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We carry out the non-perturbative renormalization of the chromo-magneticoperator in Heavy Quark Effective Theory. At order 1/m of the expansion, theoperator is responsible for the mass splitting between the pseudoscalar andvector B mesons. We obtain its two-loop anomalous dimension in a Schr"odingerfunctional scheme by successive one-loop conversions to the lattice MS schemeand the MS-bar scheme. We then compute the scale evolution of the operatornon-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 overallrenormalization factor that converts the bare lattice operator to itsrenormalization group invariant form is given for the Wilson gauge action andtwo standard discretizations of the heavy-quark action. As an application, wefind that this factor brings the previous quenched predictions of the B* - Bmass splitting closer to the experimental value than found with a perturbativerenormalization. The same renormalization factor is applicable to thespin-dependent potentials of Eichten and Feinberg.

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