The magnetic moment of $Z_{c}(3900)$ as a axial-vector molecular state.

In this article, we tentatively assign the $Z_{c}(3900)$ to be an axialvector molecular state, calculate its magnetic moment using the QCD sum rule method in external weak electromagnetic field. Starting with the two-point correlation function in the external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the mass and pole residue of the $Z_{c}(3900)$ state from the leading term in the expansion and the magnetic moment from the linear response to the external electromagnetic field. The numerical values are $m_{Z_{c}}=3.97\pm0.12\mbox{GeV}$ in agreement with the experimental value $m^{exp}_{Z_{c}}=3899.0\pm3.6\pm4.9\mbox{MeV}$, $\lambda_{Z_{c}}=2.1\pm0.4\times10^{-2}\mbox{GeV}^{5}$ and $\mu_{Z_{c}}=0.19^{+0.04}_{-0.01}\mu_{N}$.