Non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory and the B* - B mass splitting

TL;DR

This paper performs a non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory, improving the accuracy of B* - B mass splitting predictions by connecting lattice calculations with continuum schemes.

Contribution

It provides the two-loop anomalous dimension and scale evolution of the chromo-magnetic operator non-perturbatively, and applies this to refine B meson mass splitting estimates.

Findings

Renormalization factor improves B* - B mass splitting predictions

Non-perturbative scale evolution computed between 0.3 GeV and 100 GeV

Results applicable to spin-dependent potentials of Eichten and Feinberg

Abstract

We carry out the non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B mesons. We obtain its two-loop anomalous dimension in a Schr"odinger functional scheme by successive one-loop conversions to the lattice MS scheme and the MS-bar scheme. We then compute the scale evolution of the operator non-perturbatively in the N_f=0 theory between $\mu \approx 0.3$ GeV and $\mu \approx 100$ GeV, where contact is made with perturbation theory. The overall renormalization factor that converts the bare lattice operator to its renormalization group invariant form is given for the Wilson gauge action and two standard discretizations of the heavy-quark action. As an application, we find that this factor brings the previous quenched predictions of the B* - B mass splitting closer to the experimental value than found with a perturbative renormalization. The same renormalization factor is applicable to the spin-dependent potentials of Eichten and Feinberg.