The $Λ_b \to Λ (\to p π^-)μ^+μ^-$ decay in the $\text{RS}_{c}$ model

Abstract

We study the four body decay $Λ_b \rightarrow Λ( \rightarrow p π^-) μ^{+} μ^{-}$ in the Randall-Sundrum model with custodial protection $(\text{RS}_c)$. 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 $ΔF=2$ 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 $ΔC^{(\prime)}_{7,\; 9,\; 10}$ 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 $Λ$, 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 $Λ_b$ decays.