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We report new results on the conformal properties of an important stronglycoupled gauge theory, a building block of composite Higgs models beyond theStandard Model. With twelve massless fermions in the fundamental representationof the SU(3) color gauge group, an infrared fixed point of the $\beta$-functionwas recently reported in the theory (Cheng:2014jba) with uncertainty in thelocation 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 conformalfixed point and scale invariance in the theory with model-buildingimplications. Using the exact same renormalization scheme as the previousstudy, we show that no fixed point of the $\beta$-function exists in thereported interval. Our findings eliminate the only seemingly credible evidencefor conformal fixed point and scale invariance in the $N_f=12$ model whoseinfrared properties remain unresolved. The implications of the recentlycompleted 5-loop QCD beta function for arbitrary flavor number are discussedwith respect to our work.

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