Abstract
We calculate the step-scaling function, the lattice analog of the renormalization group $\ensuremath{\beta}$-function, for an SU(3) gauge theory with ten fundamental flavors. We present a detailed analysis including the study of systematic effects of our extensive data set generated with ten dynamical flavors using the Symanzik gauge action and three times stout smeared M\"obius domain wall fermions. Using up to ${32}^{4}$ volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scaling $\ensuremath{\beta}$ function for a scale change $s=2$ on up to five different lattice volume pairs. In an accompanying paper we discuss that gradient flow can promote lattice dislocations to instantonlike objects, introducing nonperturbative lattice artifacts to the step-scaling function. Motivated by the observation that Wilson flow sufficiently suppresses these artifacts, we choose Wilson flow with the Symanzik operator as our preferred analysis. We study systematic effects by calculating the step-scaling function based on alternative flows (Zeuthen or Symanzik), alternative operators (Wilson plaquette, clover), and also explore the effects of the perturbative tree-level improvement. Further we investigate the effects due to the finite value of ${L}_{s}$.
Highlights
Coupled gauge-fermion systems play a central role in different beyond the Standard Model scenarios
Using gauge field configurations generated with stoutsmeared Möbius domain wall fermions and Symanzik gauge action, we have calculated the gradient flow stepscaling function for SU(3) with ten dynamical flavors
Since Wilson flow does the best job in suppressing such dislocations compared to Zeuthen or Symanzik flow, we choose Wilson flow with Symanzik operator for our preferred analysis
Summary
Coupled gauge-fermion systems play a central role in different beyond the Standard Model scenarios. Flavor system exhibits a fast running β function close to the perturbative 1-loop prediction, whereas for Nf 1⁄4 12 our step-scaling calculation shows that the β function is small in magnitude and identifies an infrared fixed point (IRFP) in the range 5.2 ≤ g2c ≤ 6.4 using the c 1⁄4 0.250 renormalization scheme. In an accompanying paper we discuss that gradient flow on coarse configurations can promote dislocations to instantonlike objects This introduces a nonperturbative lattice artifact to the step-scaling beta function which leads to incorrect continuum limit extrapolations [25]. VI we summarize our results and comment on the comparison with perturbative predictions
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