Production mechanism of hidden-charm pentaquark states $P_{c\bar{c}s}$ with strangeness $S=-1$

TL;DR

The paper addresses the origin of singly strange hidden-charm pentaquarks $P_{c\bar{c}s}$ observed by LHCb and Belle, by applying an off-shell coupled-channel framework that respects heavy-quark spin symmetry, SU(3) flavor symmetry, and hidden local symmetry. It solves a Bethe-Salpeter equation with a kernel from one-meson exchange across nine $S=-1$ two-body channels plus $J/\psi\Lambda$, using a 3D Blankenbecler-Sugar reduction and form-factor regularization; poles in the complex energy plane identify molecular-like resonances. The authors find eight negative-parity and three positive-parity states, with $P_{c\bar{c}s}(4338)$ interpreted as a predominantly $\bar{D}\Xi_c$ bound state and $P_{c\bar{c}s}(4459)$ as a $\bar{D}^*\Xi_c$ molecule with $J^P=3/2^-$, while a nearby $P_{c\bar{c}s}(4472)$ (~spin partner) arises from the same dynamics. They also predict a two-pole structure near the $\bar{D}_s^*\Lambda_c$ and $\bar{D}\Xi_c^{'}$ thresholds (states near 4398 and 4430) and additional resonances in the $\bar{D}^*\Xi_c^*$ channel, plus three positive-parity states with smaller cross sections, suggesting a rich spectrum of molecular-scale hidden-charm pentaquarks and highlighting the role of channel couplings and threshold effects in shaping the observed signals.

Abstract

We investigate the hidden-charm pentaquark states with strangeness $S=-1$ ($P_{c\bar{c}s}$) within an off-shell coupled-channel approach based on effective Lagrangians that respect heavy-quark spin symmetry, SU(3) flavor symmetry, and hidden local symmetry. All relevant meson-baryon two-body channels composed of low-lying anti-charmed mesons and singly-charmed baryons with $S=-1$, as well as the $J/ψΛ$ channel, are included. We find a total of eleven negative-parity states and three positive-parity states. Among the negative-parity states, the $P_{c\bar{c}s}(4338)$ and $P_{c\bar{c}s}(4459)$ can possibly be interpreted as $\bar{D}Ξ_c$ and $\bar{D}^* Ξ_c$ molecular states, respectively. We identify a second state, $P_{c\bar{c}s}(4472)$, located close to the $P_{c\bar{c}s}(4459)$ but with different spin and width, which may correspond to the structure observed by the Belle Collaboration. Both states are generated from the $\bar{D}^* Ξ_c$ channel and can be interpreted as spin partners. Their properties are consistent with recent experimental observations, providing strong support for the molecular interpretation of the $P_{c\bar{c}s}$ states. We also observe a two-pole structure near the $\bar{D}_s^* Λ_c$ and $\bar{D}Ξ_c^{'}$ thresholds, and find virtual and resonance states in the $\bar{D}^* Ξ_{c}^{'}$ channel depending on spin-parity.

Figures (8)

• Figure 1: The mass spectrum of the $P_{c\bar{c}s}$'s, obtained from the present work. The experimental data are taken from the LHCb LHCb:2021chnLHCb:2022ogu and Belle Belle:2025pey measurements, respectively.
• Figure 2: Graphical representation of the coupled integral scattering equation with the two-body intermediate states.
• Figure 3: $t$-channel diagrams for the meson-exchanged diagrams. $M$ and $B$ stand for the meson and baryon, respectively.
• Figure 4: The partial-wave cross sections for the given total angular momenta $J=1/2,3/2,5/2$ with negative parity, which correspond to the spins and parities of $P_{c\bar{c}s}$, as functions of the total energy.
• Figure 5: The invariant $\mathcal{T}$ amplitudes for $\bar{D}\Xi_c'$ elastic scattering with both spin $1/2^-$ and $3/2^-$ as functions of the total energy. generated by the single $\bar{D}^*\Xi_c$ channel for $J^P=1/2^-$ (upper panel) and $J^P=3/2^-$ (lower panel).