Magnetic and quadrupole moments of the $Z_c(4020{)}^{+}$, $Z_c(4050{)}^{+}$, and $Z_c(4600{)}^{+}$ states in the diquark-antidiquark picture

Abstract

The magnetic and quadrupole moments of the $Z_c(4020{)}^{+}$, $Z_c(4050{)}^{+}$ and $Z_c(4600{)}^{+}$ states are calculated within the QCD light-cone sum rules. The compact diquark-antidiquark interpolating currents and the distribution amplitudes of the on-shell photon are used to extract the magnetic and quadrupole moments of these states. The magnetic moments are acquired as ${\mu }_{Z_c}=0.50_{-0.22}^{+0.22}{\mu }_N$, ${\mu }_{Z_c^1}=1.22_{-0.32}^{+0.34}{\mu }_N$, and ${\mu }_{Z_c^2}=2.40_{-0.48}^{+0.53}{\mu }_N$ for the $Z_c(4020{)}^{+}$, $Z_c(4050{)}^{+}$ and $Z_c(4600{)}^{+}$ states, respectively. The magnetic moments evaluated for the $Z_{c}4020{)}^{+}$, $Z_c(4050{)}^{+}$ and $Z_c(4600{)}^{+}$ states are sufficiently large to be experimentally measurable. The magnetic moment is an excellent platform for studying the internal structure of hadrons governed by the quark-gluon dynamics of QCD because it is the leading-order response of a bound system to a weak external magnetic field. The quadrupole moment results are $\mathcal{D}_{Z_c}=(0.20 ^{+0.05}_{-0.04}) \times 10^{-3}~\mbox{fm}^2 $, $\mathcal{D}_{Z_c^1}=(0.57 ^{+0.07}_{-0.08}) \times 10^{-3}~\mbox{fm}^2 $, and $\mathcal{D}_{Z_c^2}=(0.30 ^{+0.05}_{-0.04}) \times 10^{-3}~\mbox{fm}^2 $ for the $Z_c(4020{)}^{+}$, $Z_c(4050{)}^{+}$ and $Z_c(4600{)}^{+}$ states, respectively. We obtain a non-zero, but small, value for the quadrupole moments of the $Z_c$ states, which indicates a non-spherical charge distribution. The nature and internal structure of these states can be elucidated by comparing future experimental data on the magnetic and quadrupole moments of the $Z_c(4020{)}^{+}$, $Z_c(4050{)}^{+}$, and $Z_c(4600{)}^{+}$ states with the results of the present study.

arXiv commentChin.Phys.C 48 (2024) 1, 013101

References in corpus (42)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• The hidden-charm pentaquark and tetraquark states
• Observation of a charged charmoniumlike structure in e+e- to pi+pi-J/psi at \sqrt{s}=4.26 GeV
• The $XYZ$ states: experimental and theoretical status and perspectives
• Multiquark Resonances
• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• Pentaquark and Tetraquark states
• Heavy-Quark QCD Exotica
• Study of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ and Observation of a Charged Charmonium-like State at Belle
• Exotics: Heavy Pentaquarks and Tetraquarks
• An updated review of the new hadron states
• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• Observation of a charged charmoniumlike structure Z_c(4020) and search for the Z_c(3900) in e+e- to pi+pi-h_c
• QCD at Low Energies
• Observation of the resonant character of the $Z(4430{)}^{-}$ state
• New Charmonium States in QCD Sum Rules: a Concise Review
• Observation of a charged charmoniumlike structure in $e^{+}{e}^{-}\to (D^{\ast }{\bar{D}}^{\ast }{)}^{\pm }{\pi }^{\mp }$ at $\sqrt{s}=4.26$GeV
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Can the X(3872) be a 1^{++} four-quark state?
• Four-Quark Hadrons: an Updated Review
• Observation of two resonance-like structures in the pi+ chi_c1 mass distribution in exclusive B0-bar --> K- pi+ chi_c1 decays
• Photon Distribution Amplitudes in QCD
• Observation of new resonances decaying to $J/\psi K^{+}$ and $J/\psi \varphi$
• Observation of a near-threshold structure in the $K^{+}$ recoil-mass spectra in $e^{+}{e}^{-}\to K^{+}(D_s^{-}{D}^{\ast 0}+D_s^{\ast -}{D}^0)$
• Observation of a new charged charmoniumlike state in B -> J/psi K pi decays
• Measurement of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$ via Initial State Radiation at Belle
• Four-quark exotic mesons
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• Mass spectra of Zc and Zb exotic states as hadron molecules
• Magnetic moment of the Delta(1232)-resonance in chiral effective field theory
• Exotic Heavy Quarkonium Spectroscopy: A Mini-review
• Chiral effective-field theory in the Delta(1232) region: II. radiative pion photoproduction
• Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules
• Model-independent observation of exotic contributions to $B^0\to J/\psi K^{+}{\pi }^{-}$ decays
• Magnetic and quadrupole moments of the $Z_c(3900)$
• Magnetic dipole moment of the $Z_{cs}(3985)$ state: diquark-antidiquark and molecular pictures
• ${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$ molecular state with $J^P=1^{+}$
• Magnetic dipole moments of the $Z_c(4020{)}^{+}$, $Z_c(4200{)}^{+}$, $Z_{cs}(4000{)}^{+}$ and $Z_{cs}(4220{)}^{+}$ states in light-cone QCD
• The magnetic moment of the $Z_c(3900)$ as an axialvector tetraquark state with QCD sum rules
• The magnetic moment of $Z_c(3900)$ as an axial-vector molecular state
• Magnetic moments of the vector hidden-charmed tetraquark states

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