The renormalization group step scaling function of the 2-flavor SU(3) sextet model

TL;DR

This study computes the step scaling function of the 2-flavor SU(3) sextet model using the gradient flow scheme, finding results consistent with perturbation theory at weak coupling but conflicting with staggered fermion results at strong coupling, highlighting potential systematic issues.

Contribution

The paper provides a detailed non-perturbative calculation of the discrete beta function using Wilson fermions and compares multiple lattice operators and flow definitions to assess systematic effects.

Findings

Results agree with 4-loop perturbative predictions up to g^2 ≈ 5.5

Discrepancies observed with staggered fermion results at strong coupling

Continuum limit agreement achieved when gradient flow parameter c ≥ 0.35

Abstract

We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextet model using the finite volume gradient flow scheme. Our results, using clover improved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop $\overline{\textrm{MS}}$ perturbative predictions closely up to $g^2 \approx 5.5$, the strongest coupling reached in our simulation. At strong couplings the results are in tension with a recently published work using the same gradient flow renormalization scheme with staggered fermions. Since these calculations define the discrete $\beta$ function in the same continuum renormalization scheme, they should lead to the same continuum predictions, irrespective of the lattice fermion action. In order to test systematic effects in our computation we compare two different lattice operators, three different flow definitions, and two volume extrapolations. We find agreement among these different approaches in the continuum limit when the gradient flow parameter $c\gtrsim0.35$. Considering the potential phenomenological impact of this model, it is important to understand the origin of the disagreement between our work and the staggered fermion results.