Pion decays and the pion electromagnetic form factor in a σ-model with quarks

Abstract

We study in the one-loop approximation the decays of the pion and the pion electromagnetic form factor at low q 2 in the framework of a σ-model with quarks. The theory has a free parameters the quark and σ masses and the results are very insensitive to their values. We get good approximation for all processes considered except for the ratio of the axial to the vector form factor that appear in the electronic radiative decay of the charged pion. The reason is probably that our model includes the pion-pion interaction only in the isoscalar s-wave at the one-loop level.