Conformal Window of Gauge Theories with Four-Fermion Interactions and Ideal Walking

TL;DR

This paper studies how four-fermion interactions influence the conformal window in gauge theories, revealing a shrinking window and increased anomalous dimensions, which inform models of walking technicolor and can be tested via lattice simulations.

Contribution

It provides a new phase diagram accounting for four-fermion interactions, showing their impact on the conformal window and implications for realistic technicolor models.

Findings

Conformal window shrinks with four-fermion interactions.

Anomalous dimension exceeds unity at the lower boundary.

Minimal and one-family walking technicolor models are archetypes.

Abstract

We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four-fermion interactions are neglected. The anomalous dimension of the mass increases beyond the unity value at the lower boundary of the new conformal window. We plot the new phase diagram which can be used, together with the information about the anomalous dimension, to propose ideal models of walking technicolor. We discover that when the extended technicolor sector, responsible for giving masses to the standard model fermions, is sufficiently strongly coupled the technicolor theory, in isolation, must have an infrared fixed point for the full model to be phenomenologically viable. Using the new phase diagram we show that the simplest one family and minimal walking technicolor models are the archetypes of models of dynamical electroweak symmetry breaking. Our predictions can be verified via first principle lattice simulations.