Quantized linearσmodel at finite temperature, and nucleon properties

Abstract

The nucleon properties due to the restoration of the chiral symmetry at nonzero temperature $T$ are investigated within the framework of the linear $\ensuremath{\sigma}$ model. The field equations are solved using the coherent-pair approximation. In this approach, the quantum fields are treated in a nonperturbative fashion. We minimize the expectation value of the chiral Hamiltonian using the ansatz of the coherent-pair ground-state configuration. The obtained results show that the nucleon mass and mean-square radius of the proton and the neutron increase monotonically with the temperature $T$ and that the pion-nucleon coupling constant ${g}_{\ensuremath{\pi}NN}$ decreases with temperature values that are near the value of the critical temperature ${T}_{c}$. The nucleon mass and mean-square radius of the proton are examined in the $(x,T)$ plane, showing a sensitive dependence on the coherence parameter $x$. This means that an increase of both the coherence parameter $x$ and the temperature $T$ leads to an increase in the values of the nucleon mass and the mean-square radius of the proton. This is evidence for the quark-gluon deconfinement phase transition.