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

Abstract

Using the recent experimental data of $B\to D^{(*)}(π,ρ)$, $B\to D^{(*)} D_s^{(*)}$, $B\to J/ψK^{(*)}$ 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 $B\to D^{(*)}D_s^{(*)}$ and a_2 from $B\to J/ψK^{(*)}$ 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 $B\to D^{(*)}h$ are related by factorization to the measured semileptonic distribution of $B\to D^{(*)}\ell \barν$ at $q^2=m_h^2$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, $F_0^{BD}(m_π^2)=0.66\pm0.06\pm0.05$ and $A_0^{BD^*}(m_π^2)=0.56\pm0.03\pm0.04$. The determination of the magnitude of a_2 from $B\to J/ψK^{(*)}$ depends on the form factors $F_1^{BK}$, $A_{1,2}^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/ψ}$. By requiring that a_2 be process insensitive (i.e., the value of a_2 extracted from $J/ψK$ and $J/ψK^*$ states should be similar), as implied by the factorization hypothesis, we find that $B\to K^{(*)}$ form factors are severely constrained; they respect the relation $F_1^{BK}(m^2_{J/ψ})\approx 1.9 A_1^{BK^*}(m^2_{J/ψ})$. Form factors $A_2^{BK^*}$ and $V^{BK^*}$ at $q^2=m^2_{J/ψ}$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $B\to J/ψK^*$ are obtained. A stringent upper limit on a_2 is derived from the current bound on $\ov B^0\to D^0π^0$ and it is sensitive to final-state interactions.