Axial anomaly and the interplay of quark loops with pseudoscalar and vector mesons in the gamma* --> pi+ pi0 pi- process

Motivated by the ongoing measurements of the Primakoff process pi- gamma* --> pi- pi0 by COMPASS collaboration at CERN, the transition form factor for the canonical anomalous process gamma* --> pi+ pi0 pi- is calculated in a constituent quark loop model. The simplest contribution to this process is the quark "box" amplitude. In the present paper we also explicitly include the vector meson degrees of freedom, i.e., the rho and the omega, thus giving rise to additional, resonant contributions. We find that in order to satisfy the axial anomaly result, a further subtraction in the resonant part is needed. The results are then compared with the vector meson dominance model as well as the Dyson--Schwinger calculations, the chiral perturbation theory result, and the available data.