Large mass expansion in two-loop QCD corrections of para-charmonium decay

We calculate the light-by-light scattering type two-loop QCD corrections due to the light quark loops in the para-charmonium decays ηc → γγ and ηc → gg. We replace the mass of the internal charm quarks by an artificial large mass and obtain the result as a series in the large mass. The obtained series can be transformed into the good convergent ones by a change of the expansion parameter. The results are supported by two other methods to improve the convergence. We also observe that the color singlet state of ηc eliminates the potential divergences in the two-loop QCD corrections. The obtained corrections to the modes ηc → γγ and ηc → gg account for −1.25% and −0.73% of the tree level values, respectively. Comparing the ratio of the decay rates with the experimental value, we find the constrains on the unknown contributions to these decays. e-mail: [email protected] e-mail: [email protected]