Precision for B-meson matrix elements

Abstract

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.

Heavy flavour phenomenology from lattice QCD

“…The result is m MS b (m b ) = 4.347(48)GeV, very much compatible with the number quoted in [28], m MS b (m b ) = 4.42(6)GeV. That second result is also obtained in the quenched approximation and in the framework of HQET going beyond the static limit, but it is based on the SS method.…”

“…In this analysis, as well as the one in [27], the inclusion of the static point improves noticeably the control over the heavy quark mass dependence. Both numbers in [27] and [28] are in very good agreement, which gives confidence to the systematic error analyses. It is clear from the results obtained in these two calculations and those from the N f = 2 + 1 calculations mentioned above that the effect of the quenched approximation is quite noticeable in f B s .…”

“…The other quenched analysis, described in [28], is based on the use of the Step Scaling Method (SSM) [29] and the Heavy Quark Effective Theory (HQET). The authors calculate the SS functions for several heavy masses around the charm quark mass and in the static approximation.…”

Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD

“…Alternatively, finitevolume QCD results can be corrected by calculating in the full theory the finite-volume effects by means of a finite-size scaling technique [15]. These two strategies can be profitably combined as it has been done in the quenched theory [16].…”

A proposal for B-physics on current lattices

“…Due to present day computer limitations, it is not possible, however, to work directly with the heaviest quarks (as the b-quark) propagating on the simulated lattice. Various strategies, more or less inspired to the heavy quark effective theory (HQET) [7][8][9][10][11][12], have been devised to circumvent this intrinsic difficulty, which go from non-perturbative matching of HQET onto QCD [13][14][15][16][17][18] to finite size scaling methods with relativistic heavy quark(s) [19][20][21][22]. Relativistic heavy-quark actions designed (highly tuned) to have reduced cutoff effects [23][24][25][26] have also been employed for this purpose.…”