A Lattice Study of the Two-photon Decay Widths for Scalar and Pseudo-scalar Charmonium

In this exploratory study, two photon decay widths of pseudo-scalar (${\eta }_c$) and scalar (${\chi }_{c0}$) charmonium are computed using two ensembles of $N_f=2$ twisted mass lattice QCD gauge configurations. The simulation is performed two lattice ensembles with lattice spacings $a=0.067$ fm with size ${32}^3\times 64$ and $a=0.085$ fm with size ${24}^3\times 48$, respectively. The results for the decay widths for the two charmonia are obtained which are in the right ballpark however smaller than the experimental ones. Possible reasons for these discrepancies are discussed.