The magnetic moment of $$Z_{c}(3900)$$ Z c
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Regular Article - Theoretical Physics
The magnetic moment of Zc(3900) as an axial-vector molecular state Yong-Jiang Xu1,a , Yong-Lu Liu1, Ming-Qiu Huang1,2,b 1 2
Department of Physics, College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, Hunan, China Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, Hunan, China
Received: 17 August 2020 / Accepted: 2 October 2020 © The Author(s) 2020
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 = 3.97 ± 0.12 GeV in agreement with the experex p imental value m Z c = 3899.0 ± 3.6 ± 4.9MeV, λ Z c = 2.1 ± 0.4 × 10−2 GeV5 and μ Z c = 0.19+0.04 −0.01 μ N .
1 Introduction Z c (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]. Then the Belle and CLEO collaborations confirmed the existence of Z c (3900) [2,3]. In 2017, the BESIII collaboration determined the J P quantum number of Z c (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 Z c (3900)’s properties through different approaches (see Ref. [5–7] and the references therein for details). However, the underlying structure of Z c (3900) is not understood completely and more endeavors are necessary in order to arrive at a better understanding for the properties of Z c (3900). a e-mail:
[email protected] (corresponding author)
b e-mail:
[email protected]
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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. So it is interesting to study the electromagnetic multipole moments of hadron. The studies on the properties of hadrons inevitably involve the nonperturbative effects of quantum chromodynamics (QCD). The QCD sum rule method [8,9] is a nonperturbative analytic formalism firmly entrenched in QCD with minimal modeling and has been successfully applied in almost every aspect of strong interaction physics. In Refs. [10–12], the QCD sum rule method was extended to calculating the magnetic moments of the nucleon and hyperon in the externa
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