Spontaneous chiral symmetry breaking in the massless linear sigma model by fermion and boson loop corrections

Abstract

We study the effect of one-loop corrections from nucleon together with those from boson in the massless linear sigma model, where we perform the Coleman–Weinberg (CW) renormalization procedure. This renormalization procedure has a mechanism of spontaneous symmetry breaking due to radiative corrections in ϕ 4 theory. We apply this CW scheme to the system of fermions and bosons with chiral symmetry where the negative-mass term of bosons does not exist. Spontaneous chiral symmetry breaking is derived from the contribution of the fermion and boson loops which generates the masses of nucleon and scalar meson dynamically. We find that the renormalization scale plays an important role for the breaking of the symmetry between fermion and boson, and eventually for the chiral symmetry at the same time. In addition, we find that the naturalness restores by means of the introduction of the loop corrections from both fermion and boson. We obtain, thus, a stable renormalized effective potential in the chiral model for the first time. We study then the non-perturbative corrections with fermions and bosons in the Cornwall, Jackiw and Tomboulis (CJT) method. We derive the Schwinger–Dyson equations for nucleon and boson in the massless linear sigma model and compare the form of equations in the CJT method with that in the one-loop approximation with the CW renormalization procedure. Finally we apply this model to finite nuclei as an effective model with the chiral symmetry.