Twelve massless flavors and three colors below the conformal window

TL;DR

This study investigates whether a 12-flavor SU(3) gauge theory exhibits chiral symmetry breaking or conformal behavior, providing new non-perturbative evidence favoring chiral symmetry breaking over conformality.

Contribution

The paper offers comprehensive lattice simulation results testing both hypotheses for the 12-flavor SU(3) model, clarifying its non-perturbative behavior relevant to BSM physics.

Findings

Evidence supports chiral symmetry breaking over conformality.

Low confidence in the conformal scenario based on lattice data.

Finite temperature transition hints at chiral symmetry breaking.

Abstract

We report new results for a frequently discussed gauge theory with twelve fermion flavors in the fundamental representation of the SU(3) color gauge group. The model, controversial with respect to its conformality, is important in non-perturbative studies searching for a viable composite Higgs mechanism Beyond the Standard Model (BSM). To resolve the controversy, we subject the model to opposite hypotheses inside and outside of the conformal window. In the first hypothesis we test chiral symmetry breaking ($\chi{\rm SB}$) with its Goldstone spectrum, $F_\pi$, the $\chi{\rm SB}$ condensate, and several composite hadron states as the fermion mass is varied in a limited range with our best effort to control finite volume effects and extrapolation to the massless chiral limit. Supporting results for $\chi{\rm SB}$ from the running coupling based on the force between static sources and some preliminary evidence for the finite temperature transition are also presented. In the second test for the alternate hypothesis we probe conformal behavior driven by a single anomalous mass dimension under the assumption of unbroken chiral symmetry. Our results show a very low level of confidence in the conformal scenario. Staggered lattice fermions with stout-suppressed taste breaking are used throughout the simulations.