# Complete basis for the pentaquark wave function in a group theory approach

## TL;DR

This paper systematically constructs the complete wave functions for pentaquarks using group theory, analyzing symmetries and applying harmonic oscillator models to evaluate their masses with a Cornell-like potential.

## Contribution

It provides a comprehensive group-theoretic framework for pentaquark wave functions and applies it to mass calculations with a harmonic oscillator basis.

## Key findings

- Constructed all possible pentaquark wave functions systematically.
- Evaluated low-lying pentaquark masses using the complete basis.
- Applied a Cornell-like potential in mass calculations.

## Abstract

Permutation groups are applied to analyze the symmetries of pentaquark states. All possible quark configurations of the color, flavor, spin and spatial degrees of freedom are worked out in the language of permutation groups, and the corresponding wave functions are constructed systematically in the form of a Yamanouchi basis. The pentaquark spatial wave functions of various symmetries, which are derived in the harmonic-oscillator interaction, are applied as complete bases to evaluate the low-lying light $q^4\overline q$ pentaquark mass of all configurations, where the Cornell-like potential is employed.