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

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 Luescher close-quote 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. copyright 1997 The American Physical Society