The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g-2

Abstract

We revisit well-known short-distance constraints relating the hadronic light-by light Green's function to the $⟨VVA⟩$ one, that have been a subject of debate over the past years in the context of the muon $(g-2)$. Specifically, we identify a relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly that, by contrast, has not received attention in the past. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors, but further applications are discussed as well, with special focus on the role of axial-vector mesons in the HLbL contribution to the muon $(g-2)$. Our results should also contribute to a better understanding of the, so far, controversial interplay among short-distance constraints with longitudinal and transverse degrees of freedom, such as axial-vector mesons. This is key to confront the theoretical and experimental result for the muon $(g-2)$ that, currently, exhibits a $4.2\sigma$ tension.

11 pages+references; major revision including a new model; version accepted for publication in Journal of Physics G

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Cited by in corpus (8)

• On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^{+}{e}^{-}$
• A dispersive estimate of scalar contributions to hadronic light-by-light scattering
• Short-distance constraints for the longitudinal component of the hadronic light-by-light amplitude: an update
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• Constraints on the hadronic light-by-light in the Melnikov-Vainshtein regime
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• Axial-vector exchange contribution to the Hyperfine Splitting
• The light-by-light contribution to the muon anomalous magnetic moment from the axial-vector mesons exchanges within the nonlocal quark model