Predictions for the $Λ_b \to J/ψ~ Λ(1405)$ decay

We calculate the shape of the $πΣ$ and $\bar K N$ invariant mass distributions in the $Λ_b \to J/ψ\, πΣ$ and $Λ_b \to J/ψ\,\bar K N$ decays that are dominated by the $Λ(1405)$ resonance. The weak interaction part is the same for both processes and the hadronization into the different meson-baryon channels in the final state is related by SU(3) symmetry. The most important feature is the implementation of the meson-baryon final-state interaction using two chiral unitary models from different theoretical groups. Both approaches give a good description of antikaon-nucleon scattering data, the complex energy shift in kaonic hydrogen and the line shapes of $πΣK$ in photoproduction, based on the two-pole scenario for the $Λ(1405)$. We find that this reaction reflects more the higher mass pole and we make predictions of the line shapes and relative strength of the meson-baryon distributions in the final state.

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