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

TL;DR

This paper investigates the role of axial-vector mesons and their degrees of freedom in the short-distance constraints of the hadronic light-by-light contribution to muon g-2, aiming to clarify theoretical ambiguities and improve accuracy.

Contribution

It identifies a new relation enforced by the axial anomaly that helps resolve basis ambiguities in axial-vector meson form factors and enhances understanding of short-distance constraints in muon g-2 calculations.

Findings

Established a relation among longitudinal and transverse degrees of freedom due to the axial anomaly.

Provided a method to resolve basis ambiguities in axial-vector meson transition form factors.

Discussed implications for the HLbL contribution to muon g-2 and the tension with experimental results.

Abstract

We revisit well-known short-distance constraints relating the hadronic light-by light Green's function to the $\langle VVA \rangle$ 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.