Explicit results for the anomalous three point function and non-renormalization theorems

• Published in: Physics letters. B Vol. 639; no. 3-4; pp. 299 - 306
• Main Authors: Jegerlehner, F., Tarasov, O.V.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 10.08.2006; Elsevier Science
• Subjects: Exact sciences and technology; Nuclear physics; Physics; The physics of elementary particles and fields; Perturbation theory; Ward identity; Axial-vector currents; Anomaly; Correlators; Renormalization; Singlet; Time constant; Form factors; Corrections; Quantum chromodynamics
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2006.06.039

Two-loop corrections for the 〈VVA〉 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 [A. Vainshtein, Phys. Lett. B 569 (2003) 187] and Knecht et al. [M. Knecht, S. Peris, M. Perrottet, E. de Rafael, JHEP 0403 (2004) 035]. We find that as in the one-loop case also at two loops the 〈VVA〉 correlator has only three independent form-factors instead of four. 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 C2(R)αs/π in the MS¯ scheme. This holds for the full correlator, for the anomalous longitudinal as well as for the non-anomalous transversal amplitudes. The finite overall αs dependent constant has to be normalized away by renormalizing the axial current according to Witten's algebraic/geometrical constraint on the anomalous Ward identity [〈VV∂A〉 correlator]. Our observations, together with known facts, suggest that in perturbation theory the 〈VVA〉 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.