Decrypting gauge-Yukawa cookbooks

TL;DR

This paper introduces the structure delta, a new notation that simplifies calculations in gauge-Yukawa theories, making it easier for model builders to compute key quantities like beta functions and effective potentials.

Contribution

The paper presents the structure delta, a novel notation that bridges the gap between general gauge-Yukawa formulas and specific models, enhancing computational convenience.

Findings

Simplifies calculations of beta functions in gauge-Yukawa theories

Extends to spontaneous symmetry breaking and effective potential calculations

Demonstrated using the Standard Model and an SU(N_c) toy model

Abstract

For many years, theorists have calculated formulas for useful quantities in general gauge-Yukawa theories. However, these cookbooks are often very difficult to use since the general notation is far removed from practical model building. In this paper, we present the structure delta which allows us to use a surprisingly convenient notation that bridges the gap between general gauge-Yukawa theories and specific models. This is particularly useful for the computation of beta functions, but can also be extended to handle spontaneous symmetry breaking, the effective potential and a variety of other quantities. We will introduce it using the standard model of particle physics and a toy model with an SU(N_c) gauge symmetry.