# One-loop weak corrections to Higgs production

## TL;DR

This paper calculates mixed QCD-weak corrections to Higgs production at the LHC and finds they are negligible within current uncertainties, supporting the factorization of QCD and weak effects.

## Contribution

It provides the first numerical assessment of mixed QCD-weak corrections to inclusive Higgs production, confirming their insignificance compared to existing uncertainties.

## Key findings

- Mixed QCD-weak corrections are negligible for current predictions.
- The results support the factorization of QCD and weak corrections.
- Contributions from $g q
ightarrow H q$ are also insignificant.

## Abstract

We compute mixed QCD-weak corrections to inclusive Higgs production at the LHC from the partonic process $g g \rightarrow H q \bar{q}$. We start from the UV- and IR-finite one-loop weak amplitude and consider its interference with the corresponding one-loop QCD amplitude. This contribution is a $\mathcal{O}(\alpha_s\alpha)$ correction to the leading-order gluon-fusion cross section, and was not numerically assessed in previous works. We also compute the cross section from the square of this weak amplitude, suppressed by $\mathcal{O}(\alpha^2)$. Finally, we consider contributions from the partonic process $g q \rightarrow H q$, which are one order lower in $\alpha_s$, as a reference for the size of terms which are not enhanced by the large gluon luminosity. We find that, given the magnitude of the uncertainties on current state-of-the-art predictions for Higgs production, all contributions computed in this work can be safely ignored, both fully inclusively and in the boosted Higgs regime. This result supports the approximate factorisation of QCD and weak corrections to that process.