Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system

Abstract

We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group $\beta$ function. We identify an infrared fixed point at $g^2_{\mathrm{GF}\star}=6.60(62)$ in the GF scheme and calculate the leading irrelevant critical exponent $\gamma_{g}^{\star}=0.199(32)$. Our prediction for $\gamma_{g}^{\star}$ is consistent with available literature at the $1\mbox{-}2\sigma$ level.