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

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