Gauged linear sigma model and pion-pion scattering

TL;DR

This paper develops an analytic framework using a gauged linear sigma model to analyze pion-pion scattering in QCD, exploring different mass hierarchy scenarios and their implications for scalar mesons and effective theories.

Contribution

It introduces a simple, parameterized gauged linear sigma model that relates experimental inputs to theoretical parameters and distinguishes different mass hierarchy cases in QCD and technicolor models.

Findings

The model can describe pion-pion scattering near threshold and up to 800 MeV.

Different mass hierarchy scenarios lead to distinct relations between vector and axial vector mesons.

A global fit balances near-threshold accuracy with higher-energy description.

Abstract

A simple gauged linear sigma model with several parameters to take the symmetry breaking and the mass differences between the vector meson and the axial vector meson into account is considered here as a possibly useful template for the role of a light scalar in QCD as well as for (at a different scale) an effective Higgs sector for some recently proposed walking technicolor models. An analytic procedure is first developed for relating the Lagrangian parameters to four well established (in the QCD application) experimental inputs. One simple equation distinguishes three different cases:1. QCD with axial vector particle heavier than vector particle, 2. possible technicolor model with vector particle heavier than the axial vector one, 3. the unphysical QCD case where both the KSRF and Weinberg relations hold. The model is applied to the s-wave pion-pion scattering in QCD. Both the near threshold region and (with an assumed unitarization) theglobal region up to about 800 MeV are considered. It is noted that there is a little tension between the choice of bare sigma mass parameter for describing these two regions. If a reasonable globa fit is made, there is some loss of precision in the near threshold region.