Spectral functions of nucleon form factors: Three-pion continua at low energies

We study the imaginary parts of the isoscalar electromagnetic and isovector axial form factors of the nucleon close to the 3 π-threshold in covariant baryon chiral perturbation theory. At the two-loop level, the contributions arising from leading and next-to-leading order chiral πN-vertices, as well as pion-induced excitations of virtual Δ(1232) -isobars, are calculated. It is found that the heavy baryon treatment overestimates substantially these 3 π-continua. From a phenomenological analysis, that includes the narrow ω(783) -resonance or the broad a ₁ -resonance, one can recognize small windows near threshold, where chiral 3 π-dynamics prevails. However, in the case of the isoscalar electromagnetic form factors GE,Ms(t), the radiative correction provided by the πγ-intermediate state turns out to be of similar size.