Flavor decomposition of electromagnetic multipole moments in $[q_1{q}_2][{\bar{q}}_3\bar{c}]$ tetraquarks: Light-quark analogs of $T_{cs1}(2900{)}^0$ with $J^P=1^{+}$

We present a systematic study of the magnetic dipole and electric quadrupole moments of compact $[q_1{q}_2][{\bar{q}}_3\bar{c}]$ tetraquark states with quantum numbers $J^P=1^{+}$, in the diquark–antidiquark picture and within the light-cone QCD sum rule framework. By performing a flavor decomposition across all admissible $u\mathrm{/}d$ configurations, we show that the charm-quark contribution to the electromagnetic moments vanishes algebraically at the operator level – a structural feature of the specific spin organization adopted here, in which the heavy antiquark resides in a pseudoscalar antidiquark, distinct from the dynamical $1\mathrm{/}{m}_c$ suppression operative in alternative compact constructions and in hadronic molecules. The magnetic moments follow a coherent light-flavor pattern – positive for $uu$-, negative for $dd$-, and suppressed for mixed-flavor diquarks – and the quadrupole moments are non-zero throughout, corresponding, in the customary geometrical interpretation, to intrinsically deformed charge distributions. We further identify the dimensionless multipole ratio $\mathcal{D}\mathrm{/}\mu$ as a structural observable, independent of the normalization of the interpolating current, which probes the relative geometry of the spin-current and charge distributions complementary to the absolute moments. Taken together, the algebraic decoupling of the charm contribution and the operator-level distinction it implies among different singly-heavy tetraquark architectures constitute methodological signatures that discriminate among the corresponding internal organizations and, to the extent that a physical candidate is dominated by one of them, among compact and molecular interpretations.