Decoupling of heavy quarks at four loops and effective Higgs-fermion coupling

Abstract

We compute the decoupling constant $\zeta_m$ relating light quark masses of effective $n_l$-flavour QCD to $(n_l+1)$-flavour QCD to four-loop order. Immediate applications are the evaluation of the $\overline{\rm MS}$ charm quark mass with five active flavours and the bottom quark mass at the scale of the top quark or even at GUT scales. With the help of a low-energy theorem $\zeta_m$ can be used to obtain the effective coupling of a Higgs boson to light quarks with five-loop accuracy. We briefly discuss the influence on $\Gamma(H\to b\bar{b})$.