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Low-energy theorem for γ→3π: surface terms against π-a1-mixing
Authors: A. A. Osipov, M. Khalifa, B. Hiller
Ref.: Phys. Rev. D101 no.3, 034012, 034012 (2020)
Abstract: We reconsider the contribution due to πa1 mixing to the anomalous γ→π+π0π- amplitude from the standpoint of the low-energy theorem Fπ=efπ2F3π, which relates the electromagnetic form factor Fπ0→γγ=Fπ with the form factor Fγ→π+π0π-=F3π both taken at vanishing momenta of mesons. Our approach is based on a recently proposed covariant diagonalization of πa1 mixing within a standard effective QCD-inspired meson Lagrangian obtained in the framework of the Nambu-Jona-Lasinio model. We show that the two surface terms appearing in the calculation of the anomalous triangle quark diagrams or AVV- and AAA-type (A, axial-vector; V, vector) amplitudes are uniquely fixed by this theorem. As a result, both form factors Fπ and F3π are not affected by the πa1 mixing, but the concept of vector meson dominance fails for γ→π+π0π-.
