Mb and fBs from a combination of HQET and QCD

Abstract

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.

Heavy quark effective theory computation of the mass of the bottom quark

“…Our numbers for M b or m b may then be used as a benchmark result for other methods. Indeed, a comparison shows agreement with [54] and the recent extension of that work [55] m b = 4.42 (7) GeV.…”

Heavy-light decay constant at the 1/m order of HQET

“…This is due to the fact that the signal for the 1/m part in large volume is more difficult to extract than in the static case, and also because of the absence of O(a)-improvement at this order. We also note that our result is compatible with a recent computation done with a different method, but which also goes beyond the leading order of HQET [6].…”

NON-PERTURBATIVE QCD: RENORMALIZATION, O(A)-IMPROVEMENT AND MATCHING TO HEAVY QUARK EFFECTIVE THEORY

“…An interesting application has been the combination of the approach of [172,173] with the large mass behavior computed via HQET [200].…”