Mixed Electroweak-QCD Corrections to $H\to \gamma\gamma$

TL;DR

This paper computes the complete three-loop mixed electroweak-QCD corrections to the Higgs decay into two photons, significantly refining theoretical predictions and reducing scheme dependence for future collider experiments.

Contribution

First complete calculation of three-loop mixed electroweak-QCD corrections to $H o \gamma\gamma$, improving precision of Standard Model predictions.

Findings

Electroweak-QCD correction can reach up to 0.6% of the LO width.

Scheme dependence is reduced from 0.6 keV to 0.03 keV.

Predicted decay width is 9.389 to 9.420 keV.

Abstract

We present for the first time the complete three-loop mixed electroweak-QCD ($\mathcal{O}(\alpha\alpha_s)$) corrections for the decay channel $H \to \gamma\gamma$, by implementing three different on-shell $\alpha$ schemes in computing the electroweak correction. Our studies indicate that the $\mathcal{O}(\alpha_s)$ correction amounts to approximately $1.7\%$ of the leading-order prediction for the diphoton width, while the $\mathcal{O}(\alpha)$ correction varies from $-4.8\%$ to $1.4\%$ depending on the specific $\alpha$ scheme. The three-loop mixed electroweak-QCD correction may reach $0.6\%$, $0.5\%$, and $0.2\%$ of the LO diphoton width in $\alpha(0)$, $\alpha(M_Z)$, and $G_\mu$ schemes, respectively, which is much more significant than the less-than-$0.1\%$ contribution from the three-loop QCD correction. It is also worth noting that the inclusion of the ${\cal O}(\alpha\alpha_s)$ correction significantly reduces the scheme dependence of the partial width from $0.6$ keV at leading order down to $0.03$ keV. The state-of-the-art Standard Model predictions are $\Gamma[H \to \gamma\gamma] = 9.389\div 9.420$ keV, providing a valuable theoretical benchmark for future Higgs factory collider program.