Nucleon electroweak form factors: Analysis of their spectral functions

We investigate the imaginary parts of the nucleon electromagnetic and axial form factors close to threshold in the framework of heavy baryon chiral perturbation theory. For the isovector electromagnetic form factors, we recover the well-known strong enhancement near threshold. For the isoscalar ones, we show that there is no visible enhancement due to the three-pion continuum. This justifies the use of vector meson poles only in dispersion-theoretical calculations. We also calculate the imaginary part of the nucleon isovector axial form factor and show that it is small in the threshold region.