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.

arXiv comment17 pages, minor modifications. Accepted in PRD

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• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• CP violation and kaon-pion interactions in B --> K pi+ pi- decays
• Elastic s-wave B pi, D pi, D K and K pi scattering from lattice calculations of scalar form factors in semileptonic decays
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• Full determination of the CKM matrix using recent results from lattice QCD
• Semileptonic form factors D to pi, K and B to pi, K from a fine lattice
• Extracting |V(ub)| from B->pi l nu Decays Using a Multiply-subtracted Omnes Dispersion Relation
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• Exclusive $c\to s,d$ semileptonic decays of ground-state spin-1/2 doubly charmed baryons
• Exclusive $c\to s,d$ semileptonic decays of ground-state spin-1/2 and spin-3/2 doubly heavy $cb$ baryons
• ${\bar{B}}_s\to K$ semileptonic decay from an Omnès improved constituent quark model
• Heavy-to-light scalar form factors from Muskhelishvili-Omnès dispersion relations
• Constraints on the Leading-Twist Pion Distribution Amplitude from A QCD Light-Cone Sum Rule with Chiral Current
• Study of semileptonic and nonleptonic decays of the $B_c^{-}$ meson
• Semileptonic baryon decays ${\Xi }_b\to {\Xi }_c{\ell }^{-}{\bar{\nu }}_{\ell }$ in perturbative QCD
• Static and dynamic properties of hadronic systems with heavy quarks b and c
• Study of the semileptonic decays B->pi, D->pi and D->K
• Meson exchange between initial and final state and the $R_D$ ratio in the $\bar{B}\to D\bar{\nu }\ell ({\bar{\nu }}_{\tau }\tau )$ reactions