Exotic Hadrons and Underlying Z_{2,3} Symmetries

TL;DR

This paper explores how Z_{2} and Z_{3} symmetries, combined with geometric and algebraic methods, can predict new exotic hadronic states like tetraquarks and pentaquarks, based on standard model data.

Contribution

It introduces a novel approach using polygon geometries and affine Lie algebra diagrams to classify and predict exotic hadrons with specific symmetry properties.

Findings

Z_{2,3} invariance determines mesonic or baryonic nature

Hexagonal geometry yields both mesonic and baryonic states

A new class of exotic hadronic states is proposed

Abstract

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z_{2} and Z_{3} symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of \widehat{A}_{n} affine Lie algebras. It has been shown that Z_{\mathbf{2,3}} invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.