High-precisionfBsand heavy quark effective theory from relativistic lattice QCD

Abstract

We present a new determination of the Bs leptonic decay constant from lattice QCD simulations that use gluon configurations from MILC and a highly improved discretization of the relativistic quark action for both valence quarks. Our result, fB s = 0.225(4) GeV, is almost three times more accurate than previous determinations. We analyze the dependence of the decay constant on the heavy quark's mass and obtain the first empirical evidence for the leading 1/ √ m h dependence predicted by Heavy Quark Effective Theory (HQET). As a check, we use our analysis technique to calculate the mB s − mη b /2 mass difference. Our result agrees with experiment to within errors of 11 MeV (better than 2%). We discuss how to extend our analysis to other quantities in Bs and B physics, making 2%-precision possible for the first time. Lattice simulations of QCD have become essential for high-precision experimental studies of B-meson decays -studies that test our understanding and the limitations of the standard model of weak, electromagnetic and strong interactions, and also determine fundamental parameters, like the CKM matrix, in that model. Accurate theoretical calculations of QCD contributions to meson masses, decay constants, mixing amplitudes, and semileptonic form factors are critical for this program, and lattice simulation is the main tool for providing these calculations. A major complication for the lattice simulations has been the large mass of the b quark, which has necessitated the use of non-relativistic effective field theories like NRQCD to describe b dynamics in the simulations. The need for effective field theories has made it difficult to achieve better than 5-10% precision for many important quantities.Recently we overcame the analogous problem for c quarks by introducing a highly improved discretization of the relativistic quark action that gives accurate results even on quite coarse lattices: the Highly Improved Staggered-Quark (HISQ) discretization [1]. With this formalism, c quarks are analyzed in the same way as u, d, and s quarks, which greatly reduces the uncertainties in QCD simulations of D physics [2][3][4][5][6][7]. More recently we showed that the HISQ action can be pushed to much higher masses -indeed, very close to the b mass -using new lattices, from the MILC collaboration, with the smallest lattice spacing available today (a = 0.044 fm). This allowed us to extract a value for the b's MS mass that was accurate to better than 1%. Here we extend that work in a new analysis of the B s meson's leptonic decay constant f Bs , which produces the most accurate theoretical value to date.We also compute the mass difference m Bs − m η b /2, as an additional test of our analysis method. This difference is particularly sensitive to QCD dynamics because the leading (and uninteresting) dependence on the heavy quark's mass mostly cancels in the difference.It would be quite expensive to extend our new analysis directly to B-meson quantities, because of the added costs associated with very light valence and sea qua...

Pseudoscalar meson electromagnetic form factor at high Q2 from full lattice QCD

“…A Q 2 of 12 GeV 2 should be possible on 'superfine' lattices with a = 0.06 fm, and even 20 GeV 2 at a = 0.045 fm ('ultrafine'). Lower statistics calculations have already been done on such lattices [55][56][57]. See also [58] for new methods to reduce uncertainties in calculations at high Q 2 .…”

B meson decay constants f B c $$ {f}_{B_c} $$ , f B s $$ {f}_{B_s} $$ and f B from QCD sum rules

“…QCDSR calculations have narrowed the range of results to f B = 189 − 207 MeV, and f Bs = 216 − 242 MeV [16,17]- [19], while LQCD calculations, claiming high accuracy, give f B = 186 − 205 MeV, and f Bs = 224 − 244 MeV [20][21][22][23][24][25]. For B c a compilation of many LQCD determinations [26] gives values in the wide range f Bc = 380 − 680 MeV.…”

NeutralBmeson mixings andBmeson decay constants with static heavy and domain-wall light quarks

“…The data is cited from Refs. [50] (ETM '11), [12] (ALPHA '14), [51] (HPQCD '13), [52] (ETM '13A), [53,54] (HPQCD '12A, HPQCD '12B), [55] (FNAL/MILC '11), [56] (RBC/UKQCD '14), [14] (ETM '13B) and [40] (RBC/UKQCD '10). The values of fB and fB s in ETM '11 are obtained from ΦB and ΦB s divided by √ mB and √ mB s , respectively.…”