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In this article, we assume that there exist hidden charmed tetraquark stateswith the spin-parity $J^P=1^-$, and calculate their masses with the QCD sumrules. The numerical result indicates that the masses of the vector hiddencharmed 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 experimentaldata on the $\pi^+ \chi_{c1}$ invariant mass distribution.  The hidden charmed mesons $Z_1$, $Z_2$ or $Z$ may be scalar hidden charmedtetraquark states, hadro-charmonium resonances or molecular states.

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