DECOUPLING RELATIONS TO O(ALPHA(3)(S)) AND THEIR CONNECTION TO LOW-ENERGY THEOREMS

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 ze ta(m), respectively. Adopting the modified MS (MS) scheme, we derive s imple formulae which reduce the calculation of zeta(g) and zeta(m) to the solution of vacuum integrals. This allows us to evaluate zeta(g) a nd zeta(m) through three loops. We also establish low-energy theorems, valid to all orders, which relate the effective couplings of the Higg s boson to gluons and light quarks, due to the virtual presence of a h eavy quark h, to the logarithmic derivatives with respect to m(h) of z eta(g) and zeta(m), respectively. Fully exploiting the present knowled ge of the anomalous dimensions of alpha(s) and m(q), we thus calculate these effective couplings through four loops. Finally, we perform a s imilar analysis for the coupling of the Higgs boson to photons. (C) 19 98 Elsevier Science B.V.