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

Understand

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.