Comparison of the Linear Sigma Model and Chiral Perturbation Theory for Nucleon Properties

Tarek Sayed Taha Ali

doi:10.4236/jmp.2013.411176

Abstract

We compare the static nucleon properties in the Chiral Perturbation Theory (χPT) and the Linear Sigma Model (LSM). We consider a chiral model for the nucleon which is based on the linear sigma model with scalar-isoscalar and scalarisovector mesons coupled to quarks. We have solved the field equations in the mean field approximation for the hedgehog baryon state with different sets of model parameters. A good investigation of some static nucleon properties is obtained by the LSM.

Highlights

A lot of groups have made significant progress towards understanding the fundamental baryon properties using several models [1,2,3,4,5]
One of the effective models in describing hadron properties is the Linear Sigma Model (LSM) [2,4], which serves as a good low-energy effective theory in order for one gain some insight into Quantum Chromodynamics (QCD)
In [6,8], it is argued that spontaneous symmetry breaking of the QCD Lagrangian gives rise to an effective chiral Lagrangian of Gell-Mann-Levy sigma model from involving explicit quark, scalar-isoscalar meson, and pseudoscalar-isovector meson degree of freedom

Summary

Introduction

A lot of groups have made significant progress towards understanding the fundamental baryon properties using several models [1,2,3,4,5]. In [6,8], it is argued that spontaneous symmetry breaking of the QCD Lagrangian gives rise to an effective chiral Lagrangian of Gell-Mann-Levy sigma model from involving explicit quark, scalar-isoscalar meson (sigma, σ), and pseudoscalar-isovector meson (pion, π) degree of freedom. Chiral Perturbation Theory (χPT) [9,10,11] is a low momentum effective field theory for QCD written as an expansion in small momenta and quark masses, and it has become an invaluable tool for subatomic physics.

Results

Conclusion