Heavy photophilic scalar at the LHC from a varying electromagnetic coupling

We investigate the phenomenology of a heavy scalar $\phi$ of the type involved in Bekenstein's framework for varying electromagnetic coupling theories, with the difference that the scalar in our model has a large mass. The model has only two free parameters, the mass $M_{\phi}$ of the scalar and the scale $\Lambda$ of new physics. The scalar is dominantly produced through photon-photon fusion at the LHC and leads to a diphoton final state. It can also be produced by quark-antiquark fusion in association with a photon or a fermion pair. Its dominating decay is to diphotons, but it also has a large three-body branching to a fermion pair and a photon, which can provide an interesting search channel with a dilepton-photon resonance. We derive exclusion limits on the $M_{\phi}-\Lambda$ plane from the latest 13 TeV LHC diphoton resonance search data. For a benchmark mass of $M_{\phi}\sim 1$ TeV, we find a lower limit on $\Lambda$ of 18 TeV. We discuss the more complex possibility of varying couplings in the full electroweak theory and comment on the possibility that the new physics is related to extra dimensions or string theory.