Magnetic Catalysis of charmonium in the vector channel

TL;DR

This work addresses how a constant external magnetic field alters the vector charmonium channel. It extends the Hilbert moment QCD sum rules by incorporating magnetic corrections to both the perturbative and nonperturbative QCD sectors and by modifying the hadronic spectral function through a $B$-dependent continuum threshold $s_0(B)$ and resonance parameters. The vacuum calibration yields $s_0(B=0)$, $M_V(B=0)$, $f_V(B=0)$, and $\tilde{Q}^2$, which then serve as baselines to extract the $B$-dependence: as $|q_fB|$ grows, $s_0(B)$ increases, $\Gamma_V(B)\to 0$, $f_V(B)$ increases, and $M_V(B)$ stays essentially constant, signaling magnetic catalysis in the heavy-quark sector. This demonstrates that magnetic catalysis-like strengthening extends beyond light quarks and offers a robust framework to study heavy-quarkonia in magnetized environments, with potential applications to other channels and quarkonia states.

Abstract

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 $J/ψ$ resonance -- namely, its continuum threshold $s_0$, decay constant $f_V$, width $Γ_V$, and its mass $M_V$, as functions of the magnetic field strength. Our results show that $s_0$ and $f_V$ increase monotonically, while $Γ_V$ 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.

Figures (5)

• Figure 1: One-loop diagram representing the two-point correlation function in the charmonium vector channel.
• Figure 2: Squared energy pQCD threshold, $s_0$, normalized to its $|q_fB|=0$ value, as a function of the magnetic field strength.
• Figure 3: $J/\psi$ resonance width, $\Gamma_V$, normalized to its $|q_fB|=0$ value, as a function of the magnetic field strength.
• Figure 4: $J/\psi$ resonance decay constant, $f_V$, normalized to its $|q_fB|=0$ value, as a function of the magnetic field strength.
• Figure 5: $J/\psi$ resonance mass, $M_V$, normalized to its $|q_fB|=0$ value, as a function of the magnetic field strength.