Corrections For Two Photon Decays of chi_{c0} and chi_{c2} and Color   Octet Contributions
  Using the fact that the c-quark inside a charmonium moves with a small velocity v in the charmonium rest-frame, one can employ an expansion in v to study decays of charmonia and results at the leading order for chi_{c0,2} --> gamma gamma exist in the literature. We study corrections at the next-to-leading order in the framework of nonrelativistic QCD(NRQCD) factorization. The study presented here is different than previous approaches where chi_{c0,2} is taken as a bound-state of a c cbar pair and a nonrelativistic wave-function is used for the pair. We find that the corrections are consist not only of relativistic corrections, but also of corrections from Fock state components of chi_{c0,2} in which the c cbar pair is in a color-octet state. For chi_{c2} there is also a contribution from a Fock state component in which the pair is in a F-wave state. We determine the factorization formula for decay widths in the form of NRQCD matrix elements representing nonperturbative effects related to chi_{c0,2}, and calculate the perturbative coefficients at tree-level. Because the NRQCD matrix elements are unknown, a detailed prediction for the decay chi_{c0,2} --> gamma gamma can not be made, but the effect of these corrections can be determined at certain level. Estimations show that the effect is significant and can not be neglected. 
J.P.Ma and Q.Wang