Implications of recent LHCb data on CPV in b-baryon four body decays

Abstract

Motivated by the recent CPV observation, we investigate the CPV of b-baryon charmless four body decays under the U-spin symmetry. However, we find that only U-spin symmetry cannot provide effective predictions, particularly for $\Lambda_b$ decays. For giving more useful predictions, we also give a simple dynamic analysis. By counting the power($\lambda=\sqrt{\frac{\Lambda_{QCD}}{m_b}}$) of each topological diagram, we find that for the specific decay $B_b^2\to R(B_1^2 M^2 M^{\bar 2})M^2$, only one U-spin amplitude can contribute in the leading power, while for $B_b^2\to R(B_1^2 M^2)R( M^{\bar 2}M^2)$, only two U-spin amplitudes can contribute in this leading power. Then the most effective prediction can be given as \begin{align} &A_{CP}^{dir}(\Lambda_b^0 \to R( p \pi^- \pi^+ )\pi^-) = (-12.99 \pm 2.83\pm2.59\pm0.65)\%,\notag \end{align} Considering the $\Lambda_b$ can effectively produced in LHCb, we strongly encourage a more precise experimental investigation of it.