Simultaneous decoupling of bottom and charm quarks
  We compute the decoupling relations for the strong coupling, the light quark masses, the gauge-fixing parameter, and the light fields in QCD with heavy charm and bottom quarks to three-loop accuracy taking into account the exact dependence on $m_c/m_b$. The application of a low-energy theorem allows the extraction of the three-loop effective Higgs-gluon coupling valid for extensions of the Standard Model with additional heavy quarks from the decoupling constant of $\alpha_s$. 
Andrey G.Grozin, Maik Hoeschele, Jens Hoff, Matthias Steinhauser
hep-ph