Wave functions of multiquark hadrons from representations of the symmetry groups $S_n$

TL;DR

This paper introduces a novel method for constructing multiquark hadron wave functions using permutation symmetry representations, simplifying the process for systems with many quarks and ensuring Fermi statistics are satisfied.

Contribution

The authors develop a new approach based on permutation group representations to construct multiquark wave functions, overcoming complexity in traditional tensor product methods.

Findings

Constructed wave functions for pentaquarks and hexaquarks.

Partial results for systems with n=9, 12, and 24 quarks.

Demonstrated how permutation symmetries manifest in baryon wave functions.

Abstract

Construction of the wave functions of multiquark hadrons by traditional method based on tensor products of colors, flavors, spins (and orbital) parts becomes quite complex when quark numbers grow $n=5,6...12$, as it gets difficult to satisfy requirements of Fermi statistics. Our novel approach is focused directly on representations of the permutation symmetry generators. After showing how $C_3$ is manifested in the wave functions of (excited) baryons, we use it to construct the wave functions for a set of pentaquarks and hexaquarks (n=5,6). We also have some partial results for larger systems, with $n=9$ and 12, and even beyond that as far as $n=24$.