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Non-perturbative renormalization of the chromo-magnetic operator in HQET and the BB mass splitting

Presenter: Damiano Guazzini — DESY Zeuthen

A.G. Grozin, D. Guazzini, P. Marquard, H.B. Meyer, J.H. Piclum, R. Sommer and M. Steinhauser

We perform 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 vector and pseudoscalar B mesons. We obtain its two-loop anomalous dimension in a Schrödinger functional scheme with a non-vanishing background field. Thanks to a renormalization condition involving no valence quarks and the absence of mixing with lower dimensional operators, we compute, in the Nf=0 theory, the scale evolution of the operator non-perturbatively in a scale range between µ ≈ 0.3 GeV and µ ≈ 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 three standard discretizations of the heavy-quark action. At the same time we present the results for the three-loop anomalous dimension of the chromo-magnetic operator in the MS scheme and the corresponding three-loop coefficient matching HQET and QCD. As an application, we find that the new results bring the quenched predictions of the BB 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.