A simple generalization of the low-energy theorem for the effective Higgs-gluon-gluon coupling for the case of simultaneous decoupling of several heavy quarks

TL;DR

This paper presents a straightforward extension of the low-energy theorem for the effective Higgs-gluon-gluon coupling, accommodating multiple heavy quarks decoupling simultaneously, enabling higher-order calculations relevant for beyond Standard Model physics.

Contribution

It introduces a simple, generalized method to extend the low-energy theorem for Higgs-gluon interactions to cases with several heavy quarks decoupling simultaneously.

Findings

Derived a four-loop effective Higgs-gluon-gluon coupling formula.

Enabled extraction of higher-order couplings from existing three-loop decoupling results.

Applicable to models extending the Standard Model with additional heavy quarks.

Abstract

We extend in an extremely simple and straightforward way the well-known low-energy theorem for an effective Higgs-like scalar-gluon-gluon coupling [1] (as well as a similar one for for the effective coupling of the Higgs-like field to the light scalar quark currents) in QCD including arbitrary number of heavy quarks in addition to the light ones. The application of the generalized low-energy theorem allows the extraction of the four-loop effective Higgs-gluon-gluon coupling valid for extensions of the Standard Model with additional heavy quarks from the 3-loop results of [2] for the decoupling constant of $\alpha_s$.