Can the 750-GeV diphoton resonance be the singlet Higgs boson of custodial Higgs triplet model?

The observation of diphoton excess around the mass of 750 GeV in LHC Run-II motivates us to consider whether the singlet Higgs boson in the custodial Higgs triplet model can serve as a good candidate because an earlier study of comprehensive parameter scan shows that it can have the right mass in the viable mass spectra. By assuming the singlet Higgs mass at 750 GeV, its total width less than 50 GeV and imposing constraints from the LHC 8-TeV data, we identify an approximately linear region on the $(v_\Delta, \alpha)$ plane along which the exotic Higgs boson masses satisfy a specific hierarchy and have lower possible spectra, where $v_\Delta$ denotes the triplet vacuum expectation value and $\alpha$ is the mixing angle between the singlet Higgs boson and the standard model-like Higgs boson. Although the diphoton decay rate can be enhanced by charged Higgs bosons running in the loop in this region, it is mostly orders of magnitude smaller than that required for the observed production rate, except for the small $v_\Delta$ region when the diphoton fusion production mechanism becomes dominant. Nonetheless, this part of parameter space suffers from the problems of breakdown of perturbativity and large uncertainties in the photon parton distribution function of proton.