Permutation group S_N and hadron spectroscopy

TL;DR

This paper applies permutation group S_N to hadron physics, proposing a method to connect quark models with the 1/Nc expansion, and derives mass-mixing correlations that challenge gluon-exchange models based on baryon spectra.

Contribution

It introduces a novel group-theoretic method to analyze quark interactions and provides new correlations among baryon masses and mixing angles for testing quark models.

Findings

Pure gluon-exchange models are disfavored by data.

Derived correlations constrain mixing angles in baryons.

Method links quark models to effective Hamiltonians using S_N symmetry.

Abstract

We discuss the application of the permutation group S_N to a few problems in hadron physics. A method is proposed for matching a quark model Hamiltonian onto the effective Hamiltonian of the 1/Nc expansion, which makes use of the transformation properties of the states and operators under S_N. This method is used to obtain information about the spin-flavor structure of the quark interaction Hamiltonian from the spectrum of the negative parity L=1 excited baryons. Assuming the most general 2-body quark Hamiltonian, we derive two correlations among the masses and mixing angles of these states which should hold in any quark model. These correlations constrain the mixing angles, and can be used to test for the presence of 3-body quark interactions. We find that the pure gluon-exchange model is disfavored by data, independently of any assumptions about the hadronic wave functions.