Study of scalar meson f_0(980) and K_0^*(1430) from B \to f_0(980)\rho(\omega, \phi) and B \to K^*_0(1430)\rho(\omega) Decays

Abstract

In the two-quark model supposition for $f_0(980)$ and $K_0^{\ast }(1430)$, the branching ratios and the direct CP-violating asymmetries for decays ${\bar{B}}^0\to f_0(980){\rho }^0(\omega ,\varphi ),K_0^{\ast 0}(1430){\rho }^0(\omega ),K_0^{\ast -}(1430){\rho }^{+}$ and $B^{-}\to f_0(980){\rho }^{-},K_0^{\ast 0}(1430){\rho }^{-},K_0^{\ast -}(1430){\rho }^0(\omega )$ are studied by employing the perturbative QCD (PQCD)factorization approach. we find the following results: (a) if the scalar meson $f_0(980)$ is viewed as a mixture of $s\bar{s}$ and $(u\bar{u}+d\bar{d})/\sqrt{2}$, the branching ratios of the decays ${\bar{B}}^0\to f_0(980){\rho }^0(\omega ,\varphi )$ and $B^{-}\to f_0(980){\rho }^{-}$, which are induced by $b\to d$ transition, are smaller than the currently experimental upper limits, and the predictions for the decay ${\bar{B}}^0\to f_0(980)\omega ,B^{-}\to f_0(980){\rho }^{-}$ are not far away from their limits; (b) in the decays $B\to K_0^{\ast }(1430)\rho (\omega )$, which are induced by $b\to s$ transition, the branch ratio of ${\bar{B}}^0\to K_0^{\ast 0}(1430){\rho }^0$ is the smallest one in two scenarios, at the order of $10^{-7}$ for scenario I, about $4.8\times 10^{-6}$ for scenario II; (c) the direct CP-asymmetries of the decays $B\to f_0(980)\rho (\omega )$ have a strong dependent on the mixing angle $\theta$: they are large in the range of $25^{\circ }<\theta <40^{\circ }$, and small in the range of $140^{\circ }<\theta <165^{\circ }$, while the direct CP-asymmetries of the decays $B\to K_0^{\ast }(1430)\rho (\omega )$ are not large in both scenarios and most of them are less than 20% in size.

Comments: 17 pages, 5 figures, minor corrections, typos removed, accepted for publication in Phys. Rev. D