Measuring the ground-state wave functional of SU(2) Yang-Mills theory in 3+1 dimensions: Abelian plane waves

A method of measuring relative probabilities of various gauge-field configurations in the Yang-Mills vacuum was proposed long ago [Phys. Lett. B 223 (1989) 207]. We applied this method to compute the square of the YM vacuum wave functional (VWF) in numerical simulations of SU(2) lattice gauge theory in D=3+1 dimensions for sets of abelian plane waves. The results were compared to predictions based on some VWF proposals in the literature. None of them describes the data satisfactorily at large plane-wave momenta. The phenomenological best fit to data, containing three free parameters, appears to reduce in the continuum limit to the approximate form proposed in [Phys. Rev. D 77 (2008) 065003].