The ${{\boldsymbol{\Lambda }}}_{{\boldsymbol{b}}}\, \rightarrow \,{\boldsymbol{\Lambda }}\,( \rightarrow {\boldsymbol{p}}{{\boldsymbol{\pi }}}^{-}){{\boldsymbol{\mu }}}^{+}{{\boldsymbol{\mu }}}^{-}$ decay in the ${{\rm{RS}}}_{{\boldsymbol{c}}}$ model

Abstract

We study the four-body decay p m m L  L  -+ -( ) p b in the Randall-Sundrum model with custodial protection (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 RS c model and obtain the maximum allowed deviations of the Wilson coefficients D ¢ ( ) C 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 the RS c model show slight deviations from their Standard Model values and hence cannot accommodate the discrepancies between the Standard Model calculations of various observables and the LHCb measurements in Λ b decays.