Effective Multi-Higgs Couplings to Gluons

TL;DR

This paper derives an effective Lagrangian for multi-Higgs couplings to gluons up to N$^4$LO, extending previous results and providing insights into Higgs production mechanisms at the LHC.

Contribution

It extends the effective Lagrangian framework to include multiple Higgs bosons and higher-order QCD corrections up to N$^4$LO, improving theoretical precision.

Findings

Derived the effective Lagrangian for multi-Higgs gluon couplings up to N$^4$LO.

Discussed gluonic Higgs couplings up to NNLO with multiple heavy quarks.

Extended previous single-Higgs results to multiple Higgs bosons.

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.