The twelve-flavor β-function and dilaton tests of the sextet scalar

¹ University of Wuppertal, Department of Physics, Wuppertal D-42097, Germany
² Juelich Supercomputing Center, Forschungszentrum Juelich, Juelich D-52425, Germany
³ University of the Pacific, 3601 Pacific Ave, Stockton CA 95211, USA
⁴ University of California, San Diego, 9500 Gilman Drive, La Jolla CA 92093, USA
⁵ Eötvös University, Institute for Theoretical Physics
⁶ MTA-ELTE Lendulet Lattice Gauge Theory Research Group, Budapest 1117, Hungary
⁷ Universidad Autonoma, IFT UAM/CSIC and Departamento de Fisica Teorica, 28049 Madrid, Spain

Published online: 26 March 2018

Abstract

We discuss near-conformal gauge theories beyond the standard model (BSM) where interesting results on the twelve-flavor β-function of massless fermions in the fundamental representation of the SU(3) color gauge group and dilaton tests of the light scalar with two massless fermions in the two-index symmetric tensor (sextet) representation can be viewed as parts of the same BSM paradigm under investigation. The clear trend in the decreasing size of β-functions at fixed renormalized gauge coupling is interpreted as a first indicator how the conformal window (CW) is approached in correlation with emergent near-conformal light scalars. BSM model building close to the CW will be influenced by differing expectations on the properties of the emergent light 0++ scalar either as a σ-particle of chiral symmetry breaking (_ΧS B), or as a dilaton of scale symmetry breaking. The twelve-flavor β-function emerges as closest to the CW, perhaps near-conformal, or perhaps with an infrared fixed point (IRFP) at some unexplored strong coupling inside the CW. It is premature to speculate on dilaton properties of the twelveflavor model since the near-conformal realization remains an open question. However, it is interesting and important to investigate dilaton tests of the light sextet scalar whose β-function is closest to the CW in the symmetry breaking phase and emerges as the leading candidate for dilaton tests of the light scalar. We report results from high precision analysis of the twelve-flavor β-function [1] refuting its published IRFP [2, 3]. We present our objections to recent claims [4, 5] for non-universal behavior of staggered fermions used in our analysis. We also report our first analysis of dilaton tests of the light 0⁺⁺ scalar in the sextet model and comment on related post-conference developments. The dilaton test is the main thrust of this conference contribution including presentation #405 on the n_f = 12 β-function and presentation #260 on dilaton tests of the sextet model. They are both selected from the near-conformal BSM paradigm.