Updated Analysis of a_1 and a_2 in Hadronic Two-body Decays of B Mesons

Abstract

Using the recent experimental data of $B\to D^{(\ast )}(\pi ,\rho )$, $B\to D^{(\ast )}{D}_s^{(\ast )}$, $B\to J/\psi K^{(\ast )}$ and various model calculations on form factors, we re-analyze the effective coefficients a_1 and a_2 and their ratio. QCD and electroweak penguin corrections to a_1 from $B\to D^{(\ast )}{D}_s^{(\ast )}$ and a_2 from $B\to J/\psi K^{(\ast )}$ are estimated. In addition to the model-dependent determination, the effective coefficient a_1 is also extracted in a model-independent way as the decay modes $B\to D^{(\ast )}h$ are related by factorization to the measured semileptonic distribution of $B\to D^{(\ast )}\ell \bar{\nu }$ at $q^2=m_h^2$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, $F_0^{BD}(m_{\pi }^2)=0.66\pm 0.06\pm 0.05$ and $A_0^{B{D}^{\ast }}(m_{\pi }^2)=0.56\pm 0.03\pm 0.04$. The determination of the magnitude of a_2 from $B\to J/\psi K^{(\ast )}$ depends on the form factors $F_1^{BK}$, $A_{1,2}^{B{K}^{\ast }}$ and $V^{B{K}^{\ast }}$ at $q^2=m_{J/\psi }^2$. By requiring that a_2 be process insensitive (i.e., the value of a_2 extracted from $J/\psi K$ and $J/\psi K^{\ast }$ states should be similar), as implied by the factorization hypothesis, we find that $B\to K^{(\ast )}$ form factors are severely constrained; they respect the relation $F_1^{BK}(m_{J/\psi }^2)\approx 1.9A_1^{B{K}^{\ast }}(m_{J/\psi }^2)$. Form factors $A_2^{B{K}^{\ast }}$ and $V^{B{K}^{\ast }}$ at $q^2=m_{J/\psi }^2$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $B\to J/\psi K^{\ast }$ are obtained. A stringent upper limit on a_2 is derived from the current bound on $\text{ov}{B}^0\to D^0{\pi }^0$ and it is sensitive to final-state interactions.

Comments: 33 pages, 2 figures. Typos in Tables I and IX are corrected. To appear in Phys. Rev. D