Magnetic and quadrupole moments of the , , and 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 $\mu_{Z_{c}} = 0.50 ^{+0.22}_{-0.22}~\mu_N$, $\mu_{Z^{1}_{c}}=1.22 ^{+0.34}_{-0.32}~\mu_N$, $\mu_{Z^2_{c}}=2.40 ^{+0.53}_{-0.48}~\mu_N$ for the $Z_{c}(4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ states, respectively. It can be seen that the magnetic moments evaluated for the states $Z_{c}4020)^+$, $Z_{c}(4050)^+$ and $Z_{c}(4600)^{+}$ are large enough to be experimentally measurable. The magnetic moment is an excellent platform to study the internal organization of hadrons governed by the quark-gluon dynamics of QCD since it is the leading-order response of a bound system to a weak external magnetic field. The quadrupole moment results are as $\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. As seen, 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. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Analysis of the $$\mathrm {X_{AV}}$$ state through its electromagnetic properties

“…Inspired by this, in the present work, the magnetic and quadrupole moments of the theoretically predicted singly-charmed state, X AV , with the quantum numbers J P = 1 + are extracted by means of the QCD light-cone sum rules method by considering the diquark-antidiquark configuration of this state with quark contents [ud][ cs]. Several studies in the literature have extracted the magnetic and quadrupole moments of hiddencharm and singly-charmed tetraquark states [24,26,[28][29][30][31][32][33][34][35][36][37].…”