Abstract
We calculate the magnetic dipole moment of the newly observed charged hidden-charmed open strange \( Z_{cs}(3985)^- \) state, recently observed by BESIII Collaboration. Based on the information provided by the experiment and theoretical studies followed the observation, we assign the quantum numbers \( J^{P} = 1^{+}\) and the quark composition \( c {{\bar{c}}} s{{\bar{u}}} \) to this state and estimate the magnetic dipole moment of this resonance in both the compact diquark–antidiquark and molecular pictures. We apply the light cone QCD formalism and use the distribution amplitudes of the on-shell photon with different twists. The obtained results in both pictures are consistent with each other within the errors. The magnitude of the magnetic dipole moment shows that it is accessible in the experiment.
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Appendix: Photon distribution amplitudes and wave functions
Appendix: Photon distribution amplitudes and wave functions
In this Appendix, we present the matrix elements \(\langle \gamma (q)\left| {\bar{q}}(x) \Gamma _i q(0) \right| 0\rangle \) and \(\langle \gamma (q)\left| {\bar{q}}(x) \Gamma _i G_{\mu \nu }q(0) \right| 0\rangle \) in terms of the photon DAs and wave functions of different twists [67],
where \(\varphi _\gamma (u)\) is the distribution amplitude of leading twist-2, \(\psi ^v(u)\), \(\psi ^a(u)\), \({{{\mathcal {A}}}}(\alpha _i)\) and \({{{\mathcal {V}}}}(\alpha _i)\), are the twist-3 amplitudes, and \(h_\gamma (u)\), \({\mathbb {A}}(u)\), \({{{\mathcal {S}}}}(\alpha _i)\), \(\mathcal{{{{\tilde{S}}}}}(\alpha _i)\), \({{{\mathcal {T}}}}_1(\alpha _i)\), \({{{\mathcal {T}}}}_2(\alpha _i)\), \({{{\mathcal {T}}}}_3(\alpha _i)\) and \({{{\mathcal {T}}}}_4(\alpha _i)\) are the twist-4 photon DAs. The measure \({{{\mathcal {D}}}} \alpha _i\) is defined as
The expressions of the DAs entering into the above matrix elements are defined as:
Numerical values of parameters used in distribution amplitudes are: \(\varphi _2(1~GeV) = 0\), \(w^V_\gamma = 3.8 \pm 1.8\), \(w^A_\gamma = -2.1 \pm 1.0\), \(\kappa = 0.2\), \(\kappa ^+ = 0\), \(\zeta _1 = 0.4\), \(\zeta _2 = 0.3\).
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Özdem, U., Azizi, K. Magnetic dipole moment of the \(Z_{cs}(3985)\) state: diquark–antidiquark and molecular pictures. Eur. Phys. J. Plus 136, 968 (2021). https://doi.org/10.1140/epjp/s13360-021-01977-w
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DOI: https://doi.org/10.1140/epjp/s13360-021-01977-w