A detailed study of the $Lambda_b to Lambda ell^+ ell^-$ decays in the Standard Model

Based on the standard model (SM) of particle physics, we study the decays $Lambda_b to Lambda ell^+ ell^-$ in light of the available inputs from lattice and the data from LHCb. We fit the form-factors of this decay mode using the available theory and experimental inputs after defining different fit scenarios and checking their consistencies. The theory inputs include the relations between the form-factors in heavy quark effective theory (HQET) and soft collinear effective theory (SCET) at the endpoints of di-lepton invariant mass squared $q^2$. Utilizing the fit results, we have predicted a few observables related to this mode. We have also predicted the observable $R_{Lambda} = Br(Lambda_b to Lambda ell_i^+ell_i^- )/Br(Lambda_b to Lambda ell_j^+ell_j^-)$ where $ell_{i}$ and $ell_j$ are charged leptons of different generations ($i e j$). At the moment, we do not observe noticeable differences in the extracted values of the observables in fully data-driven and SM like fit scenarios.