BETHE-SALPETER AMPLITUDES AND DENSITY CORRELATIONS FOR MESONS WITH WILSON FERMIONS

We present an investigation of various gauge-invariant definitions of the qqBAR Bethe-Salpeter (BS) amplitude for mesons in lattice QCD, and compare them to the Coulomb and Landau gauge BS amplitudes. We show that the gauge-invariant BS amplitude is considerably broadened by the use of ''fat'' gauge links (constructed by smearing the links of the original lattice). A qualitative demonstration of the Lorentz contraction of the pion wave function at nonzero momentum is given. We also calculate density-density correlations and discuss the limitations in extracting the charge radius of the pion from these observables. Lastly, the polarization dependence of the BS amplitude for the p meson is exhibited, and we extract the relative admixture of l = 0 and l = 2 states showing that simple hydrogenlike wave functions provide a good fit.