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

Abstract

AbstractIn this paper, we tentatively assign $$Z_{c}(3900)$$ 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 $$Z_{c}(3900)$$ 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 $$m_{Z_{c}}=3.97\pm 0.12\,\text{ GeV }$$ m Z c = 3.97 ± 0.12 GeV in agreement with the experimental value $$m^{exp}_{Z_{c}}=3899.0\pm 3.6\pm 4.9\text{ MeV }$$ m Z c exp = 3899.0 ± 3.6 ± 4.9 MeV , $$\lambda _{Z_{c}}=2.1\pm 0.4\times 10^{-2}\,\text{ GeV}^{5}$$ λ Z c = 2.1 ± 0.4 × 10 - 2 GeV 5 and $$\mu _{Z_{c}}=0.19^{+0.04}_{-0.01}\mu _{N}$$ μ Z c = 0 . 19 - 0.01 + 0.04 μ N .