  If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS),
at higher orders, the strong coupling constant alpha_s and the quark masses m_q
exhibit discontinuities at the flavour thresholds, which are controlled by
so-called decoupling constants, zeta_g and zeta_m, respectively. Adopting the
modified MS (MS-bar) scheme, we derive simple formulae which reduce the
calculation of zeta_g and zeta_m to the solution of vacuum integrals. This
allows us to evaluate zeta_g and zeta_m through three loops. We also establish
low-energy theorems, valid to all orders, which relate the effective couplings
of the Higgs boson to gluons and light quarks, due to the virtual presence of a
heavy quark h, to the logarithmic derivatives w.r.t. m_h of zeta_g and zeta_m,
respectively. Fully exploiting present knowledge of the anomalous dimensions of
alpha_s and m_q, we thus calculate these effective couplings through four
loops. Finally, we perform a similar analysis for the coupling of the Higgs
boson to photons.
