$J/ψΛ$ femtoscopy and the nature of $P_{ψs}^Λ(4338)$

TL;DR

The paper addresses the nature of the exotic pentaquark candidate $P_{cs}(4338)$ by extracting a coupled-channel, unitarized contact-range EFT potential for $J/\psi\Lambda$, $\bar{D}\Xi_c$, and $\bar{D}_s\Lambda_c$ from the $J/\psi\Lambda$ invariant-mass spectrum in $B^- \rightarrow J/\psi \Lambda \bar{p}$ decays and by predicting femtoscopy observables. It identifies a bound state below the $\bar{D}\Xi_c$ threshold when three channels are included, with a pole near $E_p \approx 4335-5i$ MeV, consistent with $P_{cs}(4338)$, and reports scattering lengths $a_{J/\psi\Lambda}=-0.17$ fm, $a_{\bar{D}\Xi_c}=1.22$ fm, and $a_{\bar{D}_s\Lambda_c}=-0.19$ fm along with corresponding correlation functions. An SU(3) flavor partner analysis in the $J/\psi N-\bar{D}\Lambda_c-\bar{D}^*\Lambda_c$ sector yields $a_{J/\psi N}=-0.03$ fm, $a_{\bar{D}^*\Lambda_c}=-1.39$ fm, and $a_{\bar{D}\Lambda_c}=-1.89$ fm, with no near-threshold bound states, indicating stronger attraction in the $\bar{D}\Xi_c$ channel. Overall, the results demonstrate that hadron-hadron interactions encoded in the coupled-channel EFT underpin exotic-state spectroscopy and that momentum correlation functions (femtoscopy) can test these interactions and the molecular interpretation of $P_{cs}(4338)$.

Abstract

Over the past two decades, numerous exotic hadron states have been discovered, yet their underlying nature remains unclear. It is widely acknowledged that understanding hadron-hadron interactions is essential to unraveling their properties. Hadron spectroscopy is a powerful tool for this endeavor, providing rich experimental data that can shed light on exotic systems. Recently, the LHCb experiment analyzed the process $B^{-} \rightarrow J/ψΛ\bar{p}$ and observed a narrow peak in the $J/ψΛ$ invariant mass spectrum, regarding it as a candidate for a pentaquark. In this work, we extract the coupled-channel $J / ψΛ-\bar{D} Ξ_c-\bar{D}_s Λ_c$ potential based on the $J/ψΛ$ invariant mass spectrum. Our results indicate the existence of a bound state below the $\bar{D} Ξ_c$ mass threshold, corresponding to the experimentally measured state $P_{cs}(4338)$. Furthermore, we predict the scattering lengths and momentum correlation functions for the $J/ψΛ$ and $\bar{D}Ξ_c$ channels, which serve as theoretical references for future femtoscopy experiments.

Figures (7)

• Figure 1: $J/\psi \Lambda$ invariant mass spectrum for Scenario I.
• Figure 2: $J/\psi \Lambda$ invariant mass spectrum for Scenario II.
• Figure 3: Modulus squared of the $\bar{D}\Xi_c$$T$-matrix for Scenario II.
• Figure 4: Modulus squared of the $T$-matrix for Scenario I.
• Figure 5: $J/\psi \Lambda$ correlation functions obtained with the parameters of Table \ref{['table2']}.