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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 branchingratio is enhanced when the $\mathcal{CP}$-violating phase, $\xi$, of thetop-Higgs interaction is non-zero. When the modulus of the top-Higgsinteraction assumes the SM value, $y_t=y_t^{SM}$, we find that the signalsignificance reaches $2.7\sigma$ $( 7.7\sigma)$ when $\xi= 0.25\pi$ $(0.5\pi)$. Furthermore, the different couplings modify the polarisation of the topquark, and can subsequently be distinguished via asymmetries in spincorrelations with the final state leptons. The diphoton decay mode is found tobe significantly more promising than the previously considered $pp\rightarrowt(\rightarrow \ell \nu_\ell b ) h(\rightarrow b\overline{b})j$ channel.

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