The Conformal Anomaly and the Neutral Currents Sector of the Standard Model

TL;DR

This paper investigates how the conformal anomaly affects the interaction between gravity and neutral currents in the Standard Model, revealing an anomaly-induced scalar exchange that resembles a dilaton or radion in extra-dimensional theories.

Contribution

It provides a detailed analysis of the graviton-gauge-gauge vertex in the electroweak theory, highlighting the role of the conformal anomaly and the anomaly pole in mediating gravity-neutral current interactions.

Findings

Conformal anomaly induces a massless scalar interaction via an anomaly pole.

The anomaly can be attributed to a conformally coupled Higgs scalar.

The effective dilaton interpretation relates to the trace part of the graviton exchange.

Abstract

We elaborate on the structure of the graviton-gauge-gauge vertex in the electroweak theory, obtained by the insertion of the complete energy-momentum tensor ($T$) on 2-point functions of neutral gauge currents ($VV'$). The vertex defines the leading contribution to the effective action which accounts for the conformal anomaly and related interaction between the Standard Model and gravity. The energy momentum tensor is derived from the curved spacetime Lagrangian in the linearized gravitational limit, and with the inclusion of the term of improvement of a conformally coupled Higgs sector. As in the previous cases of QED and QCD, we find that the conformal anomaly induces an effective massless scalar interaction between gravity and the neutral currents in each gauge invariant component of the vertex. This is described by the exchange of an anomaly pole. We show that for a spontaneously broken theory the anomaly can be entirely attributed to the poles only for a conformally coupled Higgs scalar. In the exchange of a graviton, the trace part of the corresponding interaction can be interpreted as due to an effective dilaton, using a local version of the effective action. We discuss the implications of the anomalous Ward identity for the $TVV'$ correlator for the structure of the gauge/gauge/ effective dilaton vertex in the effective action. The analogy between these effective interactions and those related to the radion in theories with large extra dimensions is pointed out.