Electromagnetic properties of the $D_{s1}^{+}(2460)$, $D_{s1}^{+}(2536)$, and their bottom partners in a molecular configuration

TL;DR

This work computes the magnetic dipole and quadrupole moments of open-flavor axial-vector molecular states formed as $D^*K$, $DK^*$, $B^*K$, and $BK^*$ with $J^P=1^+$ using QCD light-cone sum rules with molecular currents. By separating hadronic and QCD contributions and employing photon distribution amplitudes, the study delivers a flavor-decomposed picture: light quarks dominate the EM response with suppressed heavy-quark effects, and distinct signs and deformations differentiate the $K$- and $K^*$-containing channels. The resulting moments exhibit a systematic pattern—negative for $D^*K$ and $B^*K$, positive for $DK^*$ and $BK^*$—accompanied by oblate or prolate charge distributions, respectively. These predictions serve as benchmarks for lattice QCD and provide experimentally accessible signatures in photoproduction and radiative transitions, aiding discrimination between molecular and compact tetraquark structures. The framework also emphasizes the role of light-quark dynamics and offers a concrete path for future tests at high-luminosity facilities.

Abstract

We investigate the electromagnetic properties of the axial-vector molecular states $D^* K$, $DK^*$, $B^* K$, and $BK^*$, which are used to model the charmed states $D_{s1}^{+}(2460)$, $D_{s1}^{+}(2536)$, and their bottom partners with quantum numbers $J^P = 1^+$. To our knowledge, this presents the first comprehensive calculation of the magnetic and quadrupole moments for these specific molecular configurations. Employing the QCD light-cone sum rule method with molecular-type interpolating currents, we compute these moments and perform a detailed flavor decomposition to reveal the internal distribution of the electromagnetic charge and spin. Our results demonstrate that the light up and down quarks dominate the electromagnetic response, with negligible contributions from the heavy quarks. The $D^* K$ and $B^* K$ states exhibit negative quadrupole moments and slightly oblate charge distributions, whereas the $DK^*$ and $BK^*$ states possess positive quadrupole moments and prolate distributions, with significant contributions from the strange quark. The predicted moments provide benchmarks for lattice QCD calculations and are testable through their influence on radiative transitions and photo- and electro-production observables at high-luminosity facilities, offering crucial insights into the internal structure and nature of these axial-vector states.

Figures (3)

• Figure 1: CVG analysis (upper panel) and PC analysis (lower panel) for the magnetic dipole moment of the $D K^\ast$ state as a function of $\mathrm{M^2}$ at fixed $\mathrm{s_0}$ values. In the lower panel, the vertical lines indicate the adopted Borel window, whereas the horizontal line represents the smallest PC value extracted within this region in the present study.
• Figure 2: Magnetic moments of the molecular $D^\ast K$, $D K^\ast$, $B^\ast K$ and $BK^\ast$ states as a function of $\mathrm{M^2}$ at several continuum thresholds. The area bounded by the vertical lines corresponds to the adopted Borel window.
• Figure 3: Three-dimensional visualizations of $D^\ast K$, $D K^\ast$, $B^\ast K$, and $BK^\ast$ states. Left: charge density $\rho$ (e/fm$^3$); Middle: isosurface at 5% of the peak charge density for each state; Right: quadrupole moment components (fm$^2$). These plots illustrate quadrupole-induced deformations, providing a clear view of the spatial geometry and charge distribution. All axes are in femtometers (fm).