Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group

TL;DR

This study challenges previous claims of an infrared fixed point in the SU(3) gauge theory with 12 massless fermions, showing no fixed point exists in the previously reported interval, thus questioning the conformal nature of the model.

Contribution

Using the same renormalization scheme as prior work, we demonstrate the absence of a fixed point in the earlier reported interval, clarifying the infrared behavior of the Nf=12 model.

Findings

No fixed point found in the previously reported interval

Elimination of credible evidence for conformality in the Nf=12 model

Discussion of 5-loop QCD beta function implications

Abstract

We report new results on the conformal properties of an important strongly coupled gauge theory, a building block of composite Higgs models beyond the Standard Model. With twelve massless fermions in the fundamental representation of the SU(3) color gauge group, an infrared fixed point of the $\beta$-function was recently reported in the theory (Cheng:2014jba) with uncertainty in the location of the critical gauge coupling inside the narrow $[ 6.0<g_*^2<6.4]$ interval and widely accepted since as the strongest evidence for a conformal fixed point and scale invariance in the theory with model-building implications. Using the exact same renormalization scheme as the previous study, we show that no fixed point of the $\beta$-function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the $N_f=12$ model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD beta function for arbitrary flavor number are discussed with respect to our work.