$H\rightarrow \gamma\gamma$ as a Triangle Anomaly: Possible Implications for the Hierarchy Problem

TL;DR

This paper explores the possibility that the Higgs to diphoton decay anomaly is related to a triangle anomaly, with implications for the hierarchy problem and supersymmetry, challenging standard regularization assumptions.

Contribution

It proposes a novel hypothesis that gauge-invariance-violating terms in the $d=4$ calculation cancel across all contributions, offering new insights into anomaly cancellation and hierarchy problem solutions.

Findings

Supersymmetry satisfies the derived anomaly cancellation conditions.

The $d=4$ calculation may be physically meaningful if cancellations occur.

Implications for the hierarchy problem are discussed in the context of anomaly-like conditions.

Abstract

The Standard Model calculation of $H\rightarrow\gamma\gamma$ has the curious feature of being finite but regulator-dependent. While dimensional regularization yields a result which respects the electromagnetic Ward identities, additional terms which violate gauge invariance arise if the calculation is done setting $d=4$. This discrepancy between the $d=4-\epsilon$ and $d=4$ results is recognized as a true ambiguity which must be resolved using physics input; as dimensional regularization respects gauge invariance, the $d=4-\epsilon$ calculation is accepted as the correct SM result. However, here we point out another possibility; working in analogy with the gauge chiral anomaly, we note that it is possible that the individual diagrams do violate the electromagnetic Ward identities, but that the gauge-invariance-violating terms cancel when all contributions to $H\rightarrow\gamma\gamma$, both from the SM and from new physics, are included. We thus examine the consequences of the hypothesis that the $d=4$ calculation is valid, but that such a cancellation occurs. We work in general renormalizable gauge, thus avoiding issues with momentum routing ambiguities. We point out that the gauge-invariance-violating terms in $d=4$ arise not just for the diagram containing a SM $W^{\pm}$ boson, but also for general fermion and scalar loops, and relate these terms to a lack of shift invariance in Higgs tadpole diagrams. We then derive the analogue of "anomaly cancellation conditions", and find consequences for solutions to the hierarchy problem. In particular, we find that supersymmetry obeys these conditions, even if it is softly broken at an arbitrarily high scale.