Massless Scalar Degrees of Freedom in QCD and in the Electroweak Sector from the Trace Anomaly

TL;DR

This paper explores how the trace anomaly in QCD and the electroweak sector leads to the emergence of a massless scalar degree of freedom, akin to a dilaton, in the effective action when coupled with gravity.

Contribution

It demonstrates the presence of a massless pole in the effective action related to the trace anomaly using perturbation theory and the TJJ vertex example.

Findings

Identification of a massless pole in the effective action

Connection between trace anomaly and dilaton-like degree of freedom

Perturbative illustration using the TJJ vertex

Abstract

The interaction of QCD and electroweak sector with gravity is characterized by the generation of a massless pole in a specific form factor present in the 1-loop effective action. We briefly illustrate how to single out this behaviour in perturbation theory, by taking as an example the $TJJ$ vertex, with $T$ denoting the energy momentum tensor of the Standard Model. The breaking of scale invariance, due to the trace anomaly, is then related to the appearance of a local degree of freedom in the effective action, which is of dilaton type.