Angular distribution of the rare decay $\Lambda_b \to \Lambda(\to N \pi) \ell^+\ell^-$

We provide a determination of the complete angular distribution for the four body rare decay $\Lambda_b \to \Lambda(\to N \pi) \ell^+\ell^-$, with unpolarized $\Lambda_b$ baryons and massive leptons, in the operator basis approach which includes the scalar, pseudo-scalar, vector, axial-vector and tensor operators. Especially, the contributions of tensor operators have been calculated for the first time in this work. Since the lepton mass is retained in our calculations, the lepton flavour universality and the decay mode $\Lambda_b \to \Lambda(\to N \pi) \tau^+\tau^-$ can be investigated in detail. For comparison with the experiment, we study the numerical results of observables within the Standard Model and the $S_1+S_3$ Leptoquark model. Significant deviation can be found between experiment data and the Standard Model predictions. The $S_1+S_3$ Leptoquark model can be further explored with the experimental progresses. In addition, we demonstrate the sensitivity of various angular observables to tensor operators contributions firstly, and find out that the potential New Physics effects of tensor operators can not be ignored in $b\to s\ell^+\ell^-$ transitions.