Decoupling relations to O(α s3) and their connection to low-energy theorems

• Published in: Nuclear physics. B Vol. 510; no. 1; pp. 61 - 87
• Main Authors: Chetyrkin, K.G., Kniehl, B.A., Steinhauser, M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 1998
• Subjects: Perturbative calculations; Standard-model Higgs bosons; Strong-coupling expansions; 11.15.Me; 12.38.Bx; Perturbative calculations; Strong-coupling expansions; Standard-model Higgs bosons; 14.80.Bn
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/S0550-3213(98)81004-3

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 with respect to m h , of ζ g and ζ m , respectively. Fully exploiting the 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.