Structural dissection of hadronic molecules: The $D^{(*)}\bar{K}^{(*)}$ family under QCD light-cone sum rules

TL;DR

This work computes the magnetic dipole and electric quadrupole moments of three charm–strange molecular tetraquark candidates with $J^{P}=1^{+}$, using QCD light-cone sum rules in an external electromagnetic field. By constructing molecular-like interpolating currents and performing a careful hadronic–QCD match with both perturbative and nonperturbative photon couplings, the authors obtain central values and uncertainties for $\mu$ and $\mathcal{D}$ across the $D\bar{K}^{*}$, $D^{*}\bar{K}$, and $D^{*}\bar{K}^{*}$ channels, including a vanishing moment for the neutral $D\bar{K}^{*}$ combination. A clear pattern emerges: light-quark contributions dominate the magnetic response, while the charm-quark piece is strongly suppressed, consistent with a loosely bound molecular structure; quadrupole moments are small, indicating only weak deformations. The results provide quantitative benchmarks to distinguish molecular configurations from compact multiquark pictures and offer guidance for future experimental searches of electromagnetic signatures of charm–strange exotic states.

Abstract

We investigate the static electromagnetic properties of three charm--strange molecular tetraquark candidates with quantum numbers $J^{P}=1^{+}$, namely the $D\bar{K}^{\ast}$, $D^{\ast}\bar{K}$, and $D^{\ast}\bar{K}^{\ast}$ systems. The analysis is carried out within the framework of QCD light-cone sum rules, using interpolating currents constructed from colour-singlet meson bilinears to reflect their molecular configurations. Both perturbative and non-perturbative photon contributions are included,and numerical predictions for the magnetic and electric quadrupole moments are obtained. The magnetic moments are found to lie in the range $1$--$3$ nuclear magnetons, with the largest value associated with the $D^{*}\bar{K}$ configuration. The quadrupole moments are an order of magnitude smaller, of order $10^{-3}\,\mathrm{fm}^{2}$, indicating only weak deviations from spherical charge distributions. A flavour decomposition shows that the magnetic response is dominated by the light quarks, while the charm-quark contribution is strongly suppressed, a feature naturally expected for loosely bound hadronic molecules. The present analysis extends QCD light-cone sum-rule studies of exotic hadrons by providing a systematic determination of the electromagnetic moments of the $D^{(\ast)}\bar K^{(\ast)}$ molecular systems. These results provide quantitative benchmarks that may help discriminate between molecular configurations and more compact multiquark interpretations and may offer useful guidance for future experimental studies of electromagnetic signatures of charm--strange exotic states.

Figures (1)

• Figure 1: Dependence of the sum-rule diagnostics and the extracted magnetic dipole moment on the Borel mass $\mathrm{M^2}$ for the molecular $D^*\bar{K}^*$ configuration. Panels (a) and (b) show the convergence of the CVG for the $[\bar{u}c][\bar{u}s]$ and $[\bar{d}c][\bar{d}s]$ flavor compositions, respectively. Panels (c) and (d) display the corresponding PC. In all four panels, the curves are obtained by varying the continuum threshold $\mathrm{s_0}$ over the interval given in Table \ref{['table']}. Panels (e) and (f) show the magnetic moment as a function of $\mathrm{M^2}$ for several fixed representative values of $\mathrm{s_0}$. The vertical dashed lines mark the adopted Borel working window, and the horizontal dashed line in panels (c) and (d) indicates the minimum acceptable pole contribution (40%).