Non-Hermitian extension of the Nambu–Jona-Lasinio model in 3+1 and 1+1 dimensions

• DOI: 10.1103/physrevd.101.116001
• Publication Date: 2020-06-02T16:50:51Z
• Authors: Alexander Felski; Alireza Beygi; S. P. Klevansky
• Keywords: Hamiltonian (control theory)

This paper presents a non-Hermitian $\mathcal{PT}$-symmetric extension of the Nambu--Jona-Lasinio (NJL) model quantum chromodynamics in $3+1$ and $1+1$ dimensions. In dimensions, SU(2)-symmetric NJL Hamiltonian ${\mathcal{H}}_{\mathrm{NJL}}=\overline{\ensuremath{\psi}}(\ensuremath{-}i{\ensuremath{\gamma}}^{k}{\ensuremath{\partial}}_{k}+{m}_{0})\ensuremath{\psi}\ensuremath{-}G[(\overline{\ensuremath{\psi}}\ensuremath{\psi}{)}^{2}+(\overline{\ensuremath{\psi}}i{\ensuremath{\gamma}}_{5}\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\psi}{)}^{2}]$ is extended by non-Hermitian, $\mathcal{PT}$- chiral-symmetric bilinear term $ig\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{5}{B}_{\ensuremath{\mu}}{\ensuremath{\gamma}}^{\ensuremath{\mu}}\ensuremath{\psi}$; where ${\mathcal{H}}_{\mathrm{NJL}}$ form Gross-Neveu model, it but chiral symmetry breaking $g\overline{\ensuremath{\psi}}{\ensuremath{\gamma}}_{5}\ensuremath{\psi}$. each case, gap equation derived, effects terms on generated mass are studied. We have several findings: previous calculations for free Dirac modified to include terms, contrary expectation, no real spectrum can be obtained limit. these cases, nonzero bare fermion essential realization $\mathcal{PT}$ unbroken regime. Here, which four-point interactions present, we do find values also limit vanishing masses both at least certain specific couplings $g$. Thus, interaction overrides leading parameter values. Further, that inclusion contribute mass. models, this contribution tuned small; thus fix its value when ${m}_{0}=0$ absence term, then determine coupling required so as generate Finally, rich phase structure emerges from function strengths.