Model independent New Physics analysis in $\Lambda_b\to\Lambda\mu^+\mu^-$ decay

We study the rare $\Lambda_b\to\Lambda\mu^+\mu^-$ decay in the Standard Model and beyond. Beyond the Standard Model we include new vector and axial-vector operators, scalar and pseudo-scalar operators, and tensor operators in the effective Hamiltonian. Working in the helicity basis and using appropriate parametrization of the $\Lambda_b \to \Lambda$ hadronic matrix elements, we give expressions of hadronic and leptonic helicity amplitudes and derive expression of double differential branching ratio with respect to dilepton invariant mass squared and cosine of lepton angle. Appropriately integrating the differential branching ratio over the lepton angle, we obtain the longitudinal polarization fraction and the leptonic forward-backward asymmetry and sequentially study the observables in the presence of the new couplings. To analyze the implications of the new vector and axial-vector couplings, we follow the current global fits to $b\to s\mu^+\mu^-$ data. While the impacts of scalar couplings can be significant, exclusive $\bar{B}\to X_s\mu^+\mu^-$ data imply stringent constraints on the tensor couplings and hence the effects on $\Lambda_b\to\Lambda\mu^+\mu^-$ are negligible.