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

Wen-Tao Lyu, Eulogio Oset

TL;DR

The paper proposes detecting a $P_{cs}$ state around $4200$ MeV in the Λ_b → φ η_c Λ decay, arguing that strong coupled-channel dynamics lower the mass relative to naive $P_c$-based expectations. It develops a formalism where the Λ_b decay produces a $D_s^- Λ_c^+$ pair that couples to a $P_{cs}(4200)$ resonance, which then decays to $η_c Λ$, with production dominated by an off-shell $D_s Λ_c$ intermediate state. By normalizing to the observed Λ_b^0 → φ D_s^- Λ_c^+ rate and incorporating the $P_{cs}(4200)$ pole, the authors predict Br(Λ_b → φ η_c Λ) ≈ 3.8×10^{-5} and Br(Λ_b → φ P_{cs}(4200)) ≈ 2.5×10^{-5}, with a narrow resonance width Γ_{P_{cs}} ≈ 0.22 MeV. The study suggests that the observation of this state at LHCb would illuminate the role of coupled-channel dynamics in hadron structure and the relationship between the $P_c$ and $P_{cs}$ spectra.

Abstract

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.

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

TL;DR

The paper proposes detecting a state around MeV in the Λ_b → φ η_c Λ decay, arguing that strong coupled-channel dynamics lower the mass relative to naive -based expectations. It develops a formalism where the Λ_b decay produces a pair that couples to a resonance, which then decays to , with production dominated by an off-shell intermediate state. By normalizing to the observed Λ_b^0 → φ D_s^- Λ_c^+ rate and incorporating the pole, the authors predict Br(Λ_b → φ η_c Λ) ≈ 3.8×10^{-5} and Br(Λ_b → φ P_{cs}(4200)) ≈ 2.5×10^{-5}, with a narrow resonance width Γ_{P_{cs}} ≈ 0.22 MeV. The study suggests that the observation of this state at LHCb would illuminate the role of coupled-channel dynamics in hadron structure and the relationship between the and spectra.

Abstract

We propose the reaction to observe a state around MeV, predicted at lower masses than expected from comparison with the states, stemming as a consequence of the important role played by coupled channels in the case, which does not appear in the case. That state decays to with a width of about keV. The reaction is related to , which has already been observed. We predict a branching fraction for ; of the order of , which is within present capabilities of the LHCb collaboration. The observation of this state would bring valuable light on the nature of the and states and the role played by coupled channels in hadron structure and hadron reactions.
Paper Structure (6 sections, 23 equations, 5 figures, 1 table)

This paper contains 6 sections, 23 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Formalism
  3. Extraction of A from the $\Lambda_b^0\to\phi D_s^-\Lambda_c^+$ reaction
  4. Branching ratio for $\Lambda_b\to\phi\eta_c\Lambda$
  5. Results
  6. Conclusions

Figures (5)

  • Figure 1: $\Lambda_b\to\Lambda_c\bar{c}s$, together with hadronization of the $s\bar{c}$ component.
  • Figure 2: Rescattering of $D_s^-\Lambda_c^+$ to $\eta_c\Lambda$, mediated by the resonance $P_{cs}(4200)$.
  • Figure 3: (a) Mechanism to produce $\eta_c\phi\Lambda$ in $\Lambda_b$ decay through internal emission. (b) The mechanism depicted as a tree level diagram.
  • Figure 4: $\frac{1}{\Gamma_{\Lambda_b}}\frac{d\Gamma}{dM_{\text{inv}}(\eta_c\Lambda)}$ as a function of $M_{\text{inv}}(\eta_c\Lambda)$ for the $\Lambda_b\to\phi\eta_c\Lambda$.
  • Figure 5: Coalescence $P_{cs}$ production in $\Lambda_b\to\phi P_{cs}$ driven by the $\bar{D}_s\Lambda_c$ intermediate state.