Enhanced $thj$ signal at the LHC with $h\rightarrow \gamma\gamma$ decay and $\mathcal{CP}$-violating top-Higgs coupling

We study the observability of non-standard top Yukawa couplings in the $pp\rightarrow t(\rightarrow \ell \nu_\ell b ) h(\rightarrow \gamma\gamma)j$ channel at 14 TeV high-luminosity LHC (HL-LHC). The small diphoton branching ratio is enhanced when the $\mathcal{CP}$-violating phase, $\xi$, of the top-Higgs interaction is non-zero. When the modulus of the top-Higgs interaction assumes the SM value, $y_t=y_t^{SM}$, we find that the signal significance reaches $2.7\sigma$ $( 7.7\sigma)$ when $\xi= 0.25\pi$ $(0.5\pi) $. Furthermore, the different couplings modify the polarisation of the top quark, and can subsequently be distinguished via asymmetries in spin correlations with the final state leptons. The diphoton decay mode is found to be significantly more promising than the previously considered $pp\rightarrow t(\rightarrow \ell \nu_\ell b ) h(\rightarrow b\overline{b})j$ channel.