Divergences in the hadronic light-by-light amplitude of the holographic soft-wall model

TL;DR

This paper investigates divergences in holographic soft-wall models related to the hadronic light-by-light amplitude, revealing issues with convergence and proposing modifications to address these problems.

Contribution

It uncovers divergences in the soft-wall model's calculations of the light-by-light tensor and suggests modifications to resolve these issues.

Findings

Infinite sums over resonances do not converge for certain observables.

Divergences are linked to non-commuting limits and can be mitigated using bulk-to-boundary propagators.

Modifications to the soft-wall model can resolve divergence issues.

Abstract

We use the WKB approximation to uncover divergences and instances of non-commuting limits in a large class of holographic soft-wall models. We show that the infinite sum over single resonance contributions for a variety of observables involving the Chern-Simons term, such as the VVA correlator or the hadronic light-by-light tensor, does not converge. These divergences can in some cases (such as the VVA correlator) be traced back to non-commuting limits and avoided by working directly in the 5-dimensional setup with bulk-to-boundary propagators. However, the hadronic light-by-light scattering tensor also diverges in the 5-dimensional formulation with corresponding Green functions, preventing a correct implementation of the Melnikov-Vainshtein short-distance constraint and even leading to an infinite contribution to the muon $g-2$. We also discuss modifications of the standard soft-wall model that are able to resolve this issue.