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Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems

F. Jegerlehner·O. V. Tarasov
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Abstract

Two-loop corrections for the correlator of the singlet axial and vector currents in QCD are calculated in the chiral limit for arbitrary momenta. Explicit calculations confirm the non-renormalization theorems derived recently by Vainshtein and Knecht et.al. We find that as in the one-loop case also at the two loops the correlator has only 3 independent form-factors instead of 4. From the explicit results we observe that the two-loop correction to the correlator is equal to the one-loop result times the constant factor C_2(R) alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non- anomalous thansversal amplitudes. The finite overall alpha_s dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity. Our observations, together with known facts, suggest that in perturbation theory the correlator is proportional to the one-loop term to all orders and that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries over to the full correlator.

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F. Jegerlehner, O. V. Tarasov. 2005-10-23. Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems. https://doi.org/10.1016/j.physletb.2006.06.039

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