Possible tetraquark states in the ${\pi }^{+}{\chi }_{c1}$ invariant mass distribution

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 $M_Z=(5.12\pm 0.15)\mathrm{G}\mathrm{e}\mathrm{V}$ or $M_Z=(5.16\pm 0.16)\mathrm{G}\mathrm{e}\mathrm{V}$, which are inconsistent with the experimental data on the ${\pi }^{+}{\chi }_{c1}$ 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.