$CP$ violation in two-body hadronic ${\mathrm{\Lambda }}_b$ decays in the PQCD approach

We systematically investigate the $CP$-averaged branching ratios and $CP$ violations (CPVs) for the two-body hadronic decays ${\mathrm{\Lambda }}_b\to ph$, where $h$ runs through the mesons ${\pi }^{-}$, ${\rho }^{-}$, $a_1^{-}(1260)$, $K^{-}$, $K^{\ast -}$, $K_1^{-}(1270)$ and $K_1^{-}(1400)$, in the perturbative QCD approach to order ${\alpha }_s^2$ 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 ${\mathrm{\Lambda }}_b\to p{\pi }^{-},p{K}^{-}$, different from those in similar $B$ meson decays, are as small as the current data. The low CPV in ${\mathrm{\Lambda }}_b\to p{\pi }^{-}$ results from the cancellation between the $S$- and $P$-wave CPVs, while the one in ${\mathrm{\Lambda }}_b\to p{K}^{-}$ is determined by the tiny $S$-wave CPV. However, individual partial-wave CPVs can exceed $10\mathrm{\%}$, consistent with direct CPVs in $B$ meson decays. The CPVs in the ${\mathrm{\Lambda }}_b\to p{K}_1^{-}(1270),p{K}_1^{-}(1400)$ channels are relatively larger. In particular, CPVs above $20\mathrm{\%}$ appear in the up-down asymmetries associated with the final-state angular distributions of ${\mathrm{\Lambda }}_b\to p{K}_1^{-}(1270),p{K}_1^{-}(1400)$, followed by the secondary $K_1\to K\pi \pi$ decays. These observables offer promising prospects for firmly establishing baryon CPVs. The decay asymmetry parameters of ${\mathrm{\Lambda }}_b\to ph$ are also predicted for future experimental confrontations.