Relativistic Description of Exclusive Heavy-to-Light Semileptonic Decays $B\to \pi (\rho )e\nu$

Abstract

The method of calculating electroweak decay matrix elements between heavy-heavy and heavy-light meson states is developed in the framework of relativistic quark model based on the quasipotential approach in quantum field theory. This method is applied for the study of exclusive semileptonic $B\to \pi (\rho )$ decays. It is shown that the large value of the final $\pi (\rho )$ meson recoil momentum allows for the expansion in inverse powers of $b$-quark mass of the decay form factors at $q^2=0$, where $q^2$ is a momentum carried by the lepton pair. This $1/m_b$ expansion considerably simplifies the analysis of these decays and is carried out up to the second order. The $q^2$-dependence of the form factors is investigated. It is found that the $q^2$-behaviour of the axial form factor $A_1$ is different from the other form factors. It is argued that the ratios $\Gamma (B\to \rho e\nu )/\Gamma (B\to \pi e\nu )$ and ${\Gamma }_L/{\Gamma }_T$ are sensitive probes of the $A_1$ $q^2$-dependence, and thus their experimental measurement may discriminate between different approaches. We find $\Gamma (B\to \pi e\nu )=(3.0\pm 0.6)\times |V_{ub}{|}^2\times 10^{12}$s${}^{-1}$ and $\Gamma (B\to \rho e\nu )=(5.4\pm 1.2)\times |V_{ub}{|}^2\times 10^{12}$s${}^{-1}$. The relation between semileptonic and rare radiative $B$-decays is discussed.

20 pages, two figures included, LATEX

References in corpus (4)

• B Mesons
• Exclusive semileptonic decays of B mesons into light mesons in the relativistic quark model
• RELATIVISTIC DESCRIPTION OF THE EXCLUSIVE RARE RADIATIVE DECAYS OF B MESONS
• Relativistic Description of Exclusive Semileptonic Decays of Heavy Mesons

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• Exclusive semileptonic B decays to radially excited D mesons
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• Role of Resonances in Heavy Meson Processes within Standard Model and Beyond
• Light-front holography in $B$ physics