Possible tetraquark states in the $π^+ χ_{c1}$ invariant mass distribution

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In this article, we assume that there exist hidden charmed tetraquark states with the spin-parity $J^P=1^-$, and calculate their masses with the QCD sum rules. The numerical result indicates that the masses of the vector hidden charmed tetraquark states are about $M_{Z}=(5.12\pm0.15) \rm{GeV}$ or $M_{Z}=(5.16\pm0.16) \rm{GeV}$, which are inconsistent with the experimental data on the $π^+ χ_{c1}$ invariant mass distribution. The hidden charmed mesons $Z_1$, $Z_2$ or $Z$ may be scalar hidden charmed tetraquark states, hadro-charmonium resonances or molecular states.
12 pages, 4 figures

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