# Probing the charm-Higgs Yukawa coupling via Higgs boson decay to $h_c$ plus a photon

## TL;DR

This paper studies the Higgs decay to $h_c$ plus a photon within NRQCD to probe the charm-Higgs Yukawa coupling, finding a very small branching ratio that challenges detection but remains relevant for future colliders and potential anomalous couplings.

## Contribution

It introduces the decay channel of Higgs to $h_c$ plus a photon as a novel probe of the charm Yukawa coupling, with detailed theoretical predictions and implications for future experiments.

## Key findings

- Branching ratio is about 10^{-8}.
- Detection at current colliders is unlikely due to low efficiency.
- Future improvements could make this process a valuable probe.

## Abstract

In this paper, we investigate the decay of Higgs boson to $h_c$ plus a photon in the NRQCD theoretical framework. Comparing with the Higgs decay to $J/\psi$ plus a photon channel, this process has not indirect contribution, can be used to detect the Yukawa coupling of Higgs and charm quarks. The results show that the decay branch ratio of this process is about $10^{-8}$. If we takes into account the $10^{-3}$ efficiency in the $h_c$ detection, no events will be available even in the case of $30ab^{-1}$ luminosity at FCC-pp with 100 TeV center of mass energy. However, if the detection efficiency of $h_c$ is greatly improved in the future, this process will play an important role at linear $e^+e^-$ future colliders and at LHCb. Moreover, this process should be also play an important role when the anomalous charm Yukawa couplings are larger and direct sensitivity.