The nucleon as a projected chiral soliton: Vacuum and medium properties

Abstract

Nucleon properties and nucleon form factors are computed within the framework of the projected linear chiral soliton model. To this end the Gell-Mann - Lévy lagrangian is solved by means of variational methods which include angular momentum and isospin projection with trial quark-boson Fock states in generalized hedgehog configurations. The consistency of the treatment is checked by the fulfillment of virial theorems such as Goldberger-Treiman relation. In general the q 2 dependence of the nucleon form factors are well described although some of their values at zero momentum transfer come out too large, namely for the axial- and πNN - form factors. Electromagnetic form factors for the N − Δ transition are also calculated and compared with the available experimental data. Medium effects on the nucleon properties are investigated combining the projected chiral soliton model with the Nambu-Jona-Lasinio model. The latter is employed to compute the pion decay constant and the pion and sigma masses at finite medium density. These meson properties fix the parameters in the linear sigma model, which is then solved using the same variational methods as for the zero density. The nucleon mass shows a decrease of 17% and the proton radius an increase of 19% if the medium reaches nuclear matter density. The magnetic moments and g A are less affected by the medium. The nucleon electromagnetic form factors show remarkable changes at finite transfer numbers as well.