On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$

TL;DR

This paper employs a five-dimensional model to analyze the hadronic light-by-light contribution to muon g-2, revealing the necessity of an infinite number of axial-vector states to satisfy QCD constraints.

Contribution

It introduces a novel warped five-dimensional approach to model QCD for HLbL calculations, ensuring unitarity and anomaly consistency, and highlights the importance of infinite axial-vector states.

Findings

Finite resonances cannot satisfy short-distance constraints.

Axial-vector mesons play a significant role in HLbL.

Infinite axial-vector states are required for consistency.

Abstract

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.