Electromagnetic form factors: A window into the $D\Lambda_c$, $D^*\Lambda_c$, and $D\Lambda_c^*$ molecular structure

The internal structure of exotic hadrons remains one of the most compelling puzzles in strong interaction physics. In this work, we provide crucial insights into the nature of doubly-charmed pentaquarks by investigating their electromagnetic properties. Using QCD light-cone sum rules, we present the first comprehensive calculation of the magnetic dipole moments of $D\Lambda_c$, $D^*\Lambda_c$, and $D\Lambda_c^*$ molecular pentaquarks with $J^P = \frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{3}{2}^-$, respectively. Our analysis reveals a striking hierarchy of magnetic moments: $\mu_{D\Lambda_c^*} > \mu_{D^*\Lambda_c} > \mu_{D\Lambda_c}$, driven by distinct quark-level mechanisms. While light quarks dominate the overall response, we find that charm quark contributions become strategically important when light quark contributions partially cancel. Beyond dipole moments, we predict higher multipoles -- electric quadrupole and magnetic octupole moments -- that fingerprint the spatial deformation of these states, revealing prolate versus oblate charge distributions. These results provide the first systematic predictions for electromagnetic moments of molecular pentaquark configurations, establishing essential benchmarks for future theoretical and experimental studies. The distinctive patterns we uncover will enable quantitative comparisons with alternative structural models, ultimately helping to resolve the nature of doubly-charmed exotic hadrons.