Abstract
An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients CH and CHH for one and two Higgs bosons, respectively. In this work we calculate for the first time CHH to four loops in a direct, diagrammatic way, discussing in detail all issues arising due to the renormalization of operator products. Furthermore, we also calculate the Wilson coefficient CH for the coupling of a single Higgs boson to gluons as well as all four loop decoupling relations in QCD with general SU(Nc) colour factors. The latter are related to CH and CHH via low-energy theorems, which are used to obtain five-loop results for the Wilson coefficients.
Highlights
Two-loop results for CH have been known since the beginning of the eighties [3, 4] and at three-loop order CH was obtained for the first time from a direct calculation of the Higgs-gluon vertex in the large-mt limit in ref. [5]
An important ingredient for the calculation of Higgs boson properties in the infinite top quark mass limit is the knowledge of the effective coupling between the Higgs bosons and gluons, i.e. the Wilson coefficients CH and CHH for one and two Higgs bosons, respectively
Using the three-loop decoupling constant for αs, the LET in combination with the four-loop beta function [8, 9] even leads to the four-loop result for CH
Summary
For convenience of the reader and to fix our notation we repeat the definition of the decoupling constants in QCD and the Wilson coefficients in the effective Lagrange density describing Higgs-gluon couplings. For a detailed discussion we refer to ref. We will work in the MS scheme throughout this paper, except for the heavy quark mass which we renormalize both in the MS and on-shell scheme. The MS counterterms are needed up to four-loop order [17]) and the renormalization constant for the MS to on-shell conversion for the heavy quark mass to three loops [18,19,20,21] The MS counterterms are needed up to four-loop order (see, e.g., ref. [17]) and the renormalization constant for the MS to on-shell conversion for the heavy quark mass to three loops [18,19,20,21]
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