Charm-quark Yukawa Coupling in $h\rightarrow c\bar{c}\gamma$ at LHC
It is extremely challenging to probe the charm-quark Yukawa coupling at hadron colliders primarily due to the large Standard Model (SM) background (including $h\to b\bar b$) and the lack of an effective trigger for the signal $h\to c\bar c$. We examine the feasibility of probing this coupling at the LHC via a Higgs radiative decay $h\rightarrow c\bar{c}\gamma$. The existence of an additional photon in the final state may help for the signal identification and background suppression. Adopting a refined triggering strategy and utilizing basic machine learning, we find that a coupling limit of about 8 times the SM value may be reached with $2\sigma$ sensitivity after the High Luminosity LHC (HL-LHC). Our result is comparable and complementary to other projections for direct and indirect probes of $h\to c\bar c$ at the HL-LHC. Without a significant change in detector capabilities, there would be no significant improvement for this search from higher energy hadron colliders.