The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

Abstract

Abstract:We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g GF , is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g GF . For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g 2 GF ∼ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansätz a'la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g 2 GF ∼ 6 is still not governed by possible infrared conformality.

Non-perturbative determination of the Λ-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling

“…The running can be traced via the step scaling method on the lattice. The TGF running coupling for the pure SU(2) Yang-Mills theory has been evaluated using the step scaling method [22] and extended to two-or three-color many flavor dynamical simulations [23,24].…”

“…• Set (A): all data pairs at L/a = (12, 18), (16,24), or (24,36) in each β row listed in table 1. This corresponds to u max 6.848.…”

“…• Set (C): following data pairs are excluded from the set (B): β = 6.42 for L/a = (12, 18), β = 6.62 for L/a = (16,24), and β = 6.94 for L/a = (24,36). This corresponds to u max 6.263. u and a/L by taking the correlation among u's and B LAT 3/2 (u, a/L)'s into account [36] for each data set.…”

Dilaton EFT framework for lattice data

“…Lattice simulations of strongly interacting gauge theories indicate that infrared conformal behavior sets in with a sufficiently large number of light fermions [1][2][3][4][5][6][7][8][9][10][11][12][13][14] . In addition, a remarkably light singlet scalar particle appears in the spectrum of recent simulations as this number is increased toward the critical value for the transition to conformal behavior (the "bottom of the conformal window") [15][16][17][18][19].…”

Status of a minimal composite Higgs theory

“…This IRFP is based on the study of the scale-dependent running coupling from the gradient flow with the choice c = 0.2 and has been generally accepted as the most convincing evidence that the model with twelve massless flavors in the fundamental representation is inside the conformal window. Recent work using larger c values in the gradient flow scheme does not find an IRFP in the reported range [49]. Further work would be required to resolve the tension between these two findings.…”