Theory for quarkonium: from NRQCD factorization to soft gluon factorization *

Abstract We demonstrate that the recently proposed soft gluon factorization (SGF) is equivalent to nonrelativistic QCD (NRQCD) for heavy quarkonium production or decay, which means that, any given process, these two theories are either both valid violated. use methods arrive at this conclusion. In first method, we apply physical process . Our explicit calculation shows SGF and NRQCD can correctly reproduce low energy physics of full QCD, factorizations thus equivalent. second by using equations motion, successfully deduce from effective field theory. By identifying with factorization, establish relations between prove generalized Gremm-Kapustin relation as a byproduct. Compared advantage it resums series relativistic corrections originating kinematic effects all powers, yielding better convergence expansion.