# Spectrum of the $uudc \bar c$ hidden charm pentaquark with an SU(4) flavor-spin hyperfine interaction

## TL;DR

This paper models the spectrum of the hidden charm pentaquark $uudcar c$ using an SU(4) flavor-spin hyperfine interaction, predicting the ordering of positive and negative parity states and comparing with LHCb experimental data.

## Contribution

It introduces a detailed constituent quark model with specific orbital configurations to predict pentaquark state energies and parities, aligning theoretical results with experimental observations.

## Key findings

- Lowest positive parity states are below certain negative parity states.
- Positive parity states with specific quantum numbers are identified.
- Model results are consistent with LHCb pentaquark structures.

## Abstract

We study a few of the lowest states of the pentaquark $uudc\overline{c}$, of positive and negative parity, in a constituent quark model with an SU(4) flavor-spin hyperfine interaction. For positive parity we introduce space wave functions of appropriate permutation symmetry with one unit of orbital angular momentum in the internal motion of the four-quark subsystem or an orbital excitation between the antiquark and the four quark subsystem which remains in the ground state. We show that the lowest positive parity states $1/2^+, 3/2^+$ are provided by the first alternative and are located below the $1/2^-$ and the $1/2^+$ states with all quarks in the ground state. We compare our results with the LHCb three narrow pentaquark structures reported in 2019.