Diphotons at the Z-pole in models of the 750 GeV resonance decaying to axion-like particles

Models in which the 750 GeV resonance (S) decays to two light axion-like particles (ALPs a), which in turn decay to collimated photons mimicking the observed signal, are motivated by Hidden Valley scenarios and could also provide a mechanism by which a S -> gamma gamma signal persists while S -> Z gamma, ZZ and WW remain subdued in the near future. We point out that these Hidden Valley like models invoking S -> aa -> 4 gamma must also contend with Z -> a(-> gamma gamma)gamma constraints coming from CDF and ATLAS. Within an effective field theory framework, we work out the constraints on the couplings of S to a and gauge bosons coming from photonic Z decays and ensuring that the ALPs decay inside the electromagnetic calorimeter, in two regimes - where a decays primarily to photons, and where a also has hadronic branchings. The analysis is done for both when S has a large as well as a narrow width, and for different relative contributions to the signal coming from S -> gamma gamma and a -> gamma gamma. Results for the particular case where S and a belong to the same complex field are also presented. A gamma gamma resonance at the Z-pole coming from Z -> a gamma is expected in this class of models. Taking benchmark ALP masses below around 0.4 GeV and, assuming reasonable values for the fake jet rate and the identification efficiency of the photon-jet, we find the prospects for the discovery of diphotons at the Z-pole.