Is it $SU(2)_{\mathrm{L}}$ or just $U(1)_{\mathrm{Y}}$? $750$ GeV di-photon probes of the electroweak nature of new states

The existence of a 750 GeV di-photon spin-0 resonance $S$ would imply the additional presence of new particles beyond the Standard Model, coupling directly to $S$ and electromagnetically charged. For an $SU(2)_{\mathrm{L}}$ singlet $S$, we explore the possibility of probing the $SU(2)_{\mathrm{L}}$ and $U(1)_{\mathrm{Y}}$ quantum numbers of the new states at the LHC by measuring/constraining the $WW$, $Zγ$ and $ZZ$ decays of $S$. We obtain robust prospects on the required LHC integrated luminosity to discover the new decay modes of $S$, and discuss the implications of these measurements for probing the electroweak nature of the new states. We also discuss the impact of $S$ mixing with the SM Higgs in such probes.