$B\to \pi l\bar{\nu }$ Form Factors with NRQCD Heavy Quark and Clover Light Quark Actions

We report results on semileptonic $B\to \pi l\bar{\nu }$ decay form factors near $q_{\mathrm{m}\mathrm{a}\mathrm{x}}^2$ using NRQCD heavy quark and clover light quark actions and currents improved through $O(\alpha a)$. An inconsistency with the soft pion relation $f^0(q_{\mathrm{m}\mathrm{a}\mathrm{x}}^2)=f_B\mathrm{/}{f}_{\pi }$ found in a previous work is confirmed, and a possible solution with nonperturbative renormalization is discussed. We find that $f^{+}(q^2)$ is well described by the $B^{\ast }$ pole near $q_{\mathrm{m}\mathrm{a}\mathrm{x}}^2$, and its $1\mathrm{/}{M}_B$ scaling is also consistent with the prediction of the pole dominance model.