The decay $h\to \gamma\gamma$ in the Standard-Model Effective Field Theory

TL;DR

This paper calculates the one-loop amplitude for the Higgs decay to two photons within the Standard-Model Effective Field Theory, providing a gauge-invariant, renormalization-scale independent result that helps constrain new physics effects using LHC data.

Contribution

It presents a novel, gauge-invariant calculation of the $h o \gamma ext{-}\gamma$ decay amplitude in SMEFT at one-loop, including a comprehensive analysis of Wilson coefficient bounds from LHC data.

Findings

The amplitude is finite, gauge-invariant, and similar to renormalisable theories.

Tree-level operators are constrained by LHC data, often more strongly than other searches.

One-loop corrections to tree-level operators are less than 10%.

Abstract

Assuming that new physics effects are parametrized by the Standard-Model Effective Field Theory (SMEFT) written in a complete basis of up to dimension-6 operators, we calculate the CP-conserving one-loop amplitude for the decay $h\to \gamma\gamma$ in general $R_\xi$-gauges. We employ a simple renormalisation scheme that is hybrid between on-shell SM-like renormalised parameters and running $\overline{\mathrm{MS}}$ Wilson coefficients. The resulting amplitude is then finite, renormalisation scale invariant, independent of the gauge choice ($\xi$) and respects SM Ward identities. Remarkably, the $S$-matrix amplitude calculation resembles very closely the one usually known from renormalisable theories and can be automatised to a high degree. We use this gauge invariant amplitude and recent LHC data to check upon sensitivity to various Wilson coefficients entering from a more complete theory at the matching energy scale. We present a closed expression for the ratio $\mathcal{R}_{h\to \gamma\gamma}$, of the Beyond the SM versus the SM contributions as appeared in LHC $h\to \gamma\gamma$ searches. The most important contributions arise at tree level from the operators $Q_{\varphi B}, Q_{\varphi W}, Q_{\varphi WB}$, and at one-loop level from the dipole operators $Q_{uB},Q_{uW}$. Our calculation shows also that, for operators that appear at tree level in SMEFT, one-loop corrections can modify their contributions by less than 10%. Wilson coefficients corresponding to these five operators are bounded from current LHC $h\to \gamma\gamma$ data -- in some cases an order of magnitude stronger than from other searches. Finally, we correct results that appeared previously in the literature.