We test the stability of the mean field solution in the Nambu-Jona-Lasinio model in a semi-quantitative manner. For stable solutions with respect to both the σ and π directions, we investigate effects of the mesonic loop corrections of 1/N c, which correspond to the next-to-leading order in the 1/N c expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N c = 3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.