Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD

We calculate the probability distributions of quarks in the ground state of the proton, and how they are affected in the presence of a constant background magnetic field. We focus on wave functions in the Landau and Coulomb gauges. We observe the formation of a scalar u-d diquark clustering. The overall distortion of the quark probability distribution under a very large magnetic field, as demanded by the quantisation conditions on the field, is quite small. The effect is to elongate the distributions along the external field axis while localizing the remainder of the distribution.