The ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }(\to p{\pi }^{-}){\mu }^{+}{\mu }^{-}$ decay in the ${\text{RS}}_c$ model

We study the four body decay $\Lambda_b \rightarrow \Lambda ( \rightarrow p \pi^-) \mu^{+} \mu^{-}$intheRandall-Sundrummodelwithcustodialprotection$($\text{RS}$_c)$. By considering the constraints coming from the direct searches of the lightest Kaluza-Klein (KK) excitation of the gluon, electroweak precision tests, the measurements of the Higgs signal strengths at the LHC and from $\mathrm{\Delta }F=2$ flavor observables, we perform a scan of the parameter space of the ${\text{RS}}_c$ model and obtain the maximum allowed deviations of the Wilson coefficients $\mathrm{\Delta }{C}_{7,9,10}^{(\mathrm{\prime })}$ for different values of the lightest KK gluon mass $M_{g^{(1)}}$. Later, their implications on the observables such as differential branching fraction, longitudinal polarization of the daughter baryon $\mathrm{\Lambda }$, forward-backward asymmetry with respect to leptonic, hadronic and combined lepton-hadron angles are discussed where we present the analysis of these observables in different bins of di-muon invariant mass squared $s(=q^2)$. It is observed that with the current constraints the Wilson coefficients in ${\text{RS}}_c$ model show slight deviations from their Standard Model values and hence can not accommodate the discrepancies between the Standard Model calculations of various observables and the LHCb measurements in ${\mathrm{\Lambda }}_b$ decays.