Mass of $1^{-+}$ four-quark--hybrid mixed states

TL;DR

This paper uses QCD sum rules to calculate the masses of exotic $1^{-+}$ mesons, considering four-quark and hybrid mixing, and identifies two mass states corresponding to known particles.

Contribution

It introduces a method to compute $1^{-+}$ meson masses via mixing correlation functions of four-quark and hybrid currents.

Findings

Identified two mass states around 1.2-1.4 GeV and 1.45-1.67 GeV

Correspondence with $ ext{π}_1(1400)$ and $ ext{π}_1(1600)$

Demonstrated the effectiveness of mixing correlation functions in mass calculations

Abstract

We calculate the masses of $J^{PC}=1^{-+}$ light exotic mesons by QCD sum rules; the masses are extracted from four-quark--hybrid mixing correlation functions. We construct several $1^{-+}$ four-quark currents and hybrid currents, and get two masses around $1.2\text{-}1.4\text{GeV}$ and $1.45\text{-}1.67\text{GeV}$; they can be identified as $\pi_1(1400)$ and $\pi_1(1600)$.