Magnetic and quadrupole moments of the , , and States in the Diquark-antidiquark Picture

The magnetic and quadrupole moments of the $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ 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 $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ for the $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ states, respectively. The magnetic moments evaluated for the $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ 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 $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ for the $ Z_{c}(4020)^+ $ , $ Z_{c}(4020)^+ $ , and $ Z_{c}(4020)^+ $ states, respectively. We obtain a non-zero, but small, value for the quadrupole moments of the $ Z_{c}(4020)^+ $ 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}(4020)^+ $ , and $ Z_{c}(4020)^+ $ states with the results of the present study.