Magnetic Catalysis of charmonium in the vector channel

We investigate the impact of an external magnetic field on the vector charmonium system within the framework of Hilbert moment QCD sum rules. By incorporating magnetic corrections to the perturbative contributions of the QCD sector, we analyze the behavior of the hadronic parameters of the $J/\psi$ resonance -- namely, its continuum threshold $s_0$, decay constant $f_V$, width $\Gamma_V$, and its mass $M_V$, as functions of the magnetic field strength. Our results show that $s_0$ and $f_V$ increase monotonically, while $\Gamma_V$ decreases significantly and $M_V$ remains essentially constant. These behaviors indicate a strengthening of the hadronic state in the presence of a magnetic field, consistent with the phenomenon of magnetic catalysis. Although magnetic catalysis has traditionally been associated with light-quark systems via chiral symmetry breaking, our results demonstrate that similar effects persist in the heavy-quark sector, despite the absence of chiral dynamics.