Updated analysis ofa1anda2in hadronic two-body decays ofBmesons

Abstract

Using the recent experimental data of $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}(\ensuremath{\pi},\ensuremath{\rho}),$ $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}{D}_{s}^{(*)},$ $\stackrel{\ensuremath{\rightarrow}}{B}J/\ensuremath{\psi}{K}^{(*)}$ and various model calculations on form factors, we reanalyze the effective coefficients ${a}_{1}$ and ${a}_{2}$ and their ratio. QCD and electroweak penguin corrections to ${a}_{1}$ from $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}{D}_{s}^{(*)}$ and ${a}_{2}$ from $\stackrel{\ensuremath{\rightarrow}}{B}J/\ensuremath{\psi}{K}^{(*)}$ 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 $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}h$ are related by factorization to the measured semileptonic distribution of $\stackrel{\ensuremath{\rightarrow}}{B}{D}^{(*)}l\overline{\ensuremath{\nu}}$ at ${q}^{2}{=m}_{h}^{2}$. Moreover, this enables us to extract model-independent heavy-to-heavy form factors, for example, ${F}_{0}^{\mathrm{BD}}{(m}_{\ensuremath{\pi}}^{2})=0.66\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.05$ and ${A}_{0}^{{\mathrm{BD}}^{*}}{(m}_{\ensuremath{\pi}}^{2})=0.56\ifmmode\pm\else\textpm\fi{}0.03\ifmmode\pm\else\textpm\fi{}0.04$. The determination of the magnitude of ${a}_{2}$ from $\stackrel{\ensuremath{\rightarrow}}{B}J/\ensuremath{\psi}{K}^{(*)}$ depends on the form factors ${F}_{1}^{\mathrm{BK}},$ ${A}_{1,2}^{{\mathrm{BK}}^{*}}$ and ${V}^{{\mathrm{BK}}^{*}}$ at ${q}^{2}{=m}_{J/\ensuremath{\psi}}^{2}$. By requiring that ${a}_{2}$ be process insensitive (i.e., the value of ${a}_{2}$ extracted from $J/\ensuremath{\psi}K$ and $J/\ensuremath{\psi}{K}^{*}$ states should be similar), as implied by the factorization hypothesis, we find that $\stackrel{\ensuremath{\rightarrow}}{B}{K}^{(*)}$ form factors are severely constrained; they respect the relation ${F}_{1}^{\mathrm{BK}}{(m}_{J/\ensuremath{\psi}}^{2})\ensuremath{\approx}{1.9A}_{1}^{{\mathrm{BK}}^{*}}{(m}_{J/\ensuremath{\psi}}^{2})$. Form factors ${A}_{2}^{{\mathrm{BK}}^{*}}$ and ${V}^{{\mathrm{BK}}^{*}}$ at ${q}^{2}{=m}_{J/\ensuremath{\psi}}^{2}$ inferred from the measurements of the longitudinal polarization fraction and the P-wave component in $\stackrel{\ensuremath{\rightarrow}}{B}J/\ensuremath{\psi}{K}^{*}$ are obtained. A stringent upper limit on ${a}_{2}$ is derived from the current bound on ${B}^{0}\ensuremath{\rightarrow}{D}^{0}{\ensuremath{\pi}}^{0}$ and it is sensitive to final-state interactions.