Estimate of Quantum corrections to the Mass of the Chiral Soliton in the Nambu--Jona--Lasinio Model

Abstract

The Bethe--Salpeter equation for pion fluctuations off the chiral soliton in the Nambu--Jona--Lasinio model is constructed. By Goldstone's theorem this equation has rotational and translational zero modes because the classical soliton is a localized stationary field configuration which violates rotational and translational invariance. Furthermore, the proper normalization of the fluctuating eigen--modes is obtained. Second quantization of the pion fluctuations off the chiral soliton provides an energy functional of the pion fluctuations which formally coincides with that of a harmonic oscillator. The corresponding quantum corrections to the soliton mass together with the semi--classical cranking prescription yield reasonable predictions for the masses of the nucleon and the $\Delta$--resonance when the constituent quark mass is chosen to be about 400MeV. These calculations are, to some extend, hampered by the non--confining character of the Nambu--Jona--Lasinio model. Comments on the $1/N_C$ counting scheme are added.

30 pages LaTeX, UNITU-THEP-16/1994, three figures enclosed as uuecoded postscript files

References in corpus (6)

• QCD Phenomenology based on a Chiral Effective Lagrangian
• Analysis of Data on Polarized Lepton-Nucleon Scattering
• Hyperons in the Bound State Approach to the Nambu--Jona-Lasinio Chiral Soliton
• Strange and Non-Strange Meson Fluctuations off the Nambu--Jona-Lasinio Soliton
• On the analytic properties of chiral solitons in the presence of the $\omega$--meson
• Strange S--Wave Excitation of the NJL Soliton

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• Analytic structure of meson propagators in the proper-time regularized Nambu--Jona-Lasinio model
• Hyperfine Splitting of Low-Lying Heavy Baryons
• Monopole Excitations of Baryons in the Nambu--Jona--Lasinio Soliton Model
• Chiral Soliton Models and Nucleon Structure Functions
• Degeneracy of the quarks, shell structure in the chiral soliton
• Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model
• Instability of the hedgehog shape for the octet baryon in the chiral quark soliton model
• Soliton formation in the Nambu-Jona-Lasinio model
• Nonrigid chiral soliton for the octet and decuplet baryons