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

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 (IRFP) of the β-function was recently reported in the theory [A. Cheng, A. Hasenfratz, Y. Liu, G. Petropoulos, and D. Schaich, J. High Energy Phys. 05 (2014) 137] 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 β-function exists in the reported interval. Our findings eliminate the only seemingly credible evidence for conformal fixed point and scale invariance in the Nf=12 model whose infrared properties remain unresolved. The implications of the recently completed 5-loop QCD β-function for arbitrary flavor number are discussed with respect to our work.