Residual meson-meson interaction from lattice gauge simulation in a simple (2+1)-dimensional QED model

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Abstract
The residual interaction for a meson-meson system is computed utilizing a cumulant expansion of the momentum-space time correlation matrix. The cumulant expansion serves to define free meson-meson operators. The definition of an effective interaction is then based on a comparison of the full (interacting) and the free (noninteracting) time correlation matrices. The proposed method, which may be transcribed to hadron-hadron systems in QCD, here is applied to a (2+1)-dimensional U(1) lattice gauge model tuned such that it is confining. Fermions are treated in the staggered scheme. The effective interaction exhibits a repulsive core and attraction at intermediate relative distances. These findings are consistent with an earlier study of the same model utilizing Lüscher’s method where scattering phase shifts are obtained directly. The computed residual interaction is used to calculate scattering phase shifts, relative meson-meson wave functions, and the total cross section.
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