Decoupling relations, effective Lagrangians and low-energy theorems
Abstract
Description
If 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 zeta_m, respectively. Adopting the modified MS (MS-bar) scheme, we derive simple formulae which reduce the calculation of zeta_g and zeta_m to the solution of vacuum integrals. This allows us to evaluate zeta_g and zeta_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 zeta_g and zeta_m, respectively. We also consider the effective QCD interaction of a CP-odd Higgs boson and verify the Adler-Bardeen nonrenormalization theorem at three loops.
10 pages (Latex), 4 figures (Postscript), 1 style file, to appear in the Proceedings of the IVth International Symposium on Radiative Corrections (RADCOR 98), Barcelona, Spain, 8-12 September 1998, edited by J. Sola
10 pages (Latex), 4 figures (Postscript), 1 style file, to appear in the Proceedings of the IVth International Symposium on Radiative Corrections (RADCOR 98), Barcelona, Spain, 8-12 September 1998, edited by J. Sola