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

Abstract

We use the Wentzel-Kramers-Brillouin (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 vector-vector-axial (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.

arXiv commentREVTeX, 28 pages, 8 figures, 3 tables, v2: references and one appendix on WSS model added, v3 (published version): minor typos corrected

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