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

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 ansatz 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.

arXiv comment24 pages, 6 figures; Published version; Appendix A added for tabulating data; One reference included; Typos corrected

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• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
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• Strong dynamics, composite Higgs and the conformal window
• Crawling technicolor
• Large scale separation and resonances within LHC range from a prototype BSM model
• Large scale separation and hadronic resonances from a new strongly interacting sector
• Gradient flow step-scaling function for SU(3) with twelve flavors
• Short flow-time coefficients of CP-violating operators
• Non-perturbative determination of the $\Lambda$-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• Infrared fixed point of SU(2) gauge theory with six flavors
• The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors
• Chiral symmetry breaking and confinement: separating the scales
• The twisted gradient flow coupling at one loop
• Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors