Decoupling constant for α s and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

Abstract

We compute the three-loop QCD corrections to the decoupling constant for α s which relates the Minimal Supersymmetric Standard Model to Quantum Chromodynamics with five or six active flavours. The new results can be used to study the stability of α s evaluated at a high scale from the knowledge of its value at M Z . We furthermore derive a low-energy theorem which allows the calculation of the coefficient function of the effective Higgs boson-gluon operator from the decoupling constant. This constitutes the first independent check of the matching coefficient to three loops.

Supersymmetric next-to-next-to-leading order corrections to Higgs boson production in gluon fusion

“…The three-loop results for the matching coefficients which are presented in this paper have been confirmed by an independent calculation in Ref. [29]. Note that the calculations in the paper are performed in the framework of the MSSM, however, they are in principle not limited to the minimal version and could, e.g., also be applied to the so-called Next-to-Minimal Supersymmetric Standard Model (NMSSM) where an additional singlet Higgs field is added as compared to the MSSM.…”

“…In order to select the representation which leads to the best approximation we define two quantities which we require to be small (see also Ref. [29]). The first one controls the deviation to the exact two-loop result and is defined through…”

“…Exact results can be obtained from the calculations performed in Ref. [40] but also from [29] explicit result is provided. Note that it is important to have at hand the one-loop term of ζ αs up to order since at this step C 0 1 still contains poles originating from the light degrees of freedom.…”

Higgs boson production in the SM and MSSM to NNLO and beyond

“…In Refs. [18,19] hierarchies in the occurring masses have been defined in such a way that phenomenological interesting scenarios can be studied. Furthermore, sophisticated expansion schemes have been defined which select the representation of the perturbative series with largest radius of convergence.…”

“…The results of [18] have been cross-checked in Ref. [19] where a low-energy theorem has been used in order to obtain C 1 from the decoupling constant of α s .…”