Probing Charm Yukawa Coupling through $ch$ Associated Production at the Hadron Colliders

At present, the study of the charm-quark Yukawa coupling at the Large Hadron Collider mainly focuses on the Higgs decay processes. Such signal suffers from overwhelming QCD background and derives its sensitivity primarily from the $Vh$ associated production channel. In addition, sensitivity to a possible CP phase in charm-quark Yukawa at the hadron collider is not discussed. We investigate the charm-Higgs associated production signal, that contains a potentially detectable interference term between $cch$ Yukawa coupling mediated diagrams and $ggh$ coupling mediated diagram. Such interference term is sensitive to the relative CP phase between contributing diagrams. High dimensional kinematic information are exploited by machine learning techniques to separate the different contribution, and sensitivity on the coupling is derived. Assuming a real $\kappa_c$ modification framework, 1$\sigma$ bound of $-5.6 < \kappa_c < 5.6$ (HL-LHC) and $-1.51 < \kappa_c < 1.62$ (FCC) are achieved. When allowing for CP-phase in the charm Yukawa, a combined 1$\sigma$ bound of $0.32<|\kappa_c|<1.69$, $-77^\circ < \alpha < 77^\circ$ (HL-LHC) and $0.70<|\kappa_c|<1.29$, $-55^\circ < \alpha < 55^\circ$ (FCC) can be achieved on the magnitude and CP phase of the coupling respectively.