Counting similarities between tetraquark and mesonic/gluonic operators

TL;DR

This paper investigates the operator counting and mixing in large-N_c QCD, revealing similarities between tetraquark, mesonic, and gluonic operators and discussing implications for exotic meson states.

Contribution

It introduces a novel comparison of tetraquark operators with mesonic and gluonic operators, highlighting their similar counting and operator mixing in large-N_c QCD.

Findings

Tetraquark operators have similar counting orders to mesonic and gluonic operators.

Different counting orders for tetraquark operators are identified.

Operator mixing between tetraquark, mesonic, and gluonic operators is observed.

Abstract

After the study of the preclusion of exotic meson states in large-$N_c$ limit QCD, combining Weinberg's opposite proposal, we get different counting orders for a tetraquark operator to create or destroy an one-tetraquark state. Meanwhile, by comparing tetraquark operator with the mesonic and gluonic operators, we find that tetraquark operators are similar with mesonic and gluonic operators in the counting. Furthermore, we find a mixing of different kinds of operators.