Search for rare decays of Z and Higgs bosons to J$\mathrm{/}\psi$ and a photon in proton-proton collisions at $\sqrt{s}=$ 13 TeV

A search is presented for decays of Z and Higgs bosons to a J$\mathrm{/}\psi$ meson and a photon, with the subsequent decay of the J$\mathrm{/}\psi$ to ${\mu }^{+}{\mu }^{-}$. The analysis uses data from proton-proton collisions with an integrated luminosity of 35.9 fb${}^{-1}$ at $\sqrt{s}=$ 13 TeV collected with the CMS detector at the LHC. The observed limit on the Z $\to$ J$\mathrm{/}\psi \gamma$ decay branching fraction, assuming that the J$\mathrm{/}\psi$ meson is produced unpolarized, is 1.4 $\times$ 10${}^{-6}$ at 95% confidence level, which corresponds to a rate higher than expected in the standard model by a factor of 15. For extreme-polarization scenarios, the observed limit changes from -13.6 to +8.6% with respect to the unpolarized scenario. The observed upper limit on the branching fraction for H $\to$ J$\mathrm{/}\psi \gamma$ where the J$\mathrm{/}\psi$ meson is assumed to be transversely polarized is 7.6 $\times$ 10${}^{-4}$, a factor of 260 larger than the standard model prediction. The results for the Higgs boson are combined with previous data from proton-proton collisions at $\sqrt{s}=$ 8 TeV to produce an observed upper limit on the branching fraction for H $\to$ J$\mathrm{/}\psi \gamma$ that is a factor of 220 larger than the standard model value.