Any particle that is charged under SU(3)$_C$ and U(1)$_{EM}$ can mediate the $gg→γγ$ process through loops. Near the threshold for the new particle pair production, gauge boson exchanges necessitate the resummation of ladder diagrams. We discuss the leading log order matching of the one-loop result with non-relativistic effective theory resummed result. We show how the diphoton invariant mass spectrum varies depending on decay width, color representation and electric charge of the new particle. The exclusion limits on the product of SU(3)$_C$ and U(1)$_{EM}$ charges of the new scalar or fermion particle are obtained from current LHC data.