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

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.

24 pages, 12 figures. Comments inserted in the last paragraph of Sec. II; One reference added; Published in PRD; Title slightly changed upon request by PRD

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• Magnetic field effects on the static quark potential at zero and finite temperature
• Heavy meson spectroscopy under strong magnetic field
• Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case
• Entropic force and real-time dynamics of holographic quarkonium in a magnetic field
• Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature
• Magnetic renormalons in a scalar self interacting $\lambda {\varphi }^4$ theory