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

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 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.

The errant life of a heavy quark in the quark–gluon plasma

“…At the same time the cutoff effects were found to be controllable. In [29], the chromo-magnetic field B was also discretized with HYP-link variables, yielding also a benefit in statistical error reduction. Following this example, we use HYP-links for the chromo-electric field as well.…”

“…While the renormalization factor for the B field was computed in [29] (it is scale-dependent), the corresponding factor for the chromo-electric field remains to be computed. The same methods apply to the renormalization of this factor, but in the mean time we use a preliminary way of normalizing the chromo-electric operator.…”

“…Therefore the absolute normalization of the chromoelectric field can be obtained by requiring that the lattice correlator match the NLO perturbative that with the procedure adopted here, we cannot disentangle discretization errors from the barecoupling dependence of the renormalization factor of E. Our results should accordingly be regarded as preliminary. Eventually the renormalization factor should be computed along the lines of [29], where the B operator was treated instead.…”

The static-light baryon spectrum from twisted mass lattice QCD

“…experimentally the mass difference between Σ b and Σ * b is only around 21 MeV. Lattice methods to evaluate such 1/m Q contributions have been established and tested in quenched studies of B mesons [19,20,21,22]. We intend to explore these contributions using lattice techniques subsequently.…”

The continuum limit of the static-light meson spectrum

“…This correction is expected be relatively small for b quarks, but larger for c quarks. Lattice methods to evaluate these 1/m Q contributions to the B meson hyperfine splittings have been established and tested in quenched studies [17,18,19,20,21]. We intend to explore these contributions using lattice techniques subsequently.…”