Off-shell pion electromagnetic form factor from a gauge-invariant Nambu-Jona-Lasinio model

The off–shell electromagnetic vertex function of pions and kaons is studied in a bosonized Nambu–Jona-Lasinio model with a gauge–invariant proper–time cutoff. The slope of the pion form factor with respect to the pion 4–momentum is found to be equal to the on–shell pion charge radius in the chiral limit. The off–shell slope of the $K^0$ form factor is zero, that of the $K^{\pm }$ about 15% smaller than that of the pion. We compare our results with those of a recent calculation in chiral perturbation theory.