Effective multi-Higgs couplings to gluons

Michael Spira

doi:10.1007/jhep10(2016)026

Abstract

Standard-Model Higgs bosons are dominantly produced via the gluon-fusion mechanism $gg \to H$ at the LHC, i.e. in a loop-mediated process with top loops providing the dominant contribution. For the measured Higgs boson mass of $\sim 125$ GeV the limit of heavy top quarks provides a reliable approximation as long as the relative QCD corrections are scaled with the full mass-dependent LO cross section. In this limit the Higgs coupling to gluons can be described by an effective Lagrangian. The same approach can also be applied to the coupling of more than one Higgs boson to gluons. We will derive the effective Lagrangian for multi-Higgs couplings to gluons up to N$^4$LO thus extending previous results for more than one Higgs boson. Moreover we discuss gluonic Higgs couplings up to NNLO, if several heavy quarks contribute.

Highlights

Standard-Model Higgs bosons are dominantly produced via the gluon-fusion mechanism gg → H at the LHC, i.e. in a loop-mediated process with top loops providing the dominant contribution
The effective Lagrangians can be used for the computation of the production of one or several Higgs bosons in gluon fusion at hadron colliders in the limit of heavy quarks
In the second part we extended the analysis to the case of several heavy quarks coupling to the Higgs bosons up to NNLO

Summary

Gaμν Gaμν v v

P replacement mt (μ2R ) → mt (μ2R )(1 + i ci Hi /v) has to be implemented, where ci are the top quark Yukawa couplings normalized to the SM coupling. → 6 p−m of the top-quark propagators inside the gluonic correlation functions up to 4th p−mt t v 6 p−mt order in the gluon fields at the point where mt is either the unrenormalized or the pure MS mass [28] This step corresponds to adding the external MS-renormalized self-energies and twopoint-function contributions to the vertices involving top quarks at vanishing external momentum. JHEP10(2016)[026] where H denotes the physical Higgs field, v the vacuum expectation value and Πt the contribution to the Wilson coefficient with the shifted top-quark mass.[3] Based on this replacement it is obvious that only the logarithmic Lt terms of Πt are relevant for the effective gluonic Higgs couplings. A final comment addresses the removal of one-particle-reducible contributions in eq (2.4): this corresponds to the removal of one-particle-reducible diagrams of the type shown in figure 1 after attaching external Higgs bosons according to eq (2.6). We have checked this correspondence explicitly for Higgs boson pair production in the heavy-topquark limit at NLO [55]

Several heavy quarks

Conclusions