Probing new physics effects in $\Lambda_b \to \Lambda (\to p\pi^-)\ell^+\ell^-$ decay via model independent approach

The New Physics (NP) effects are studied in the rare baryonic decay $\Lambda_b \to \Lambda (\to p\pi^-)\ell^{+}\ell^{-}$, with unpolarized $\Lambda_b$ using most general model independent approach by introducing new axial(vector), (pseudo)scalar and tensor operators in the weak effective Hamiltonian corresponding to $b\to s$ transitions. Recently, for $\Lambda_b \to \Lambda (\to p\pi^-)\mu^{+}\mu^{-}$ decay the LHCb collaboration has measured the branching ratio $(d\mathcal{B}/ds)$, lepton- and hadron-side forward-backward asymmetries, denoted by $A_{FB}^{\ell}$ and $A_{FB}^{\Lambda}$, respectively, and the longitudinal polarization fraction $F_L$ both in the low- and high-recoil regions. To see whether the new $VA$, $SP$ and $T$ couplings can accommodate the available experimental data of these observables, first we have examined their influence on these observables and later we have checked the imprints of these new couplings on a number of interesting but yet not measured observables. It is found that compared to the $VA$ the $SP$ couplings favor experimental data for all the four observables but still no individual coupling is able to accommodate all of the available data simultaneously. To achieve this goal, the pairs of new WCs are taken to check their range that simultaneously satisfy constraints of $B$-Physics and available LHCb data on $d\mathcal{B}/ds$, $F_L$, $A_{FB}^{\ell}$ and $A_{FB}^{\Lambda}$ in several bins for the decay channel under consideration. We find that most of the available data could be accommodated by the different pairs of $VA$ and $SP$ WCs giving more severe constraints on the parametric space of these WCs that is still satisfied with the $B$-physics data.