Indirect probes of the trilinear Higgs coupling: $gg \to h$ and $h \to \gamma \gamma$

TL;DR

This paper investigates how Higgs production and decay processes indirectly constrain the trilinear Higgs coupling within the Standard Model effective field theory, using advanced two-loop calculations to analyze current and future collider sensitivities.

Contribution

It provides the first detailed two-loop calculations of the effects of the trilinear Higgs coupling on gluon fusion and diphoton decay amplitudes, enhancing the understanding of indirect constraints.

Findings

Current loop-level probes outperform double-Higgs production constraints.

Future colliders could achieve 5% precision on the Higgs trilinear coupling.

Precision measurements of $gg o h$ and $h o \gamma \gamma$ are valuable for Higgs self-coupling studies.

Abstract

In the framework of the Standard Model effective field theory, we examine the indirect constraints on the trilinear Higgs coupling $\lambda$ that arise from Higgs production in gluon-gluon-fusion and diphoton Higgs decays. We calculate 2-loop contributions to the $gg \to h$ and $h \to \gamma \gamma$ amplitudes that are affected by modifications of the trilinear Higgs-boson vertex. This calculation involves both the computation of anomalous dimensions and finite matching corrections. Based on our new results, we analyse the sensitivity of present and future measurements of the $hgg$ and $h \gamma \gamma$ couplings to shifts in $\lambda$. Under the assumption that $O_6 = - \lambda \left (H^\dagger H \right )^3$ is the only dimension-6 operator that alters the trilinear Higgs interactions, we find that at present the considered loop-level probes provide stronger constraints than $pp \to 2h$. At future high-energy colliders indirect ${\cal O} (5)$ determinations of the trilinear Higgs coupling may be possible, making precision measurements of $gg \to h$ and $h \to \gamma \gamma$ a useful addition to direct extractions of $\lambda$ through double-Higgs production.