Chiral Structure and Selection Rules in Light-Front Nucleon-Pentaquark Mixing

TL;DR

This paper analyzes nucleon-pentaquark mixing using a light-front Hamiltonian approach, revealing that symmetry selection rules and chiral structure strongly constrain the contributing channels and determine the five-quark content.

Contribution

It provides a systematic classification of pentaquark configurations and demonstrates the dominance of a few channels in nucleon-pentaquark mixing due to symmetry and chiral considerations.

Findings

Only 6 of 27 channels contribute to nucleon wave function.

Total five-quark probability is approximately 29%.

Contributions from $\sigma$- and $\pi$-induced amplitudes are related by a fixed phase.

Abstract

We present a light-front Hamiltonian analysis of nucleon-pentaquark mixing induced by $\sigma$- and $\pi$-type transition operators in a fully Pauli-consistent five-quark basis. The pentaquark configurations are constructed using a systematic permutation-group classification of orbital, spin-flavor, and color degrees of freedom, and the hyperfine interaction is diagonalized to obtain orthonormal eigenchannels with definite quantum numbers. We compute the mixing coefficients for all 27 positive-parity $P$-wave pentastates and find a highly sparse structure: only 6 channels contribute to the nucleon wave function, while the remaining 21 vanish due to symmetry selection rules. The nonzero contributions are concentrated in a small set of hyperfine eigenchannels, demonstrating a strong dominance pattern. The $\sigma$- and $\pi$-induced amplitudes populate the same subset of states and are related by a fixed phase, reflecting their common chiral structure, which eliminates interference in the normalization. As a result, their contributions add incoherently, yielding a total five-quark probability of about $29\%$, with the remaining $71\%$ residing in the three-quark core. These results show that nucleon-pentaquark mixing is governed primarily by symmetry selection rules and chiral structure, and that the five-quark content is dominated by a small number of dynamically selected channels.