Interference in the $gg\rightarrow h \rightarrow \gamma\gamma$ On-Shell Rate and the Higgs Boson Total Width

We consider interference between the Higgs signal and QCD background in $gg\rightarrow h \rightarrow \gamma\gamma$ and its effect on the on-shell Higgs rate. The existence of sizable strong phases leads to destructive interference of about 2% of the on-shell cross section in the Standard Model. This effect can be enhanced by beyond the standard model physics. In particular, since it scales differently from the usual rates, the presence of interference allows indirect limits to be placed on the Higgs width in a novel way, using on-shell rate measurements. Our study motivates further QCD calculations to reduce uncertainties. We discuss potential width-sensitive observables, both using total and differential rates and find that the HL-LHC can potentially indirectly probe widths of order tens of MeV.