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We study the decays of $\Lambda_b \to \Lambda(\to p \pi^-) \ell ^+ \ell^-$with $\ell = (e, \mu, \tau)$. In particular, we examine the full angulardistributions with polarized $\Lambda_b$ and identify the time-reversalasymmetries or T-odd observables. By using the homogeneous bag model, we findthat the decay branching fractions of $\Lambda_b \to \Lambda \ell^+\ell^-$ are$(9.1\pm 2.5,7.9\pm 1.8, 2.1\pm 0.2)\times 10^{-7}$ for $\ell =(e, \mu ,\tau)$,respectively. In addition, we obtain that $A_{FB}^{\ell} = -0.369\pm 0.007$ and$A_{FB}^{h}=-0.333\pm 0.004$, averaged in the range of $15 \leq q^2 \leq 20~\text{GeV}^2$. These results are well consistent with the current experimentaldata. We also explore the T-odd observables in $\Lambda_b \to \Lambda(\to p\pi^-) \mu^+ \mu^-$, which are sensitive to new physics~(NP). Explicitly, weillustrate that the current experimental measurement from one of the T-oddobservables favors the existence of NP, such as the extra $Z$-boson model.

Time-reversal asymmetries in $\Lambda_b \to \Lambda(\to p \pi^-)\ell^+\ell^-$