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

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 ${\pi }_1(1600)$.

Comments: 10 pages, 6 figures, 3 tables