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A search for the electroweak production of a vector-like quark T$'$, decayingto a top quark and a Higgs boson is presented. The search is based on a sampleof 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 firstT$'$ search that exploits the Higgs boson decay to a pair of photons. Fornarrow isospin singlet T$'$ states with masses up to 1.1 TeV, the excellentdiphoton invariant mass resolution of 1-2% results in an increased sensitivitycompared to previous searches based on the same production mechanism. Theelectroweak production of a T$'$ quark with mass up to 960 GeV is excluded at95% confidence level, assuming a coupling strength $\kappa_\mathrm{T}$ = 0.25and a relative decay width $\Gamma/M_{\mathrm{T}'}$ $\lt$ 5%.

Search for a vector-like quark T$'$ $\to$ tH via the diphoton decay mode of the Higgs boson in proton-proton collisions at $\sqrt{s}$ = 13 TeV