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, at $\beta =6.4$ on a $24^3\times 60$ lattice, using the Wilson action in the quenched approximation. We obtain $f_K^{+}(0)=0.65\pm 0.18$, $V(0)=0.95\pm 0.34$, $A_1(0)=0.63\pm 0.14$ and $A_2(0)=0.45\pm 0.33$. We also obtain $A_1(q_{max}^2)=0.62\pm 0.09$, $V(0)/A_1(0)=1.5\pm 0.28$ and $A_2(0)/A_1(0)=0.7\pm 0.4$. The results for $f_K^{+}(0)$, $V(0)$ 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 have also extrapolated the form factors to the B meson, showing a behaviour compatible with the predictions by the heavy quark effective theory (HQET). Within large uncertainties, our results suggest that $A_2/A_1$ increases with the heavy quark mass. We also get very rough estimates for the partial decay widths $B\to \pi l{\nu }_l)=|V_{ub}{|}^2(12\pm 8)10^{12}{s}^{-1}$ and $\Gamma (B\to \rho l{\nu }_l)=|V_{ub}{|}^2(13\pm 12)10^{12}{s}^{-1}$, which can be used to give upper bounds on the rates

Comments: 21 pages, LaTeX