# Next-to-leading-order QCD corrections to $e^+e^-\to H+\gamma$

## TL;DR

This paper calculates the next-to-leading-order QCD corrections to the rare Higgs plus photon production process at lepton colliders, finding modest effects at low energies and significant enhancements at energies around 400 GeV, with implications for future collider experiments.

## Contribution

The work provides the first detailed NLO QCD correction calculation for the $e^+e^- o H ext{+} ext{photon}$ process, highlighting energy-dependent effects relevant for collider searches.

## Key findings

- QCD corrections are negligible below 300 GeV.
- At 400 GeV, corrections can increase cross section by 20%.
- Maximum cross section around 0.08 fb at 250 GeV.

## Abstract

The associated production of Higgs boson with a hard photon at lepton collider, i.e., $e^+e^-\to H\gamma$, is known to bear a rather small cross section in Standard Model, and can serve as a sensitive probe for the potential new physics signals. Similar to the loop-induced Higgs decay channels $H\to \gamma\gamma, Z\gamma$, the $e^+e^-\to H\gamma$ process also starts at one-loop order provided that the tiny electron mass is neglected. In this work, we calculate the next-to-leading-order (NLO) QCD corrections to this associated $H+\gamma$ production process, which mainly stem from the gluonic dressing to the top quark loop. The QCD corrections are found to be rather modest at lower center-of-mass energy range ($\sqrt{s}<300$ GeV), thus of negligible impact on Higgs factory such as CEPC. Nevertheless, when the energy is boosted to the ILC energy range ($\sqrt{s}\approx 400$ GeV), QCD corrections may enhance the leading-order cross section by $20\%$. In any event, the $e^+e^-\to H\gamma$ process has a maximal production rate $\sigma_{\rm max}\approx 0.08$ fb around $\sqrt{s}= 250$ GeV, thus CEPC turns out to be the best place to look for this rare Higgs production process. In the high energy limit, the effect of NLO QCD corrections become completely negligible, which can be simply attributed to the different asymptotic scaling behaviors of the LO and NLO cross sections, where the former exhibits a milder decrement $\propto 1/s$ , but the latter undergoes a much faster decrease $\propto 1/s^2$.