double kFacW(double mass)
// mass dependent NNLO/LO* K-Factor
// = sigma_NNLO(MSTW2008NNLO)/sigma_LO(MRST2007LO*)
// for W+- (average over charges)
// mass in GeV
// parameterization valid for 10GeV<mass<3TeV (<1% accuracy for mass<2TeV)
{
  double par[5]={ -0.0005348, -3.866e-05, -4.729e-07, -2.039e-06, -7.019e-08 };
  // fix K-factor at M=80GeV and account for additional 1.6% correction
  // to match inclusive W cross section NNLO prediction (difference due to
  // different parameter settings)
  double kF=1.151*1.016;
  if(mass<80.)
    {
      kF *= 1.+par[0]*(mass-80.)+par[1]*(mass-80.)*(mass-80.)+par[2]*(mass-80.)*(mass-80.)*(mass-80.);
    }
  else
    {
      kF *= 1.+par[3]*(mass-80.)+par[4]*(mass-80.)*(mass-80.);
    }
  return kF;
}

double kFacWp(double mass)
// mass dependent NNLO/LO* K-Factor
// = sigma_NNLO(MSTW2008NNLO)/sigma_LO(MRST2007LO*)
// for W+
// mass in GeV
// parameterization valid for 10GeV<mass<3TeV (<1% accuracy for mass<2TeV)
{
  double par[5]={ -0.0004491, -3.62e-05, -4.321e-07, -1.19e-05, -6.911e-08 };
  // fix K-factor at M=80GeV and account for additional 1.6% correction
  // to match inclusive W cross section NNLO prediction (difference due to
  // different parameter settings)
  double kF=1.156*1.016;
  if(mass<80.)
    {
      kF *= 1.+par[0]*(mass-80.)+par[1]*(mass-80.)*(mass-80.)+par[2]*(mass-80.)*(mass-80.)*(mass-80.);
    }
  else
    {
      kF *= 1.+par[3]*(mass-80.)+par[4]*(mass-80.)*(mass-80.);
    }
  return kF;
}

double kFacWm(double mass)
// mass dependent NNLO/LO* K-Factor
// = sigma_NNLO(MSTW2008NNLO)/sigma_LO(MRST2007LO*)
// for W-
// mass in GeV
// parameterization valid for 10GeV<mass<3TeV (<1% accuracy for mass<2TeV)
{
  double par[5]={ -0.0004639, -3.58e-05, -4.749e-07, 1.968e-05, -7.301e-08 };
  // fix K-factor at M=80GeV and account for additional 1.6% correction
  // to match inclusive W cross section NNLO prediction (difference due to
  // different parameter settings)
  double kF=1.145*1.016;
  if(mass<80.)
    {
      kF *= 1.+par[0]*(mass-80.)+par[1]*(mass-80.)*(mass-80.)+par[2]*(mass-80.)*(mass-80.)*(mass-80.);
    }
  else
    {
      kF *= 1.+par[3]*(mass-80.)+par[4]*(mass-80.)*(mass-80.);
    }
  return kF;
}