Perturbative and nonperturbative renormalization of anomalous quark triangles

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler–Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, χ=−Nc/(4π2Fπ2).