If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant α s and the quark masses m q exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, ζ g and ζ m , respectively. Adopting the modified MS (MS) scheme, we derive simple formulae which reduce the calculation of ζ g and ζ m to the solution of vacuum integrals. This allows us to evaluate ζ g and ζ 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 ζ g and ζ m , respectively. Fully exploiting present knowledge of the anomalous dimensions of α 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.