Quark-model search for compact $c\bar c uds$ pentaquark states

TL;DR

This work investigates whether the LHCb-observed $P_{c\bar{c}s}^0$ with $J^P=1/2^-$ can be a compact $c\bar{c}uds$ pentaquark by solving a five-body nonrelativistic quark-model problem with the Gaussian Expansion Method and by applying the Real Scaling Method to distinguish resonances from meson-baryon scattering states. The authors include both color-singlet and color-octet configurations and account for explicit meson-baryon thresholds, finding that, despite a notable energy gain from color-octet configurations, no sharp resonances emerge near the observed mass; all discrete states melt into the continuum when open channels are included. The results favor a hadronic molecular interpretation (e.g., near-threshold $\Xi_c\bar{D}$-like structures) over a compact five-quark resonance for the $P_{c\bar{c}s}^0$, and highlight the crucial role of threshold coupling and color-spin dynamics in shaping the spectrum. These findings inform the understanding of exotic hadrons and suggest directions for exploring heavier systems and residual interactions relevant to molecular binding.

Abstract

A potential quark model is used to search for a $P_{c\bar{c}s}^0=(c\bar{c}uds)^0$, $J^P=1/2^-$ pentaquark state that has recently been observed experimentally by the LHCb collaboration at 4338.2 MeV, with a width of 7.0 MeV and high statistical significance $>15σ$. Our model Hamiltonian reproduces the masses of the low-lying charmed and strange hadrons. We use the Gaussian expansion method {to solve the} five-body Schrödinger equation. Employing the real scaling method {including} the relevant meson-baryon thresholds explicitly, sharp resonances are distinguished from the meson-baryon scattering states. We incorporate new color states of the color-octet meson and baryon configurations as well as the color-singlet configurations for the five-quark states. We find no $ J^P=1/2^-$ resonance close to the observed state, and also none in the $ J^P=3/2^-$ state. This increases the likelihood that $P^0_{c\bar{c}s}$ is a $Ξ_c\bar{D}$ hadronic molecule rather than a compact state.

Figures (6)

• Figure 1: Types of the Jacobi coordinate systems for the GEM calculation. The K-type configurations $(3q)+(q\bar{q})$ have two choices of color assignments as explained in the text. For the H-type we consider only the $\overline{\bf 3}$ diquarks. $R$ is the relative coordinate between the baryon and the meson, which is scaled by a factor $\alpha$ in the real scaling method.
• Figure 2: Results of the calculation with the confined H and K(8) configurations for $J^P=1/2^-$ and $3/2^-$ states.
• Figure 3: Real scaling results for $J^P=1/2^-$. for the (a) H+K(1) and (b) H+K(8)+K(1) configurations. The horizontal lines indicate the model values of the thresholds, $\Lambda\eta_c$, $\Lambda_cD_s$, $\Lambda J/\psi$, $\Xi_c D$, $\Lambda_c D_s^*$ and $\Xi_c' D$ from bottom to top.
• Figure 4: Real scaling results for $J^P=3/2^-$ for the (a) H+K(1) and (b) H+K(8)+K(1) configurations. The horizontal lines indicate the model values of the thresholds of $\Lambda J/\psi$ (lower) and $\Lambda_c D_s^*$ (higher).
• Figure 5: Real scaling results for $J^P=1/2^-$ with selected open channels. (a) H +K(8) +K(1, $\Lambda\eta_c$), (b) H +K(8) +K(1, $\Lambda\eta_c+ \Lambda_cD_s$), (c) H +K(8) +K(1, $\Lambda\eta_c+\Lambda_cD_s+\Lambda J/\psi$), (d) H +K(8) +K(1, $\Lambda\eta_c+\Lambda_cD_s+\Lambda J/\psi+ \Lambda_c D_s^*$). The red-dashed lines indicate the "resonance-like" states and the green horizontal lines represent the thresholds