Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball

We generalize the dispersive approach to axial anomaly by A. D. Dolgov and V. I. Zakharov [Nucl. Phys. B27, 525 (1971).] to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the π0, η, η′ → γγ∗ transition form factors. Using them,...

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Bibliographic Details
Published in:Physical review. D 2021-07, Vol.104 (1), p.1, Article 016011
Main Authors: Khlebtsov, Sergey, Klopot, Yaroslav, Oganesian, Armen, Teryaev, Oleg
Format: Article
Language:English
Subjects:
Form factors
Gluons
Photons
Sum rules
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Summary:We generalize the dispersive approach to axial anomaly by A. D. Dolgov and V. I. Zakharov [Nucl. Phys. B27, 525 (1971).] to a non-Abelian case with arbitrary photon virtualites. We derive the anomaly sum rule for the singlet current and obtain the π0, η, η′ → γγ∗ transition form factors. Using them, we established the behavior of a nonperturbative gluon matrix element ⟨0|GG|γγ∗ (q2) ⟩ in both spacelike and timelike regions. We found a significant contribution of the non-Abelian axial anomaly to the processes with one virtual photon, comparable to that of the electromagnetic anomaly. The duality between the axial and the vector channels was observed: the values of duality intervals and mixing parameters in the axial channel were related to vector resonances' masses and residues. The possibility of a light pseudoscalar glueball-like state is conjectured.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.104.016011