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

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. The gradient flow $\beta$ function exhibits a zero at $g_{\mathrm{GF}\star }^2=6.60\left(62\right)$, implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent ${\gamma }_g^{\star }=0.199\left(32\right)$. Our prediction for ${\gamma }_g^{\star }$ is consistent with available literature at the $1\text{−}2\sigma$ level.