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// -*- C++ -*-
//
// AlphaS.h is a part of Herwig - A multi-purpose Monte Carlo event generator
// Copyright (C) 2018-2019 The Herwig Collaboration
//
// Herwig is licenced under version 3 of the GPL, see COPYING for details.
// Please respect the MCnet academic guidelines, see GUIDELINES for details.
//
#ifndef HERWIG_UtilAlphaS_H
#define HERWIG_UtilAlphaS_H
namespace Herwig {
namespace Math {
/**
* The derivative of \f$\alpha_S\f$ with respect to \f$\ln(Q^2/\Lambda^2)\f$
* @param q The scale
* @param lam \f$\Lambda_{\rm QCD}\f$
* @param nf The number of flavours
*/
inline double derivativeAlphaS(Energy q, Energy lam,
unsigned int nf, unsigned int nloop) {
using Constants::pi;
double lx = log(sqr(q/lam));
double b0 = 11. - 2./3.*nf;
double b1 = 51. - 19./3.*nf;
double b2 = 2857. - 5033./9.*nf + 325./27.*sqr(nf);
if(nloop==1)
return -4.*pi/(b0*sqr(lx));
else if(nloop==2)
return -4.*pi/(b0*sqr(lx))*(1.+2.*b1/sqr(b0)/lx*(1.-2.*log(lx)));
else
return -4.*pi/(b0*sqr(lx))*
(1. + 2.*b1/sqr(b0)/lx*(1.-2.*log(lx))
+ 4.*sqr(b1)/(sqr(sqr(b0))*sqr(lx))*(1. - 2.*log(lx)
+ 3.*(sqr(log(lx) - 0.5)+b2*b0/(8.*sqr(b1))-1.25)));
}
/**
* The 1,2,3-loop parametrization of \f$\alpha_S\f$.
* @param q The scale
* @param lam \f$\Lambda_{\rm QCD}\f$
* @param nf The number of flavours
*/
inline double alphaS(Energy q, Energy lam,
unsigned int nf, unsigned int nloop) {
using Constants::pi;
double lx(log(sqr(q/lam)));
double b0 = 11. - 2./3.*nf;
double b1 = 51. - 19./3.*nf;
double b2 = 2857. - 5033./9.*nf + 325./27.*sqr(nf);
// one loop
if(nloop==1)
{return 4.*pi/(b0*lx);}
// two loop
else if(nloop==2) {
return 4.*pi/(b0*lx)*(1.-2.*b1/sqr(b0)*log(lx)/lx);
}
// three loop
else
{return 4.*pi/(b0*lx)*(1.-2.*b1/sqr(b0)*log(lx)/lx +
4.*sqr(b1)/(sqr(sqr(b0))*sqr(lx))*
(sqr(log(lx) - 0.5) + b2*b0/(8.*sqr(b1)) - 5./4.));}
}
}
}
#endif

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