Lattice study ofB→πsemileptonic decay using nonrelativistic lattice QCD

Abstract

We present an exploratory lattice study of $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\pi}$ semileptonic decay form factors using nonrelativistic lattice QCD for a heavy quark with a Wilson light quark on a ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ quenched lattice at $\ensuremath{\beta}=5.8$. The matrix elements are calculated at eight values of the heavy quark mass in the range of 1.5--8 GeV and with three values of light quark mass. The ${1/m}_{B}$ corrections to the matrix elements are found to be fairly small except for the spatial component proportional to the $B$-meson momentum. We find that the ${q}^{2}$ dependence of the form factor ${f}^{+}{(q}^{2})$ near ${q}_{\mathrm{}\mathrm{max}}^{2}$ becomes much stronger for a larger heavy quark mass, which may suggest an increase in the pole contribution. We perform a model independent fit of the form factors and study whether the ${q}^{2}$ dependence is consistent with the pole contribution. Although the soft pion theorem predicts ${f}^{0}{(q}_{\mathrm{}\mathrm{max}}^{2})$ ${=f}_{B}{/f}_{\ensuremath{\pi}}$ in the chiral limit, we observe a significant violation of this relation.