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 $K_0^{*}(1430)$, 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 $\bar B_s^0\to K^{*0}_0(1430)\phi, K^{*0}_0(1430)\omega, K^{*0}_0(1430)\rho^0, K^{*+}_0(1430)\rho^-$ 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 $\bar B_s^0\to K^{*+}_0(1430)\rho^-$ is much larger than those of the other three decays and arrives at $(3.4^{+0.8}_{-0.7})\times 10^{-5}$ 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 $\bar B^0_s\to K^{*0}_0(1430)\omega, K^{*0}_0(1430)\rho^0$, 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 ${\cal B}(\bar B_s^0\to K^*_0(1430)\omega)=(8.2^{+1.8}_{-1.7})\times 10^{-7}, {\cal B}(\bar B_s^0\to K^*_0(1430)\rho^0)=(9.9^{+2.1}_{-2.0})\times 10^{-7}, \acp^{dir}(\bar B^0_s\to K^{*0}_0(1430)\omega)=-24.1^{+2.8}_{-2.5}, \acp^{dir}(\bar B^0_s\to K^{*0}_0(1430)\rho^0)=26.6^{+2.5}_{-2.5}.$ (c) For the decay $\bar B^0_s\to K^*_0(1430)\phi$, 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.