Slope of the beta function at the fixed point of SU(2) gauge theory with six or eight flavors

TL;DR

This paper measures the slope of the beta function at the fixed point in SU(2) gauge theories with six and eight flavors, providing insights into their conformal properties using gradient flow methods.

Contribution

It presents a novel measurement of the leading irrelevant scaling exponent at the fixed point for SU(2) theories with six and eight flavors, employing continuum extrapolation and different discretizations.

Findings

For eight flavors, γ_g* = 0.19(8)_{-0.09}^{+0.21}.

For six flavors, γ_g* = 0.648(97)_{-0.1}^{+0.16}.

Results are consistent with previous analyses.

Abstract

We consider measurement of the leading irrelevant scaling exponent $\gamma_g^\ast$, given by the slope of the beta function, at the fixed point of SU(2) gauge theory with six or eight flavors. We use the running coupling measured using the gradient flow method and perform the continuum extrapolation by interpolating the measured beta function. We study also the dependence of the results on different discretization of the flow. For the eight flavor theory we find $\gamma_g^\ast=0.19(8)_{-0.09}^{+0.21}$. Applying the same analysis also for the six flavor theory, we find $\gamma_g^\ast=0.648(97)_{-0.1}^{+0.16}$ consistently with the earlier analysis.