NRQCD Factorization for Twist-2 Light-Cone Wave-Functions of Charmonia

Abstract

We show that the twist-2 light-cone wave-functions of eta_c and J/\psi can be factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. The factorization is achieved by expanding the small velocity v, which the c- or \bar c- quark moves inside a rest quarkonium with. At leading order of v the twist-2 light-cone wave-functions of eta_c and J/\psi can be factorized as the product of a perturbative function and a NRQCD matrix element. The perturbative function is calculated at one-loop level and free from any soft divergence. Our results can be used for the production of J/\psi\eta_c through e^+e^- -annihilation and of a charmonium in B-decays, which are studied in experiment of two B-factories.