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 $m_{Z_c}=3.97\pm 0.12\text{mbox}GeV$ in agreement with the experimental value $m_{Z_c}^{exp}=3899.0\pm 3.6\pm 4.9\text{mbox}MeV$, ${\lambda }_{Z_c}=2.1\pm 0.4\times 10^{-2}\text{mbox}{GeV}^5$ and ${\mu }_{Z_c}=0.19_{-0.01}^{+0.04}{\mu }_N$.

Comments: 14 page, 8 figures, published version