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The $Λ_b \to J/ψ~ K ~ Ξ$ decay and the higher order chiral terms of the meson baryon interaction

We study the weak decay of the $Λ_b$ into $ J/ψ~ K ~ Ξ$ and $J/ψ~ η~ Λ$ states, and relate these processes to the $Λ_b \to J/ψ~ \bar K ~N$ decay mode. The elementary weak transition at the quark level proceeds via the creation of a $J/ψ$ meson and an excited $sud$ system with $I=0$, which upon hadronization leads to $\bar K N$ or $ηΛ$ pairs. These states undergo final state interaction in coupled channels and produce a final meson-baryon pair. The $K Ξ$ state only occurs via rescattering, hence making the $Λ_b \to J/ψ~ K ~ Ξ$ process very sensitive to the details of the meson-baryon interaction in strangeness $S=-1$ and isospin $I=0$. We show that the corresponding invariant mass distribution is dominated by the next-to-leading order terms of the chiral interaction. The $I=0$ selectivity of this decay, and its large sensitivity to the higher order terms, makes its measurement very useful and complementary to the $K^- p \to K Ξ$ cross section data. The rates of the $Λ_b \to J/ψ~ K ~ Ξ$ and $Λ_b \to J/ψ~ η~ Λ$ invariant mass distributions are sizable compared to those of the $Λ_b \to J/ψ~ \bar K ~N$ decay, which is measured experimentally, thus, we provide arguments for an experimental determination of these decay modes that will help us understand better the chiral dynamics at higher energies.