Renormalization in Reparameterization Invariance

The renormalization issue of the reparameterization invariance in heavy quark effective theory and NRQCD is investigated. I argue that the renormalization of the transformation of the heavy quark field under the variation of the velocity parameter V is attributed to the renormalization of the small component field in the proposed transformation. I show that the matching condition for determining the renormalized small component field can be obtained by imposing an infinitesimal transformation of V on the relations between the Green's functions in QCD full theory and those in the effective theory. As an application, I determine the renormalized transformation to order 1/m^2 using the matching condition. The obtained result is in disagreement with that determined by indirect method.