Variational path-integral approach to back-reactions of composite mesons in the Nambu-Jona-Lasinio model
| Autor: | Dietmar Ebert, David Blaschke |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Quark
Nuclear and High Energy Physics Particle physics Meson Nuclear Theory High Energy Physics::Lattice FOS: Physical sciences 01 natural sciences Nuclear Theory (nucl-th) Pion High Energy Physics - Phenomenology (hep-ph) Nambu–Jona-Lasinio model 0103 physical sciences lcsh:Nuclear and particle physics. Atomic energy. Radioactivity 010306 general physics Effective action Physics 010308 nuclear & particles physics High Energy Physics::Phenomenology Propagator High Energy Physics - Phenomenology Goldstone boson Path integral formulation lcsh:QC770-798 High Energy Physics::Experiment |
| Zdroj: | Nuclear Physics B Nuclear Physics B, Vol 921, Iss C, Pp 753-768 (2017) |
| DOI: | 10.48550/arxiv.1703.08964 |
| Popis: | For the investigation of back-reactions of composite mesons in the NJL model, a variational path-integral treatment is formulated which yields an effective action $\mathscr{A}_{\rm eff}[D_{\sigma},D_{\pi}; S]$, depending on the propagators $D_\sigma$, $D_\pi$ of $\sigma-$ and $\pi-$mesons and on the full quark propagator $S$. The stationarity conditions $\delta \mathscr{A}_{\rm eff}/ \delta S = 0$, $\delta \mathscr{A}_{\rm eff}/ \delta D_\sigma = 0$, $\delta \mathscr{A}_{\rm eff}/ \delta D_\pi = 0$, then lead to coupled Schwinger-Dyson (SD) equations for the quark self-energy and the meson polarization functions. These results reproduce and extend results of the so-called "$\Phi-$derivable" approach and provide a functional formulation for diagrammatic resummations of $1/N_c-$corrections in the NJL model. Finally, we perform a low-momentum estimate of the quark and meson loop contributions to the polarization function of the pion and on this basis discuss the Goldstone theorem. Comment: 21 pages, 3 figures, minor text corrections, 2 references added, version published in Nucl. Phys. B |
| Databáze: | OpenAIRE |
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