The "Closed" Chiral Symmetry and Its Application to Tetraquark

TL;DR

This paper explores the chiral symmetry properties of tetraquarks, revealing how certain configurations transform similarly to mesons and constructing specific tetraquark currents with particular quantum numbers.

Contribution

It provides a detailed analysis of the chiral transformation properties of tetraquarks and constructs local tetraquark currents with specific quantum numbers based on these symmetries.

Findings

Tetraquarks with same chirality quark pairs transform like mesons.

A unique chiral multiplet transforms differently from others.

Constructed local tetraquark currents with J^{PC}=1^{-+}.

Abstract

We investigate the chiral (flavor) structure of tetraquarks, and study chiral transformation properties of the "non-exotic" [(3_bar,3)+(3,3_bar)] and [(8,1)+(1,8)] tetraquark chiral multiplets. We find that as long as this kind of tetraquark states contains one quark and one antiquark having the same chirality, such as (q_L q_L \bar q_L \bar q_R + q_R q_R \bar q_R \bar q_L), they transform in the same way as the lowest level (\bar q q) chiral multiplets under chiral transformations. There is only one [(3_bar,3)+(3,3_bar)] chiral multiplet whose quark-antiquark pairs all have the opposite chirality (q_L q_L \bar q_R \bar q_R + q_R q_R \bar q_L \bar q_L), and it transforms differently from others. Based on these studies, we construct local tetraquark currents belonging to the "non-exotic" chiral multiplet [(3_bar,3)+(3,3_bar)] and having quantum numbers J^{PC}=1^{-+}.