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

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

1994-08-22

arxiv.org/abs/hep-ph/9408343v1

Nucl.Phys.A582:484-516,1995

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/0375-9474(94)00480-B

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.

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