Higher Order Dilaton Interactions in the Nearly Conformal Limit of the Standard Model

TL;DR

This paper explores the interactions of the dilaton in the nearly conformal limit of the Standard Model, deriving higher-order couplings from anomalous Ward identities to distinguish it from the Higgs.

Contribution

It provides a systematic method to compute higher-order dilaton interactions in the nearly conformal Standard Model using anomalous Ward identities.

Findings

Derived dilaton couplings up to quartic order in the conformal breaking scale.

Established a framework to extend calculations to higher orders.

Provided a phenomenological distinction between the Higgs and dilaton.

Abstract

We investigate the Standard Model in the nearly conformal limit, in which conformal symmetry is broken only by the dilatation anomaly, through a hierarchy of anomalous Ward identities for the divergence of its dilatation current. In this approximation, the identities allow to extract the coupling of the dilaton to the trace anomaly, which we compute up to the quartic order in the conformal breaking scale. Our approach can be easily extended to discuss the anomaly contributions to the dilaton effective action to an arbitrarily high order. They allow to make a distinction between the Higgs and a dilaton at a phenomenological level.