Charmonia and bottomonia in a magnetic field

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.