Lattice Charge Overlap I: Elastic Limit of Pi and Rho Mesons

Using lattice QCD on a ${16}^3\times 24$ lattice at $\beta =6.0$, we examine the elastic limit of charge overlap functions in the quenched approximation for the pion and rho meson; results are compared to previous direct current insertion calculations. A good signal is seen for the pion, but the electric and magnetic rho meson results are considerably noisier. We find that the pion and rho results are characterized by a monopole mass to rho mass ratio of $0.97(8)$ and $0.73(10)$, respectively. Assuming the functional form of the electric and magnetic form factors are the same, we also find a rho meson g-factor of $g=2.25(34)$, consistent with the nonrelativistic quark model.