Eur. Phys. J. Plus (2014) 129: 159
https://doi.org/10.1140/epjp/i2014-14159-2

Regular Article

Decrypting gauge-Yukawa cookbooks

CP3-Origins and the Danish Institute for Advanced Study DIAS, University of Southern Denmark, Campusvej 55, DK-5230, Odense M, Denmark

^* e-mail: molgaard@cp3-origins.net

Received: 7 May 2014
Accepted: 29 June 2014
Published online: 29 July 2014

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.