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

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 243x60 lattice, using the Wilson action in the quenched approximation. From the study of the matrix element left angle K-vertical stroke Jμvertical stroke D0 right angle we obtain fK+(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 left angle anti K*0vertical stroke Jμvertical stroke D+ right angle we obtain V(0)=0.86±0.24, A1(0)=0.64±0.16 and A2(0)=0.40±0.28±0.04. We also obtain A1(q2max)=0.67±0.05, V(0)/A1(0)=1.3±0.2 and A2(0)/A1(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 errors. The results for fK+(0), V(0) and A1(0) are consistent with the experimental data and with previous lattice determinations with larger lattice spacings. In the case of A2(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 A2/A1 increases with the heavy quark mass. For B-mesons A2/A1 can be as large as 1.5-2.0. We also get very rough estimates for the partial decay widths Γ(B→πlνl)=vertical stroke Vubvertical stroke 2(9±6)x1012 s-1 and Γ(B→ρlνl)=vertical stroke Vubvertical stroke 2(14±12)x1012 s-1, which can be used to give upper bounds on the rates. (orig.)