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

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 $π_1(1400)$ and $π_1(1600)$.

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