Decoupling relations, effective Lagrangians and low-energy theorems

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If QCD is renormalized by minimal subtraction (MS), at higher orders, the strong coupling constant alphaₛ and the quark masses mq exhibit discontinuities at the flavour thresholds, which are controlled by so-called decoupling constants, zetag and zetaₘ, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zetag and zetaₘ to the solution of vacuum integrals. This allows us to evaluate zetag and zetaₘ 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. mₕ of zetag and zetaₘ, respectively. We also consider the effective QCD interaction of a CP-odd Higgs boson and verify the Adler-Bardeen nonrenormalization theorem at three loops.