The magnetic moment of the Z_c(3900) as an axialvector tetraquark state with QCD sum rules

Zhi-Gang Wang

doi:10.1140/epjc/s10052-018-5794-0

Abstract

In this article, we assign the Z_c^pm (3900) to be the diquark-antidiquark type axialvector tetraquark state, study its magnetic moment with the QCD sum rules in the external weak electromagnetic field by carrying out the operator product expansion up to the vacuum condensates of dimension 8. We pay special attention to matching the hadron side with the QCD side of the correlation function to obtain solid duality, the routine can be applied to study other electromagnetic properties of the exotic particles.

Highlights

In 2013, the BESIII collaboration studied the process e+e− → π +π − J/ψ at a center-of-mass energy of 4.260 GeV, and observed a structure Zc(3900) in the π ± J/ψ invariant mass distribution [1]
In Ref. [28], Ioffe and Smilga introduce a static electromagnetic field which couples to the quarks and polarizes the QCD vacuum, and extract the nucleon magnetic moments from linear response to the external electromagnetic field with the QCD sum rules
This approach has been applied successfully to study the magnetic moments of the octet baryons and decuplet baryons [30,31,32,33,34]. We extend this approach to study the magnetic moment of the hidden-charm tetraquark state Zc(3900)

Summary

Introduction

In 2013, the BESIII collaboration studied the process e+e− → π +π − J/ψ at a center-of-mass energy of 4.260 GeV, and observed a structure Zc(3900) in the π ± J/ψ invariant mass distribution [1]. We tentatively assign the Zc(3900) to be the diquark-antidiquark type tetraquark state and study its magnetic moment with the QCD sum rules in the external weak electromagnetic field. [29], Balitsky and Yung) introduce a static electromagnetic field which couples to the quarks and polarizes the QCD vacuum, and extract the nucleon magnetic moments from linear response to the external electromagnetic field with the QCD sum rules. Z(4430) = 181 ± 31 MeV can be absorbed into the continuum states (the Z (4430) can be tentatively assigned to be the first radial excitation of the Zc(3900) based on the QCD sum rules [37]), the zero width approximation in the hadronic spectral density works, the contaminations of the intermediate meson-loops are expected to be small and can be neglected safely [38]. . . . can be neglected approximately, the non-diagonal transitions can be approximated as λ2Z C exp

Numerical results and discussions

Conclusion