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

Abstract

We study the four body decay ${\Lambda }_b\to \Lambda (\to p{\pi }^{-}){\mu }^{+}{\mu }^{-}$ 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 $\Delta F=2$ 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 $\Delta C_{7,9,10}^{(\prime )}$ 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 $\Lambda$, 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 ${\Lambda }_b$ decays.

arXiv comment22 pages, 2 figures, references added, minor changes, matches published version

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