Charmonium Spectroscopy in Strong Magnetic Fields by QCD Sum Rules: S-Wave Ground States

TL;DR

This paper uses QCD sum rules to analyze how strong magnetic fields affect the mass spectra of charmonium states, revealing dominant mixing effects between $ ext{eta}_c$ and $J/ ext{psi}$.

Contribution

It develops a framework for QCD sum rules in magnetic fields and quantifies mass shifts of charmonium ground states, highlighting mixing effects as the main cause.

Findings

Mass shifts of $ ext{eta}_c$ and $J/ ext{psi}$ are calculated in magnetic fields.

Dominant mass shift origin is mixing between $ ext{eta}_c$ and $J/ ext{psi}$.

Subdominant effects include mixing with excited states and continua.

Abstract

We investigate quarkonium mass spectra in external constant magnetic fields by using QCD sum rules. We first discuss a general framework of QCD sum rules necessary for properly extracting meson spectra from current correlators computed in the presence of strong magnetic fields, that is, a consistent treatment of mixing effects caused in the mesonic degrees of freedom. We then implement operator product expansions for pseudoscalar and vector heavy-quark current correlators by taking into account external constant magnetic fields as operators, and obtain mass shifts of the lowest-lying bound states $\eta_c$ and $J/\psi$ in the static limit with their vanishing spatial momenta. Comparing results from QCD sum rules with those from hadronic effective theories, we find that the dominant origin of mass shifts comes from a mixing between $\eta_c$ and $J/\psi$ with a longitudinal spin polarization, accompanied by other subdominant effects such as mixing with higher excited states and continua.