Estimates of exchange topological contributions and CP -violating observables in Λb→Λϕ decay

Abstract

The penguin-dominated two-body weak decay of ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\phi}$ is studied based on the perturbative QCD approach. In addition to the penguin emission diagrams, the penguin exchange and $W$ exchange ones are also accounted for. It is found that the penguin exchange contribution is in fact important and comparable to the penguin emission one, while the $W$ exchange contribution is highly Cabibbo-Kobayashi-Maskawa (CKM) suppressed. The predicted branching ratio, $\mathcal{B}({\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\ensuremath{\phi})={6.9}_{\ensuremath{-}2.0\ensuremath{-}1.6}^{+1.9+1.8}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, is larger than the previous theoretical estimates but in comparison with the data from Particle Data Group at the level of 1 standard deviation. We also explore some pertinent decay asymmetry parameters that characterize the angular decay distributions. The inclusion of the $W$ exchange contribution provides the nonzero weak phase difference, consequently, allowing us to estimate the direct $CP$ violation and true triple product asymmetries in the concerned process. The numerical results demonstrate that the direct $CP$ violation is at the level of a few percent, and the true triple product asymmetries are also predicted to be tiny, of order ${10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}4}$. The observed small $CP$-violating observables have shown no significant deviations from zero. Our predictions will be subject to stringent tests with precise data from LHCb in the future.