Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays

Abstract

Within the framework of perturbative QCD approach, we study the charmless two-body decays $B_s\to a_1(1260)(b_1(1235))P(V)$ ($P,V$ represent the light pseudo-scalar and vector mesons, respectively.). Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) The decays ${\bar{B}}_s^0\to a_1^{-}{K}^{+}(K^{\ast +})$ have the contributions from the factorization emission diagrams with a large Wilson coefficient $C_2+C_1/3$ (order of 1), so they have the largest branching ratios and arrive at $10^{-5}$ order. While for the decays ${\bar{B}}_s^0\to a_1^0{K}^0(K^{\ast 0})$, the Wilson coefficient is $C_1+C_2/3$ in tree level and color suppressed, so their branching ratios are small and fall in the order of $10^{-7}\sim 10^{-8}$. For the decays ${\bar{B}}_s^0\to b_{1}K(K^{\ast })$, all of their branching ratios are of order few times $10^{-6}$. (b) For the pure annihilation type decays ${\bar{B}}_s^0\to a_1(b_1)\rho$ except the decays ${\bar{B}}_s^0\to a_1\pi$ having large branching ratios of order few times $10^{-6}$, the most other decays have the branching ratios of $10^{-7}$ order. The branching ratios of the decays ${\bar{B}}_s^0\to a_1^0(b_1^0)\omega$ are the smallest and fall in the order of $10^{-8}\sim 10^{-9}$. (c)The branching ratios and the direct CP-asymmetries of decays ${\bar{B}}_s^0\to a_1^0(b_1^0){\eta }^{(\prime )}$ are very sensitive to take different Gegenbauer moments for ${\eta }^{(\prime )}$. (d) Except for the decays ${\bar{B}}_s^0\to a_1^0{K}^{\ast 0},a_1^0\omega ,b_1^0\omega$, the longitudinal polarization fractions of other ${\bar{B}}_s^0\to a_1(b_1)V$ decays are very large and more than 90%. (e) Compared with decays ${\bar{B}}_s^0\to a_1(b_1)P$, most of ${\bar{B}}_s^0\to a_1(b_1)V$ decays have smaller direct CP asymmetries.

Comments: 17 pages, 5 figures