Hidden-charm $uds\,c\bar c$ pentaquarks as flavor eigenstates in a constituent quark model

TL;DR

This study employs a diffusion Monte Carlo method within a constituent quark model to analyze $udscar c$ pentaquarks, revealing structures consistent with observed states and predicting additional potential states.

Contribution

It introduces a flavor eigenstate approach in a non-relativistic quark model to explain pentaquark states and predicts new states above certain thresholds.

Findings

Two structures match the $J/ ext{psi}\Lambda$ spectrum.

Imposing flavor eigenstates yields two compatible structures.

One structure below the $J/ ext{psi}\Lambda$ threshold when only isospin is imposed.

Abstract

We use a diffusion Monte Carlo (DMC) algorithm to solve the Schr\"odinger equation that describes $udsc\bar c$ pentaquarks within the framework of a non-relativistic constituent quark model. We considered only multiquark states with defined values of parity, color, spin and isospin, selected to be compatible with the experimentally favored assignment $J^P=1/2^-$ for one of the candidates, and assumed $I=0$. However, we found that, to explain the existence of the $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquarks, we need the total wavefunction to be also an eigenvector of the SU(3) {\em flavor} operator. When we impose that condition, we obtain two structures compatible with the masses extracted from the $J/\psi\Lambda$ spectrum. In addition, two states are predicted below the $J/\psi\Lambda$ threshold but above the $\eta_c\Lambda$ one that would not appear in that channel. If we only impose the $I=0$ condition, we obtain a {\em single} (not two) structure compatible with the experimental quantum numbers, with a mass below the $J/\psi\Lambda$ threshold.