A Method to Extract Charged Hadron Properties from Lattice QCD in Magnetic Fields

By analyzing the external field dependence of correlation functions, the magnetic properties of hadrons can be determined using lattice QCD in magnetic fields. To compute the magnetic moments and polarizabilities of charged hadrons, for example, one requires sufficiently weak magnetic fields. Such field strengths, however, lead to closely spaced Landau levels that are not straightforwardly resolved using standard lattice spectroscopy. Focusing on charged spinless hadrons, we introduce a simple projection technique that can be used to isolate the lowest Landau level. As the technique requires the explicit coordinate-space wave-function, we investigate the extent to which the continuum, infinite volume wave-function can be employed. We find that, in practice, the effects of discretization can be handled using a perturbative expansion about the continuum. Finite volume corrections are taken into account by using the discrete magnetic translational invariance of the torus. We show that quantized magnetic fields can lead to pernicious volume effects which depend on the magnetic flux quantum, rather than on the lattice volume.