The magnetic moment of $Z_c(3900)$ as an axial-vector molecular state

Abstract

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 external weak electromagnetic field. Starting with the two-point correlation function in external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the mass and pole residue of $Z_c(3900)$ 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 $m^{exp}_{Z_{c}}=3899.0\pm3.6\pm4.9\mbox{MeV}$, $λ_{Z_{c}}=2.1\pm0.4\times10^{-2}\mbox{GeV}^{5}$ and ${\mu }_{Z_c}=0.19_{-0.01}^{+0.04}{\mu }_N$.

14 page, 8 figures, published version