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 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}}=3.97pm 0.12,text{ GeV } in agreement with the experimental value m^{exp}_{Z_{c}}=3899.0pm 3.6pm 4.9text{ MeV }, lambda _{Z_{c}}=2.1pm 0.4times 10^{-2},text{ GeV}^{5} and mu _{Z_{c}}=0.19^{+0.04}_{-0.01}mu _{N}.
Highlights
Zc(3900), as a good candidate of exotic hadrons, was observed by the BESIII collaboration in 2013 in the π ± J/ψ invariant mass distribution of the process e+e− → π +π − J/ψ at a center-of-mass energy of 4.260 GeV [1]
The electromagnetic multipole moments of hadron encode the spatial distributions of charge and magnetization in the hadron and provide important information about the quark configurations of the hadron and the underlying dynamics
We study the magnetic moment of Zc(3900) as an axialvector molecular state with quantum number J P = 1+ by the quantum chromodynamics (QCD) sum rule method
Summary
Zc(3900), as a good candidate of exotic hadrons, was observed by the BESIII collaboration in 2013 in the π ± J/ψ invariant mass distribution of the process e+e− → π +π − J/ψ at a center-of-mass energy of 4.260 GeV [1]. In 2017, the BESIII collaboration determined the J P quantum number of Zc(3900) to be J P = 1+ with a statistical significance larger than 7σ over other quantum numbers in a partial wave analysis of the process e+e− → π +π − J/ψ [4] Inspired by this experimental progress, there have been plentiful theoretical studies on Zc(3900)’s properties through different approaches We study the magnetic moment of Zc(3900) as an axialvector molecular state with quantum number J P = 1+ by the QCD sum rule method. The magnetic moment is extracted from the linear term in Fμν (external electromagnetic field) of the correlation function. Μν( p) can be calculated theoretically via the OPE method at the quark–gluon level To this end, one can insert the interpolating current Jμ(x) (2) into the correlation function (1), contract the relevant quark fields via Wick’s theorem and obtain. 4.6 GeV (real line) and s (dashed line) and dividing it by the original expression, one has
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