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

Anna Hasenfratz; David Schaich

doi:10.1007/JHEP02(2018)132

paper

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

arXiv:1610.10004 · doi:10.1007/JHEP02(2018)132

Abstract

We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $g ~_{c}^{2} (L)$ we determine the continuum-extrapolated discrete beta function up to $g_{c}^{2} \approx 8.2$ . We observe an IR fixed point at $g_{⋆}^{2} = 7.3 (_{- 2}^{+ 8})$ in the $c = 8 t / L = 0.25$ 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 $(a / L) \to 0$ extrapolations, the interpolation of $g ~_{c}^{2} (L)$ 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 $L \leq 12$ , 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 $L \geq 16$ . At the IR fixed point we measure the leading irrelevant critical exponent to be $γ_{g}^{⋆} = 0.26 (2)$ , comparable to perturbative estimates.

arXiv commentOne of four consistency checks corrected, changing some systematic uncertainty estimates

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

Abstract

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