Semi-leptonic decays of heavy flavours on a fine grained lattice

Abstract

We present the results of a numerical calculation of semi-leptonic form factors relevant for heavy flavour meson decays into light mesons. The results have been obtained by studying two- and three-point correlation functions at β = 6.4 on a 24 3 × 60 lattice, using the Wilson action in the quenched approximation. From the study of the matrix element 〈 K −| J μ | D 0〉 we obtain ƒ K + (0) = 0.60±0.15±0.07 , where the first error is the statistical error and the second a systematic error. The latter comes from the difference between matrix elements extracted using two different procedures explained in the text. From the matrix element 〈 K ∗0|J μ|D +〉 we obtain V (0) = 0.86 ± 0.24, A 1 (0) = 0.64±0.16 and A 2 (0) = 0.40±0.28±0.04. We also obtain A 1 ( q max 2) = 0.67±0.05, V (0)/ A 1 (0) = 1.3 ± 0.2 and A 2 (0)/ A 1 (0) = 0.6 ± 0.3. For these form factors, the difference between the results obtained using the two procedures are negligible with respect to the statistical error. The results for ƒ K + (0), V (0) and A 1 (0) are consistent with the experimental data and with previous lattice determinations with larger lattice spacings. In the case of A 2 (0) the errors are too large to draw any firm conclusion. We also show, with the help of the heavy quark effective theory (HQET), that it is possible to extrapolate the form factors to the B-meson. Our calculations show that the form factors follow a behaviour compatible with the predictions from HQET. Within large uncertainties, our results suggest that A 2/ A 1 increases with the heavy quark mass. For B-mesons A 2/ A 1 can be as large as 1.5–2.0. We also get very rough estimates for the partial decay widths Γ(B → πℓ ν ℓ) = | V ub| 2 (9 ± 6) × 10 12s −1 and Γ(B → ϱlν l ) = | V ub 2 (14 ± 12) × 10 12s −1, which can be used to give upper bounds on the rates.