Charmonia and Bottomonia in a Magnetic Field

TL;DR

This paper investigates how strong magnetic fields influence charmonium and bottomonium states, revealing that their properties depend on center-of-mass momentum due to a new conserved quantity called pseudomomentum, with numerical results on mass and mixing changes.

Contribution

It introduces the concept of pseudomomentum for quarkonia in magnetic fields and analyzes their mass and state mixing dependence on magnetic field strength and momentum.

Findings

Masses of quarkonia depend on magnetic field strength.

Magnetic field induces mixing between eta and vector states.

Properties vary with center-of-mass momentum in magnetic fields.

Abstract

We study the effect of a static homogeneous external magnetic field on charmonium and bottomonium states. In an external magnetic field, quarkonium states do not have a conserved center-of-mass momentum. Instead there is a new conserved quantity called the pseudomomentum which takes into account the Lorentz force on the particles in the system. When written in terms of the pseudomomentum, the internal and center-of-mass motions do not decouple and, as a result, the properties of quarkonia depend on the states' center-of-mass momentum. We analyze the behavior of heavy particle-antiparticle pairs subject to an external magnetic field assuming a three dimensional harmonic potential and Cornell potential plus spin-spin interaction. In the case of the Cornell potential, we also take into account the mixing of the eta_c and J/psi states and eta_b and Upsilon states due to the background magnetic field. We then numerically calculate the dependence of the masses and mixing fractions on the magnitude of the background magnetic field and center-of-mass momentum of the state.