NRQCD factorization for twist-2 light-cone wave-functions of charmonia

We show that the twist-2 light-cone wave-functions of ηc and J/ψ can be factorized with nonrelativistic QCD (NRQCD) at the one-loop level, where the nonperturbative effects are represented by NRQCD matrix elements. In quarkonium at rest the c- or c¯-quark moves with a small velocity v. The factorization is achieved by expanding the small velocity v. To the leading order of v, the twist-2 light-cone wave-functions of ηc and J/ψ can be factorized as the product of a perturbative function and an NRQCD matrix element. The perturbative function is calculated at the one-loop level and is free from any soft divergences. Our results can be used for exclusive productions of quarkonia, which are studied in an experiment with two B-factories.