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Hypercharge Axion and the Diphoton $750$ GeV Resonance

The CMS and ATLAS reports on a possible excess of diphoton events at $750$ GeV are the cause of great excitement and hope. We show that a pseudoscalar axion coupled to the topological density of hypercharge, suggested in the past by Brustein and Oaknin as a candidate for inducing baryogenesis, can explain the signal in the diphoton channel. The hypercharge axion (HCA) can also decay to $Zγ$ and $ZZ$. The expected number of events in these channels is too small to have been detected, but such decays should be observed in the future. The HCA can be produced via vector boson fusion (VBF) or via associated production (AP). The latter should be manifested by a characteristic decay to 3 photons which should be observed soon. We adapt the previous analysis of possible detection of the HCA at the LHC by Brustein and Oaknin and by Elfgren to the case that the mass of the HCA is 750 GeV and find the expected cross section and decay width in terms of the HCA coupling. We find that the expected cross-section fits well the observed number of excess events and that there is tension between the measured cross-section and the reported partial decay width. The tension is caused because for both VBF and AP the production cross-section and the decay width depend linearly on each other. We therefore expect that if the new resonance is indeed the HCA, either its width should be significantly smaller than the reported width or the production cross-section should be significantly higher than the reported one.