Identity of the imaginary-time and real-time thermal propagators for scalar bound states in a one-generation Nambu-Jona-Lasinio model

TL;DR

This paper rigorously proves that the thermal propagators for scalar bound states in a fermion condensate model are identical in both imaginary-time and real-time formalisms, clarifying a key theoretical discrepancy.

Contribution

It establishes the equivalence of imaginary-time and real-time thermal propagators for scalar bound states in a specific NJL model, resolving previous doubts.

Findings

Thermal propagators are identical in both formalisms.

Thermal transformation matrices are similar for bound states and elementary particles.

Decay or growth of composite Higgs amplitude depends on fermion mass differences.

Abstract

By rigorous reanalysis of the results, we have proven that the propagators at finite temperature for scalar bound states in one-generation fermion condensate scheme of electroweak symmetry breaking are in fact identical in the imaginary-time and the real-time formalism. This dismisses the doubt about possible discrepancy between the two formalisms in this problem. Identity of the derived thermal transformation matrices of the real-time matrix propagators for scalar bound states without and with chemical potential and the ones for corresponding elementary scalar particles shows similarity of thermodynamic property between the two types of particles. Only one former inference is modified, i.e. when the two flavors of fermions have unequal nonzero masses, the amplitude of the composite Higgs particle will decay instead grow in time.