The Constructive Standard Model: Part I

TL;DR

This paper constructs the complete set of minimal 3-point vertices for the massive Standard Model and gravity using symmetry principles, analyzing their high-energy behavior without relying on traditional field theory methods.

Contribution

It introduces a purely symmetry-based constructive method to derive all minimal 3-point vertices for the massive SM and gravity, bypassing gauge symmetries and Feynman rules.

Findings

Derived all minimal 3-point vertices for the massive SM and gravity.

Analyzed high-energy behavior and normalized vertices against massless cases.

Provided comprehensive tables of vertices for future research.

Abstract

In this paper, we construct the complete set of minimal 3-point vertices for the massive Standard Model (SM) based purely on symmetry principles, mass dimension and high-energy behavior and without any recourse to field theory, gauge symmetries or Feynman rules. Because the gravitational vertices are no more challenging than any other vertices in this constructive method, we include them as well. We also calculate the high-energy behavior of these vertices and compare with the well-known massless vertices, both as a check and as a way to pin down the normalization constants. We include all these vertices in tables as a reference for future investigations.