Branching Ratio and CP Asymmetry of B_s \to K^*_0(1430)\rho(\omega,\phi) Decays in the PQCD Approach

Abstract

In the two-quark model supposition for $K_0^{\ast }(1430)$, which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct CP-violating asymmetries for decays ${\bar{B}}_s^0\to K_0^{\ast 0}(1430)\varphi ,K_0^{\ast 0}(1430)\omega ,K_0^{\ast 0}(1430){\rho }^0,K_0^{\ast +}(1430){\rho }^{-}$ are studied by employing the perturbative QCD factorization approach. We find the following results: (a) Enhanced by the color allowed tree amplitude with large Wilson coefficients $a_1=C_2+C_1/3$, the branching ratio of ${\bar{B}}_s^0\to K_0^{\ast +}(1430){\rho }^{-}$ is much larger than those of the other three decays and arrives at $(3.4_{-0.7}^{+0.8})\times 10^{-5}$ in scenario I, even $10^{-4}$ order in scenario II, and its direct CP violating asymmetry is the smallest, around 10%, so this channel might be measurable in the current LHC-b experiments, where a large number (about $10^{12}$) of $B$ mesons will be produced per year. This high statistics will make the measurement possible. (b) For the decay modes ${\bar{B}}_s^0\to K_0^{\ast 0}(1430)\omega ,K_0^{\ast 0}(1430){\rho }^0$, their direct CP-violating asymmetries are large, but it might be difficult to measure them, because their branching ratios are small and less than (or near) $10^{-6}$ in both scenarios. For example, in scenario I, these values are $\mathcal{B}({\bar{B}}_s^0\to K_0^{\ast }(1430)\omega )=(8.2_{-1.7}^{+1.8})\times 10^{-7},\mathcal{B}({\bar{B}}_s^0\to K_0^{\ast }(1430){\rho }^0)=(9.9_{-2.0}^{+2.1})\times 10^{-7},{\text{acp}}^{dir}({\bar{B}}_s^0\to K_0^{\ast 0}(1430)\omega )=-24.1_{-2.5}^{+2.8},{\text{acp}}^{dir}({\bar{B}}_s^0\to K_0^{\ast 0}(1430){\rho }^0)=26.6_{-2.5}^{+2.5}.$ (c) For the decay ${\bar{B}}_s^0\to K_0^{\ast }(1430)\varphi$, the predicted branching ratios are also small and a few times $10^{-7}$ in both scenarios; there is no tree contribution at the leading order, so its direct CP-violating asymmetry is naturally zero.

Comments: 15 Pages, 4 figures