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

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 $[6.0<g_{\ast }^2<6.4]$ 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.

6 pages, 6 figures, published version, added discussion on 5-loop beta-function

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• The twisted gradient flow coupling at one loop
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• Tantalizing dilaton tests from a near-conformal EFT
• Gradient flow step-scaling function for SU(3) with $N_f$ = 6 or 4 fundamental flavors
• Center vortices and the $\mathrm{SU}(3)$ conformal window
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• Beyond the Standard Model: Charting Fundamental Interactions via Lattice Simulations
• Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories
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• Taming lattice artifacts with Pauli--Villars fields
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