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 Schrödinger functional scheme by successive one-loop conversions to the lattice MS scheme and the MS scheme. We then compute the scale evolution of the operator non-perturbatively in the N f = 0 theory 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 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.

We demonstrate how HQET and the Step Scaling Method for B-physics, pioneered by the Tor Vergata group, can be combined to reach a further improved precision. The observables considered are the mass of the b-quark and the B smeson decay constant. The demonstration is carried out in quenched lattice QCD. We start from a small volume, where one can use a standard O(a)-improved relativistic action for the b-quark, and compute two step scaling functions which relate the observables to the large volume ones. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m b . The physical point m b is then reached by an interpolation of the continuum results in 1/m. The essential, expected and verified, feature is that the step scaling fuctions have a weak mass-dependence resulting in an easy interpolation to the physical point. With r 0 = 0.5 fm and the experimental B s and K masses as input, we find F Bs = 191(6) MeV and the renormalization group invariant mass M b = 6.88(10) GeV, translating into m b (m b ) = 4.42(6) GeV in the MS scheme. This approach seems very promising for full QCD.

We compute the mass of the b-quark and the B s meson decay constant in quenched lattice QCD using a combination of HQET and the standard relativistic QCD Lagrangian. We start from a small volume, where one can directly deal with the b-quark, and compute the evolution to a big volume, where the finite size effects are negligible through step scaling functions which give the change of the observables when L is changed to 2L. In all steps we extrapolate to the continuum limit, separately in HQET and in QCD for masses below m b . The point m b is then reached by an interpolation of the continuum results. With r 0 = 0.5 fm and the experimental B s and K masses we find f B s = 191(6) MeV and the renormalization group invariant mass M b = 6.89(11) GeV, translating into m b (m b ) = 4.42(7) GeV in the MS scheme.

We calculate analytically the improvement coefficients of the static axial and vector currents in O(a) improved lattice QCD at one-loop order of perturbation theory. The static quark is described by the hypercubic action, previously introduced in the literature in order to improve the signal-to-noise ratio of static observables. Within a Schrödinger Functional setup, we derive the Feynman rules of the hypercubic link in time-momentum representation. The improvement coefficients are obtained from on-shell correlators of the static axial and vector currents. As a by-product, we localise the minimum of the static self-energy as a function of the smearing parameters of the action at one-loop order and show that the perturbative minimum is close to its non-perturbative counterpart.

We improve a previous quenched result for heavy-light pseudoscalar meson decay constants with the light quark taken to be the strange quark. A finer lattice resolution (a ≈ 0.05 fm) in the continuum limit extrapolation of the data computed in the static approximation is included. We also give further details concerning the techniques used in order to keep the statistical and systematic errors at large lattice sizes L/a under control. Our final result, obtained by combining these data with determinations of the decay constant for pseudoscalar mesons around the D s , follows nicely the qualitative expectation of the 1/m-expansion with a (relative) 1/m-term of about −0.5 GeV/m PS. At the physical b-quark mass we obtain F Bs = 193(6) MeV, where all errors apart from the quenched approximation are included.