Lattice study of semileptonicBdecays:B¯→Dlν¯ decays

Abstract

We present a study of semi-leptonicB → Dℓν decays in quenched lattice QCD through a calculation of the matrix element D|cγ µ b|B on a 24 3 × 48 lattice at β = 6.2, using an O (a)-improved fermion action. We perform the calculation for several values of the initial and final heavy-quark masses around the charm mass, and three values of the light-(anti)quark mass around the strange mass. Because the charm quark has a bare mass which is almost 1/3 the inverse lattice spacing, we study the ensuing mass-dependent discretization errors, and propose a procedure for subtracting at least some of them non-perturbatively. * Present address: HLRZ, 52425 Jülich, Germany † Present address: Dept. of Physics and Astronomy, The University, Glasgow G12 8QQ, Scotland ‡ Present address: FNAL, PO Box 500, Batavia IL 60510, USA § Unité Propre de Recherche 7061. 1We extract the form factors h + and h − . After radiative corrections, we find that h + displays no dependence on the heavy-quark mass, enabling us to identify it with an Isgur-Wise function ξ. Interpolating the light-quark mass to that of the strange, we obtain an Isgur-Wise function relevant for − 2 (syst.) at zero recoil. We observe a slight decrease in the magnitude of the central value of the slope as the mass of the light quark is reduced; given the errors, however, the significance of this observation is limited.We then use these functions, in conjunction with heavy-quark effective theory, to extract V cb with no free parameters from theB → D * ℓν decay rate measured by the ALEPH, ARGUS and CLEO collaborations. Using the CLEO data, for instance, we obtain |V cb | = 0.037, where δ 1/m 2 c is the power correction inversely proportional to the square of the charm quark mass, and β A 1 (1) is the relevant radiative correction at zero recoil. Here, the first set of errors is experimental, the second represents the statistical error and the third represents the systematic error in our evaluation of the Isgur-Wise function. We also use our Isgur-Wise functions and heavyquark effective theory to calculate branching ratios forB (s)

B Decays and Cp Violation

“…where c G ≃ 1.1, and we have used (87) and (90). The uncertainty in the value of the ratio τ (B s )/τ (B d ) arises from unknown SU(3)-violating effects in the matrix elements of B s mesons.…”

Exclusive Semileptonic $B$ Decays: Dispersive Bounds and Lattice Results

“…(2.14) enforces nonperturbative lattice to continuum matching and should lead to cancellations of discretisation errors as well as subtract some zero-recoil power corrections to the heavy quark limit. Following [47,48], they study the heavy-quark mass dependence "ξ(w)" for heavy-quark masses around the charm and find that it is consistent with 0, in the range 1 ≤ w ≤ 1.2. Thus, "ξ(w)" is to a good approximation the Isgur-Wise function ξ(w), at least in the above range of w, confirming the earlier results of [47,48].…”

“…Following [47,48], they study the heavy-quark mass dependence "ξ(w)" for heavy-quark masses around the charm and find that it is consistent with 0, in the range 1 ≤ w ≤ 1.2. Thus, "ξ(w)" is to a good approximation the Isgur-Wise function ξ(w), at least in the above range of w, confirming the earlier results of [47,48]. The calculation is performed at two values of the lattice spacing, β = 6.2 (finer) and 6.0 (coarser).…”

Form factors and branching ratios of the FCNC $$B \rightarrow a_1 \ell ^{+}\ell ^{-}$$ B → a 1 ℓ + ℓ - decays

“…We choose the values of the quark, lepton, and meson masses and also the leptonic decay constants thus: m b = 4.8 GeV [12], m μ = 0.105 GeV, m τ = 1.776 GeV, m a 1 = 1.260 GeV, m B = 5.280 GeV [13], f a 1 = (238 ± 10) MeV [14]. For the value of the f B , we shall use f B = 140 MeV.…”