Time-reversal asymmetries and angular distributions in $\Lambda_b \to \Lambda V$

We study the spin correlations to probe time-reversal~(T) asymmetries in the decays of $\Lambda_b \to \Lambda V ~(V=\phi, \rho^0, \omega, K^{*0})$. The eigenstates of the T-odd operators are obtained along with definite angular momenta. We obtain the T-odd spin correlations from the complex phases among the helicity amplitudes. We give the angular distributions of $\Lambda_b \to \Lambda(\to p \pi^-)V(\to PP')$ and show the corresponding spin correlations, where $P^{(\prime)}$ are the pseudoscalar mesons. Due to the helicity conservation of the $s$ quark in $\Lambda$, we deduce that the polarization asymmetries of $\Lambda$ are close to $-1$. Since the decay of $\Lambda_b \to \Lambda \phi$ in the standard model~(SM) is dictated by the single weak phase from the product of CKM elements, $V_{tb}V_{ts}^*$, the true T and CP asymmetries are suppressed, providing a clean background to test the SM and search for new physics. In the factorization approach, as the helicity amplitudes in the SM share the same complex phase, T-violating effects are absent. Nonetheless, the experimental branching ratio of $Br(\Lambda_b \to \Lambda \phi) = (5.18\pm 1.29 )\times 10^{-6}$ suggests that the nonfactorizable effects or some new physics play an important role. By parametrizing the nonfactorizable contributions with the effective color number, we calculate the branching ratios and direct CP asymmetries. We also explore the possible T-violating effects from new physics.