Charmonia and bottomonia in a magnetic field

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 Y 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.