# If the Weak Were Strong and the Strong Were Weak

## TL;DR

This paper investigates how the phase structure of the Standard Model changes when varying the strengths of the weak and strong forces, revealing smooth transformations and phase transitions, and introduces a new extended gauge theory with complex phase behavior.

## Contribution

It provides a detailed analysis of the phase structure of the Standard Model under force strength variations and introduces a novel two-parameter extended gauge theory with rich phase dynamics.

## Key findings

- No phase transition between SU(3) and SU(2) confining phases with one generation.
- Massless neutrino transforms into a massless down-quark smoothly in certain regimes.
- New extended gauge theory exhibits complex phase structure as coupling strengths vary.

## Abstract

We explore the phase structure of the Standard Model as the relative strengths of the SU(2) weak force and SU(3) strong force are varied. With a single generation of fermions, the structure of chiral symmetry breaking suggests that there is no phase transition as we interpolate between the SU(3)-confining phase and the SU(2)-confining phase. Remarkably, the massless left-handed neutrino, familiar in our world, morphs smoothly into a massless right-handed down-quark. With multiple generations, a similar metamorphosis occurs, but now proceeding via a phase transition. In the second half of the paper we introduce a two-parameter extension of the Standard Model, a chiral gauge theory with gauge group U(1) x Sp(r) x SU(N). We again explore the phase structure of the theory as the relative strengths of the Sp(r) and SU(N) gauge couplings vary.