$CP$ violation in two-body hadronic $\hat{I}{›}_b$ decays in the PQCD approach

Abstract

We systematically investigate the $CP$-averaged branching ratios and $CP$ violations (CPVs) for the two-body hadronic decays $\hat{I}{›}_b\to ph$, where $h$ runs through the mesons $\ddot{I}{€}^{-}$, $\ddot{I}{}^{-}$, $a_1^{-}(1260)$, $K^{-}$, $K^{\ast -}$, $K_1^{-}(1270)$ and $K_1^{-}(1400)$, in the perturbative QCD approach to order $\hat{I}{\pm }_s^2$ in the strong coupling. Various topological amplitudes are obtained by incorporating subleading-twist hadron distribution amplitudes, which exhibit reasonable hierarchical patterns, sizable strong phases, and non-negligible higher-power corrections. The predicted direct CPVs in $\hat{I}{›}_b\to p\ddot{I}{€}^{-},p{K}^{-}$, different from those in similar $B$ meson decays, are as small as the current data. The low CPV in $\hat{I}{›}_b\to p\ddot{I}{€}^{-}$ results from the cancellation between the $S$- and $P$-wave CPVs, while the one in $\hat{I}{›}_b\to p{K}^{-}$ is determined by the tiny $S$-wave CPV. However, individual partial-wave CPVs can exceed $10\%$, consistent with direct CPVs in $B$ meson decays. The CPVs in the $\hat{I}{›}_b\to p{K}_1^{-}(1270),p{K}_1^{-}(1400)$ channels are relatively larger. In particular, CPVs above $20\%$ appear in the up-down asymmetries associated with the final-state angular distributions of $\hat{I}{›}_b\to p{K}_1^{-}(1270),p{K}_1^{-}(1400)$, followed by the secondary $K_1\to K\ddot{I}€\ddot{I}€$ decays. These observables offer promising prospects for firmly establishing baryon CPVs. The decay asymmetry parameters of $\hat{I}{›}_b\to ph$ are also predicted for future experimental confrontations.

73 pages, 19 figures, 31 tables, the version published in Phys.Rev.D