Search for rare decays of and Higgs bosons to and a photon in proton-proton collisions at = 13

A search is presented for decays of $$ and Higgs bosons to a $$ meson and a photon, with the subsequent decay of the $$ to $$ . The analysis uses data from proton-proton collisions with an integrated luminosity of 35.9 $$ at $$ collected with the CMS detector at the LHC. The observed limit on the $$ decay branching fraction, assuming that the $$ meson is produced unpolarized, is $$ at 95% confidence level, which corresponds to a rate higher than expected in the standard model by a factor of 15. For extreme-polarization scenarios, the observed limit changes from $$ to $$ with respect to the unpolarized scenario. The observed upper limit on the branching fraction for $$ where the $$ meson is assumed to be transversely polarized is $$ , 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 $$ to produce an observed upper limit on the branching fraction for $$ that is a factor of 220 larger than the standard model value.