M_PI * M_PI / 3. + 6 * M_PI / 4 / alphas;
    if ( lne3 > 0 ) lne3 = -7. / 4. - sqrt( lne3 );
    else lne3 = -7. / 4.;
    _epsilon3 = exp( lne3 );
  }
  else _epsilon3 = 1;
}

~EvtVubdGamma()

EvtVubdGamma::~EvtVubdGamma ( )

virtual

Definition at line 83 of file EvtVubdGamma.cc.

{}

Member Function Documentation

delta()

double EvtVubdGamma::delta ( const double & x, const double & xmin, const double & xmax )

protected

Definition at line 133 of file EvtVubdGamma.cc.

                                                                                    {
  if ( xmin > 0 || xmax < 0 ) return 0.;
  if ( _epsilon1 < x && x < _epsilon2 ) return 1. / ( _epsilon2 - _epsilon1 );
  return 0.0;
}

Referenced by getdGdxdzdp().

getdGdxdzdp()

double EvtVubdGamma::getdGdxdzdp	(	const double &	x,
		const double &	z,
		const double &	p2 )

Definition at line 89 of file EvtVubdGamma.cc.

                                                                                     {
  // check phase space
 
  double xb = ( 1 - x );
 
  if ( x < 0 || x > 1 || z < xb || z > ( 1 + xb ) ) return 0;
 
  // not used
  // double mx = (0>z-1?0:z-1);
 
  double p2min = ( 0 > z - 1. ? 0 : z - 1. );
  double p2max = ( 1. - x ) * ( z - 1. + x );
 
  if ( p2 < p2min || p2 > p2max ) return 0;
 
  //  // check the phase space
  //  return 1.;
 
  double dG;
 
  if ( p2 > _epsilon1 && p2 < _epsilon2 )
  {
 
    double W1      = getW1delta( x, z );
    double W4plus5 = getW4plus5delta( x, z );
 
    dG = 12. * delta( p2, p2min, p2max ) *
         ( ( 1. + xb - z ) * ( z - xb ) * W1 + xb * ( z - xb ) * ( W4plus5 ) );
  }
  else
  {
 
    double W1 = getW1nodelta( x, z, p2 );
    double W2 = getW2nodelta( x, z, p2 );
    double W3 = getW3nodelta( x, z, p2 );
    double W4 = getW4nodelta( x, z, p2 );
    double W5 = getW5nodelta( x, z, p2 );
 
    dG = 12. * ( ( 1. + xb - z ) * ( z - xb - p2 ) * W1 + ( 1. - z + p2 ) * W2 +
                 ( xb * ( z - xb ) - p2 ) * ( W3 + W4 + W5 ) );
  }
  return dG;
}

getW1delta()

double EvtVubdGamma::getW1delta ( const double & x, const double & z )

protected

Definition at line 139 of file EvtVubdGamma.cc.

                                                                  {
  double mz = 1. - z;
  // double p2min = (0>z-1.?0:z-1.);
  // double p2max = (1.-x)*(z-1.+x);
 
  double lz;
  if ( z == 1 ) lz = -1.;
  else lz = log( z ) / ( 1. - z );
 
  // ddilog_(&z) is actually the dilog of (1-z) in maple,
  // also in Neuberts paper the limit dilog(1) = pi^2/6 is used
  // this corresponds to maple's dilog(0), so
  // I take ddilog_(&mz) where mz=1-z in order to satisfy Neubert's definition
  // and to compare with Maple the argument in maple should be (1-mz) ...
 
  double dl = 4. * ddilog_( &mz ) + 4. * pow( M_PI, 2 ) / 3.;
 
  double w = -( 8. * pow( log( z ), 2 ) - 10. * log( z ) + 2. * lz + dl + 5. ) +
             ( 8. * log( z ) - 7. ) * log( _epsilon3 ) - 2. * pow( log( _epsilon3 ), 2 );
 
  return ( 1. + w * _alphas / 3. / M_PI );
}

Referenced by getdGdxdzdp().

getW1nodelta()

double EvtVubdGamma::getW1nodelta ( const double & x, const double & z, const double & p2 )

protected

Definition at line 162 of file EvtVubdGamma.cc.

                                                                                      {
 
  double z2 = z * z;
  double t2 = 1. - 4. * p2 / z2;
  double t  = sqrt( t2 );
 
  double w = 0;
  if ( p2 > _epsilon2 )
    w += 4. / p2 * ( log( ( 1. + t ) / ( 1. - t ) ) / t + log( p2 / z2 ) ) + 1. -
         ( 8. - z ) * ( 2. - z ) / z2 / t2 +
         ( ( 2. - z ) / 2. / z + ( 8. - z ) * ( 2. - z ) / 2. / z2 / t2 ) *
             log( ( 1. + t ) / ( 1. - t ) ) / t;
  if ( p2 > _epsilon3 ) w += ( 8. * log( z ) - 7. ) / p2 - 4. * log( p2 ) / p2;
 
  return w * _alphas / 3. / M_PI;
}

Referenced by getdGdxdzdp().

getW2nodelta()

double EvtVubdGamma::getW2nodelta ( const double & x, const double & z, const double & p2 )

protected

Definition at line 179 of file EvtVubdGamma.cc.

                                                                                      {
 
  double z2  = z * z;
  double t2  = 1. - 4. * p2 / z2;
  double t   = sqrt( t2 );
  double w11 = ( 32. - 8. * z + z2 ) / 4. / z / t2;
 
  double w = 0;
  if ( p2 > _epsilon2 )
    w -= ( z * t2 / 8. + ( 4. - z ) / 4. + w11 / 2. ) * log( ( 1. + t ) / ( 1. - t ) ) / t;
  if ( p2 > _epsilon2 ) w += ( 8. - z ) / 4. + w11;
 
  return ( w * _alphas / 3. / M_PI );
}

Referenced by getdGdxdzdp().

getW3nodelta()

double EvtVubdGamma::getW3nodelta ( const double & x, const double & z, const double & p2 )

protected

Definition at line 194 of file EvtVubdGamma.cc.

                                                                                      {
  double z2 = z * z;
  double t2 = 1. - 4. * p2 / z2;
  double t4 = t2 * t2;
  double t  = sqrt( t2 );
 
  double w = 0;
 
  if ( p2 > _epsilon2 )
    w += ( z * t2 / 16. + 5. * ( 4. - z ) / 16. - ( 64. + 56. * z - 7. * z2 ) / 16. / z / t2 +
           3. * ( 12. - z ) / 16. / t4 ) *
         log( ( 1. + t ) / ( 1. - t ) ) / t;
  if ( p2 > _epsilon2 )
    w += -( 8. - 3. * z ) / 8. + ( 32. + 22. * z - 3. * z2 ) / 4. / z / t2 -
         3. * ( 12. - z ) / 8. / t4;
 
  return ( w * _alphas / 3. / M_PI );
}

Referenced by getdGdxdzdp().

getW4nodelta()

double EvtVubdGamma::getW4nodelta ( const double & x, const double & z, const double & p2 )

protected

Definition at line 213 of file EvtVubdGamma.cc.

                                                                                      {
  double z2 = z * z;
  double t2 = 1. - 4. * p2 / z2;
  double t4 = t2 * t2;
  double t  = sqrt( t2 );
 
  double w = 0;
 
  if ( p2 > _epsilon2 )
    w -= ( ( 8. - 3. * z ) / 4. / z - ( 22. - 3. * z ) / 2. / z / t2 +
           3. * ( 12. - z ) / 4. / z / t4 ) *
         log( ( 1. + t ) / ( 1. - t ) ) / t;
  if ( p2 > _epsilon2 )
    w += -1. - ( 32. - 5. * z ) / 2. / z / t2 + 3. * ( 12. - z ) / 2. / z / t4;
 
  return w * _alphas / 3. / M_PI;
}

Referenced by getdGdxdzdp().

getW4plus5delta()

double EvtVubdGamma::getW4plus5delta ( const double & x, const double & z )

protected

Definition at line 231 of file EvtVubdGamma.cc.

                                                                       {
 
  double w = 0;
 
  if ( z == 1 ) w = -2;
  else w = 2. * log( z ) / ( 1. - z );
 
  return ( w * _alphas / 3. / M_PI );
}

Referenced by getdGdxdzdp().

getW5nodelta()

double EvtVubdGamma::getW5nodelta ( const double & x, const double & z, const double & p2 )

protected

Definition at line 241 of file EvtVubdGamma.cc.

                                                                                      {
  double z2 = z * z;
  double t2 = 1. - 4. * p2 / z2;
  double t4 = t2 * t2;
  double t  = sqrt( t2 );
 
  double w = 0;
  if ( p2 > _epsilon2 )
    w += ( 1. / 4. / z - ( 2. - z ) / 2. / z2 / t2 + 3. * ( 12. - z ) / 4. / z2 / t4 ) *
         log( ( 1. + t ) / ( 1. - t ) ) / t;
  if ( p2 > _epsilon2 ) w += -( 8. + z ) / 2. / z2 / t2 - 3. * ( 12. - z ) / 2. / z2 / t4;
 
  return ( w * _alphas / 3. / M_PI );
}

Referenced by getdGdxdzdp().

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

• EvtVubdGamma.hh
• EvtVubdGamma.cc