Semileptonic $B\to \pi$ Decays from an Omnès Improved Nonrelativistic Constituent Quark Model

Abstract

The semileptonic $B\to \pi l^{+}{\nu }_l$ decay is studied starting from a simple quark model which includes the influence of the $B^{\ast }$ pole. To extend the predictions of a nonrelativistic constituent quark model from its region of applicability near $q_{\max }^2=(m_B-m_{\pi }{)}^2$ to all $q^2$ values accessible in the physical decay, we use a novel multiply-subtracted Omnès dispersion relation, which considerably diminishes the form factor dependence on the elastic $\pi B\to \pi B$ scattering amplitudes at high energies. By comparison to the experimental branching fraction we extract $|V_{ub}|=0.0034\pm 0.0003(\exp )\pm 0.0007(\mathrm{theory})$. To further test our framework, we also study $D\to \pi$ and $D\to K$ decays and find excellent results $\frac{f_{\pi }^{+}(0)}{f_K^{+}(0)}=0.80\pm 0.03,\frac{\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)}{\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e)}=0.079\pm 0.008$. In particular for the $D\to \pi$ case, we reproduce, with high accuracy, the three-flavor lattice QCD results recently obtained by the Fermilab-MILC-HPQCD Collaboration. While for the $D\to K$ case, we successfully describe the data for $f^{+}(q^2)/f^{+}(0)$ recently measured by the FOCUS Collaboration.

Comments: 17 pages, minor modifications. Accepted in PRD