The magnetic moment of Z${}_c$(3900) as an axial-vector molecular state

In this paper, we tentatively assign Z${}_c$(3900) to be an axialvector molecular state, and calculate its magnetic moment using the QCD sum rule method in an external weak electromagnetic field. Starting with the two-point correlation function in the external electromagnetic field and expanding it in powers 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±0.12 GeV in agreement with the experimental value m${}_{Z_c}^{exp}$=3899.0±3.6±4.9 MeV, λ${}_{Z_c}$=2.1±0.4×10${}^{-2}$ GeV${}^5$ and μ${}_{Z_c}$=0.19${}_{-0.01}^{+0.04}$μ${}_N$.