Quarkonium physics: nrqcd factorization formula for j/ !e+e

In this lecture, we briefly review the nonrelativistic QCD (NRQCD) factorization approach to describe the quarkonium production and decay. In the NRQCD factorization formula, the long-distance nature of a heavy quarkonium is factorized into the NRQCD long-distance matrix elements (LDMEs) and a physical measurable is expressed as a linear combination of the LDMEs. If we apply the perturbation theory to enhance the theoretical accuracies in the short-distance contributions there is no way to avoid non-analytic Coulomb divergences in the static limit of the heavy quark and infrared divergences. A systematic procedure to isolate such long-distance contributions out of the correction terms in the short-distance coefficients is called matching. As a heuristic example of finding the NRQCD factorization formula for a specific process, we demonstrate the matching procedure of determining the short-distance coefficients involving the leptonic decay of the S-wave spin-triplet state.