Renormalization group improvement of the nonrelativistic QCD Lagrangian and heavy quarkonium spectrum

Abstract

We complete the leading-log renormalization group scaling of the nonrelativistic (NRQCD) Lagrangian at O(1/m2). The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation mαs≫ΛQCD. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation mαs2≳ΛQCD. When ΛQCD≪mαs2, this is equivalent to obtain the whole set of O(mαs(n+4)1nnαs) terms in the heavy quarkonium spectrum. The implications of our results in the nonperturbative situation mαs∼ΛQCD are also mentioned.