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 ${\mathcal{D}}_{Z_c}=(0.20_{-0.04}^{+0.05})\times 10^{-3}\text{mbox}{fm}^2$, ${\mathcal{D}}_{Z_c^1}=(0.57_{-0.08}^{+0.07})\times 10^{-3}\text{mbox}{fm}^2$, and ${\mathcal{D}}_{Z_c^2}=(0.30_{-0.04}^{+0.05})\times 10^{-3}\text{mbox}{fm}^2$ 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.

Comments: Chin.Phys.C 48 (2024) 1, 013101