Decoupling relations to O(αs3) and their connection to low-energy theorems Original Research Article

If quantum chromodynamics (QCD) is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant αs and the quark masses mq exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, ζg and ζm, respectively. Adopting the modified MS (MS) scheme, we derive simple formulae which reduce the calculation of ζg and ζm to the solution of vacuum integrals. This allows us to evaluate ζg and ζm 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 with respect to mh, of ζg and ζm, respectively. Fully exploiting the present knowledge of the anomalous dimensions of αs and mq, we thus calculate these effective couplings through four loops. Finally, we perform a similar analysis for the coupling of the Higgs boson to photons.