# Anomalous dimensions of potential top-partners

## TL;DR

This paper investigates the anomalous dimensions of potential top-partner operators in theories of Partial Compositeness, extending previous calculations and exploring conditions under which large anomalous dimensions are plausible.

## Contribution

It extends prior work on anomalous dimensions, providing general results for all matter representations and spins, and discusses the feasibility of large anomalous dimensions in specific models.

## Key findings

- Perturbation theory suggests some models can have large anomalous dimensions.
- Revisits and extends previous computations of fermionic trilinear anomalous dimensions.
- Provides practical group theory results for gauge theories with multiple fermion representations.

## Abstract

We discuss anomalous dimensions of top-partner candidates in theories of Partial Compositeness. First, we revisit, confirm and extend the computation by DeGrand and Shamir of anomalous dimensions of fermionic trilinears. We present general results applicable to all matter representations and to composite operators of any allowed spin. We then ask the question of whether it is reasonable to expect some models to have composite operators of sufficiently large anomalous dimension to serve as top-partners. While this question can be answered conclusively only by lattice gauge theory, within perturbation theory we find that such values could well occur for some specific models. In the Appendix we collect a number of practical group theory results for fourth-order invariants of general interest in gauge theories with many irreducible representations of fermions.