Charmless B decays to a scalar meson and a vector meson

The hadronic charmless B decays into a scalar meson and a vector meson are studied within the framework of QCD factorization. The main results are: (i) The decay rates for the $f_0(980)K^{*-}$ and $f_0(980)\ov K^{*0}$ modes depend on the $f_0-\sigma$ mixing angle $\theta$. The experimental measurements can be accommodated for $\theta\approx 20^\circ$. (ii) If the $a_0(980)$ is a $q\bar q$ bound state, the predicted branching ratios for the channels $a_0^+\rho^-$ and $a_0^0\rho^-$ will be very large, of order $30\times 10^{-6}$ and $23\times 10^{-6}$, respectively. If the observation of or the experimental limit on theses two modes is much smaller than the expectation of $\sim 25\times 10^{-6}$, this could hint at a four-quark nature for the $a_0(980)$. (iii) For the $a_0(1450)$ channels, $a_0^+(1450)\rho^-$ and $a_0^0(1450)\rho^-$ are found to have branching ratios of order $16\times 10^{-6}$ and $22\times 10^{-6}$, respectively. A measurement of them at the predicted level will favor the $q\bar q$ structure for the $a_0(1450)$. (iv) Contrary to the naive expectation that $\Gamma(B^-\to a_0^0\rho^-)\sim {1\over 2}\Gamma(\bar B^0\to a_0^+\rho^-)$, we found that they have comparable rates due to additional contributions to the $a_0\rho^-$ mode from the $a_0^0$ emission. (v) The predicted central value of $Br(\bar B^0\to\ov K^{*0}_0(1430)\phi)$ is larger than experiment, though it can be accommodated within theoretical errors. The decays $B\to K^{*}_0(1430)\rho$ are expected to have rates substantially larger than that of $B\to K^{*}_0(1430)\pi$ owing to the constructive (destructive) interference between the $a_4$ and $a_6$ penguin terms in the former (latter). Experimentally, it is thus important to check if the $B\to K^{*}_0\rho$ modes are enhanced relative to the corresponding $K_0^*\pi$ channels.