1997/11/18 by A. S. Johnson, J. A. McNeil, J. R. Shepard
Physics and Astronomy · #Chiral perturbation theory #Chiral symmetry breaking #Functional renormalization group #High-Energy Particle Collisions Research #Mathematical physics #Meson #Nonlinear system #Nucleon #Observable #Particle physics #Particle physics theoretical and experimental studies #Phenomenology (philosophy) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #Renormalization #Renormalization group #Sigma #Sigma model #Symmetry breaking #hep-ph
paper · pdf · doi:10.1103/physrevd.58.014001
published as Phys.Rev.D58:014001,1998 · 22 pages, 4 figures
arxiv created 1997/11/18 · openalex publication_date 1998/05/07 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a nonperturbative renormalization group solution of the Gell-Mann--Levy \ensuremathσ-model which was originally proposed as a phenomenological description of the dynamics of nucleons and mesons. In our version of the model the fermions are interpreted as quarks which interact via the \ensuremathσ and \ensuremathπ mesons. We derive and numerically solve renormalization group flow equations using the local potential approximation to study the behavior of the model as it evolves from high to low momentum scales. We develop an expansion in chiral-symmetry-breaking which enables us to track this symmetry breaking with the evolution of the scale. We use infrared observables to constrain the phenomenology allowing predictions of other quantities such as \ensuremathπ\ensuremath-\ensuremathπ scattering lengths. The results show improvement over the tree level calculation and are consistent with experiment and the results of alternate theoretical approaches such as chiral perturbation theory and lattice gauge theory.