Abstract
We present a new lattice study of the discrete beta function for SU(3) gauge theory with Nf=8 massless flavors of fermions in the fundamental representation. Using the gradient flow running coupling, and comparing two different nHYP-smeared staggered lattice actions, we calculate the 8-flavor step-scaling function at significantly stronger couplings than were previously accessible. Our continuum-extrapolated results for the discrete beta function show no sign of an IR fixed point up to couplings of g^2~14. At the same time, we find that the gradient flow coupling runs much more slowly than predicted by two-loop perturbation theory, reinforcing previous indications that the 8-flavor system possesses nontrivial strongly coupled IR dynamics with relevance to BSM phenomenology.
Highlights
Since interest in 8-flavor SU(3) gauge theory revolves around its strongly coupled IR dynamics, lattice gauge theory is an indispensable approach to study the system nonperturbatively, from first principles
We find that the gradient flow coupling runs much more slowly than predicted by two-loop perturbation theory, reinforcing previous indications that the 8-flavor system possesses nontrivial strongly coupled IR dynamics with relevance to BSM phenomenology
Eigenmode studies can investigate chiral symmetry breaking by comparing the low-lying Dirac spectrum with random matrix theory, or by considering the scale dependence of the effective mass anomalous dimension predicted by the eigenmode number
Summary
The gradient flow is a continuous transformation that smooths lattice gauge fields to systematically remove short-distance lattice cutoff effects [39]. To use the gradient flow coupling in step-√scaling analyses, we tie the energy scale to the lattice volume L4 by fixing the ratio c = 8t/L, as proposed by refs. The function C(L, c) is a four-dimensional finite-volume sum in lattice perturbation theory, which depends on the action, flow and operator It is computed at tree level by ref. Since we use periodic BCs for the gauge fields, the correction C(L, c) includes a term that accounts for the zero-mode contributions Even with this tree-level improvement, the gradient flow step scaling can show significant cutoff effects. For O(a)-improved actions like those we use, a simple calculation shows that it is possible to choose an optimal τ0 value τopt such that the t-shift removes the O(a2) corrections of the coupling gG2 F(μ; a) defined in eq (2.3). We will account for these discrepancies as one source of systematic uncertainty
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