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Journal of High Energy Physics

, 2018:132 | Cite as

Nonperturbative β function of twelve-flavor SU(3) gauge theory

  • Anna Hasenfratz
  • David Schaich
Open Access
Regular Article - Theoretical Physics

Abstract

We study the discrete β function of SU(3) gauge theory with N f = 12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling \( {\tilde{g}}_c^2(L) \) we determine the continuum-extrapolated discrete β function up to g c 2  ≈ 8.2. We observe an IR fixed point at g 2  = 7.3( − 2 + 8 ) in the \( c=\sqrt{8t}/L=0.25 \) scheme, and g 2  = 7.3( − 3 + 6 ) with c = 0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the (a/L) → 0 extrapolations, the interpolation of \( {\tilde{g}}_c^2(L) \) as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller c ≲ 0.2 with smaller L ≤ 12, leading to an IR fixed point at g 2  = 5.9(1.9) in the c = 0.2 scheme, which resolves to g 2  = 6.9( − 1 + 6 ) upon considering only L ≥ 16. At the IR fixed point we measure the leading irrelevant critical exponent to be γ g  = 0.26(2), comparable to perturbative estimates.

Keywords

Lattice Quantum Field Theory Renormalization Group Technicolor and Composite Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of ColoradoBoulderU.S.A.
  2. 2.Department of PhysicsSyracuse UniversitySyracuseU.S.A.
  3. 3.AEC Institute for Theoretical PhysicsUniversity of BernBernSwitzerland

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