Decoupling constant for $\alpha_s$ and the effective gluon-Higgs coupling to three loops in supersymmetric QCD

TL;DR

This paper calculates three-loop QCD corrections to the decoupling constant for the strong coupling and derives a low-energy theorem to relate the effective Higgs-gluon coupling to these corrections, aiding high-scale alpha_s evaluations.

Contribution

It provides the first three-loop independent calculation of the Higgs-gluon effective coupling coefficient using decoupling constants in supersymmetric QCD.

Findings

Three-loop decoupling constant for alpha_s computed.

Derived a low-energy theorem linking Higgs-gluon coupling to decoupling constant.

First independent three-loop check of the matching coefficient.

Abstract

We compute the three-loop QCD corrections to the decoupling constant for $\alpha_s$ 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 $\alpha_s$ 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.