Search for a vector-like quark T${}^{\mathrm{\prime }}$ $\to$ tH via the diphoton decay mode of the Higgs boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV

A search for the electroweak production of a vector-like quark T${}^{\mathrm{\prime }}$, decaying to a top quark and a Higgs boson is presented. The search is based on a sample of proton-proton collision events recorded at the LHC at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb${}^{-1}$. This is the first T${}^{\mathrm{\prime }}$ search that exploits the Higgs boson decay to a pair of photons. For narrow isospin singlet T${}^{\mathrm{\prime }}$ states with masses up to 1.1 TeV, the excellent diphoton invariant mass resolution of 1-2% results in an increased sensitivity compared to previous searches based on the same production mechanism. The electroweak production of a T${}^{\mathrm{\prime }}$ quark with mass up to 960 GeV is excluded at 95% confidence level, assuming a coupling strength ${\kappa }_{\mathrm{T}}$ = 0.25 and a relative decay width $\mathrm{\Gamma }\mathrm{/}{M}_{{\mathrm{T}}^{\mathrm{\prime }}}$ $<$ 5%.