Nucleon bound state at finite temperature

Abstract

We study the nucleon at finite temperature using Bethe-Salpeter equation (BSE) where it is considered as a bound state of a scalar-diquark and a quark. The interaction between the diquark and the quark is taken as an exchange quark.The constituent quark and diquark substructures are considered momentum and temperature dependent based on the lattice QCD and dynamical chiral symmetry breaking (DCSB). The kernel interaction modification with temperature is approximated using the mixed representation in the imaginary time formalism and then we adopt an adiabatic (instantaneous) approximation after evaluating the Matsubara frequencies sum. The results of BSE are compared with those for MIT bag model. We argue the bag pressure is a temperature dependent and it decreases smoothly with temperature to be consistent with the results for BSE. Furthermore, the nucleon bound state obtained by BSE ceases to exist just below the critical temperature and this indicates that the nucleon deconfines to its constituent quarks at the critical temperature. The nucleon mass decreases with temperature as $M_N(T)/M_N(0)\approx {\cal R}^{\delta}(T)$ where ${\cal R}(T)=(1-b\frac{T^2}{T^2_c})^{1/2}$ and $\delta\approx 1$ and this suggests $B(T)/B(0)={\cal R}^{4\delta}(T)$ for MIT bag.