Searching for a $P_{cs}(4200)$ state in the $Λ_b oϕη_cΛ$ reaction

We propose the $Λ_b\toϕη_c Λ$ reaction to observe a $P_{cs}$ state around $4200$ MeV, predicted at lower masses than expected from comparison with the $P_c$ states, stemming as a consequence of the important role played by coupled channels in the $P_{cs}$ case, which does not appear in the $P_c$ case. That state decays to $η_c Λ$ with a width of about $200$ keV. The reaction is related to $Λ_b^0\toϕD_s^- Λ_c^+$, which has already been observed. We predict a branching fraction for $Λ_b\toϕP_{cs}(4200)$; $P_{cs}\toη_c Λ$ of the order of $10^{-5}$, which is within present capabilities of the LHCb collaboration. The observation of this state would bring valuable light on the nature of the $P_c$ and $P_{cs}$ states and the role played by coupled channels in hadron structure and hadron reactions.

💡 Research Summary

The authors propose a realistic experimental strategy to search for a yet‑unobserved hidden‑charm strange pentaquark, denoted P_cs(4200), in the decay Λ_b → φ η_c Λ. Their motivation stems from the already observed Λ_b^0 → φ D_s^− Λ_c^+ channel, which provides a natural production mechanism for the intermediate D_s^− Λ_c^+ pair. In the coupled‑channel picture, the P_cs family differs fundamentally from the P_c family: while the P_c states (e.g., P_c(4312), P_c(4440), P_c(4457)) are essentially single‑channel molecular states (¯D Σ_c or ¯D* Σ_c) with only tiny admixtures, the P_cs states involve strong mixing among several channels such as ¯D Ξ_c, ¯D_s Λ_c, ¯D* Ξ_c, and ¯D*_s Λ_c. This strong channel coupling lowers the mass of the state that couples predominantly to ¯D Ξ_c, producing a resonance around 4200 MeV, well below the naïve expectation based on a simple Σ_c ↔ Ξ_c replacement.

The paper details two production mechanisms. The dominant one is an external‑emission diagram where the weak b → c transition creates a φ meson and a ¯c s pair; the latter hadronizes into D_s^− Λ_c^+. The D_s^− Λ_c^+ pair then rescatters via the P_cs(4200) resonance into η_c Λ (Fig. 2). A subleading internal‑emission diagram (color‑suppressed by 1/N_c) also contributes (Fig. 3). The total amplitude is written as
t_total = A β + A G_{¯D_s Λ_c}(M_{inv}) t_{¯D_s Λ_c, η_c Λ},
where A encodes the weak vertex strength, G is the loop function of the intermediate D_s^− Λ_c^+ system, and t is the resonant scattering amplitude modeled by a Breit‑Wigner form with couplings g_{¯D_s Λ_c} and g_{η_c Λ}.

Using the measured branching fraction for Λ_b → φ D_s^− Λ_c^+ (≈10⁻⁴) and the known Λ_b lifetime, the authors extract A²/Γ_{Λ_b}=2.23×10⁻¹⁰ MeV⁻³. The loop function G and the couplings are taken from their earlier coupled‑channel study (Ref.