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

Abstract

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 g˜c2L $$ {\tilde{g}}_c^2(L) $$ 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=8t/L=0.25 $$ c=\sqrt{8t}/L=0.25 $$ 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 g˜c2L $$ {\tilde{g}}_c^2(L) $$ 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