750 GeV Composite Axion as the LHC Diphoton Resonance
  We propose that the 750 GeV resonance, presumably observed in the early LHC Run 2 data, could be a heavy composite axion that results from condensation of a hypothetical quark in a high-colour representation of conventional QCD. The model, motivated by a recently proposed solution to the strong CP problem, is very economical and is essentially defined by the properties of the additional quark - its colour charge, hypercharge and mass. The axion mass and its coupling to two photons (via axial anomaly) can be computed in terms of these parameters. The axion is predominantly produced via photon fusion ($\gamma\gamma \to {\cal A}$) which is followed by $ Z $ vector boson fusion and associated production at the LHC. We find that the total diphoton cross section of the axion can be fitted with the observed excess. Combining the requirement on the cross-section, such that it reproduces the diphoton excess events, with the bounds on the total width ($\Gamma_{tot} \leqslant 45$ GeV), we obtain the effective coupling in the range $1.6\times 10^{-4}$ GeV$^{-1}\gtrsim C_{{\cal A}} \gtrsim 6.5\times 10^{-5}$ GeV$^{-1}$. Within this window of allowed couplings the model favours a narrow width resonance and $ y_{Q}^2 \sim \mathcal{O}(10)$. In addition, we observe that the associated production $q\bar{q} \to {\cal A}\gamma\to \gamma\gamma\gamma$ can potentially produce a sizeable number of three photon events at future LHC and $ e^{+} e^{-} $ colliders. However, the rare decay $Z\to\mathcal{A}^*\gamma \to \gamma\gamma\gamma$ is found to be too small to be probed at the LHC. 
Neil D. Barrie, Archil Kobakhidze, Matthew Talia and Lei Wu
hep-ph