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We investigate the discrete $\beta$ function of the 2-flavor SU(3) sextetmodel using the finite volume gradient flow scheme. Our results, using cloverimproved nHYP smeared Wilson fermions, follow the (non-universal) 4-loop$\overline{\textrm{MS}}$ perturbative predictions closely up to $g^2 \approx5.5$, the strongest coupling reached in our simulation. At strong couplings theresults are in tension with a recently published work using the same gradientflow renormalization scheme with staggered fermions. Since these calculationsdefine the discrete $\beta$ function in the same continuum renormalizationscheme, they should lead to the same continuum predictions, irrespective of thelattice fermion action.  In order to test systematic effects in our computation we compare twodifferent lattice operators, three different flow definitions, and two volumeextrapolations. We find agreement among these different approaches in thecontinuum limit when the gradient flow parameter $c\gtrsim0.35$. Consideringthe potential phenomenological impact of this model, it is important tounderstand the origin of the disagreement between our work and the staggeredfermion results.

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