arXiv subjects

Curtis Taylor Peterson

Publications and source records attributed to Curtis Taylor Peterson.

3 recordsLinked to original sources

arXiv2024

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 $β$ 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 $γ_{g}^{\star}=0.199(32)$. Our prediction for $γ_{g}^{\star}$ is consistent with available literature at the $1\mbox{-}2σ$ level.

hep-lat↗

arXiv2024

Constrained curve fitting for semi-parametric models with radial basis function networks

Common to many analysis pipelines in lattice gauge theory and the broader scientific discipline is the need to fit a semi-parametric model to data. We propose a fit method that utilizes a radial basis function network to approximate the non-parametric component of such models. The approximate parametric model is fit to data using the basin hopping global optimization algorithm. Parameter constraints are enforced through Gaussian priors. The viability of our method is tested by examining its use in a finite-size scaling analysis of the $q$-state Potts model and $p$-state clock model with $q=2,3$ and $p=4,\infty$.

hep-lat↗

arXiv2023

$Λ$ parameter of the SU(3) Yang-Mills theory from the continuous $β$ function

Nonperturbative determinations of the renormalization group $β$ function are essential to connect lattice results to perturbative predictions of strongly coupled gauge theories and to determine the $Λ$ parameter or the strong coupling constant. The continuous $β$ function is very well suited for this task because it is applicable both in the weakly coupled deconfined regime as well as the strongly coupled confined regime. Here we report on our results for the $β$ function of the pure gauge SU(3) Yang-Mills theory in the gradient flow scheme. Our calculations cover the renormalized coupling range $g^2_{\textrm{GF}} \sim 1.2 - 27$, allowing for a direct determination of $\sqrt{8t_0} Λ_{\overline{\textrm{MS}}}$ in this system. Our prediction, $\sqrt{8 t_0} Λ_{\overline{\textrm{MS}}}=0.622(10)$, is in good agreement with recent direct determinations of this quantity.

hep-lat↗