3 the onset of the charged pion condensation. We show that the equality between the electric chemical poten- tial and the “in-medium” pion mass, | µ$_{e}$ | = M$_{π}$ , as a threshold, persists even for a composite pion system in the medium, provided the transition to the pion con- densed phase is of the second order (the same qualitative picture has been found also in a recent analysis in the massive Gross-Neveu model [13]). Moreover, we have found that the pion condensate in neutral quark matter is extremely fragile to the symmetry breaking effect via a finite current quark mass m , and is ruled out for m larger than the order of 10 keV. The neutrality line manifestly shows the impossibility of finding a π c condensate, in this physical situation. A final comment is in order. In this study the con- tribution to finite baryon density comes only from the constituent quarks and not from nucleons. The presence of nucleons may make the pion condensation even less favorable. The reason can be found in the Tomozawa- Weinberg pion-nucleon interaction, which is isospin odd, giving rise to a repulsive pion self-energy at the physi- cal situation where the neutron density is larger than the proton density (see Ref. [17]). For this reason an inter- esting investigation may consider the pion condensation with the presence of nucleon degrees of freedom within NJL model (see Ref. [18] for useful prescriptions). This work was supported in part by the U.S. Depart- ment of Energy, Office of Nuclear Physics, under contract no. DE-AC02-06CH11357. We have studied the pion condensation in two-flavor neutral quark matter using the Nambu–Jona-Lasinio model of QCD at finite density. We have investigated the role of electric charge neutrality, and explicit sym- metry breaking via quark mass, both of which control V. CONCLUSIONS [1] A.B. Migdal, Zh. Eksp. Teor. Fiz. 61 , 2210 (1971) [Sov. Phys. JETP 36 , 1052 (1973)]; A. B. Migdal, E. E. Saper- stein, M. A. Troitsky and D. N. Voskresensky, Phys. Rept. 192 , 179 (1990). [9] H. Abuki, R. Anglani, R. Gatto, M. Pellicoro and M. Ruggieri, Phys. Rev. D 79 , 034032 (2009) [10] H. Abuki, M. Ciminale, R. Gatto, N. D. Ippolito, G. Nar- dulli and M. Ruggieri, Phys. Rev. D 78 , 014002 (2008); H. Abuki, M. Ciminale, R. Gatto, G. Nardulli and M. Ruggieri, Phys. Rev. D 77 , 074018 (2008); H. Abuki, R. Anglani, R. Gatto, G. Nardulli and M. Ruggieri, Phys. Rev. D 78 , 034034 (2008). [11] D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86 , 592 (2001). [2] R.F. Sawyer, Phys. Rev. Lett. 29 , 382 (1972); D.J. Scalapino, Phys. Rev. Lett. 29 , 386 (1972). G. Baym and D.K. Campbell in: Mesons and Nuclei , v. 3, eds. M. Rho and D. Wilkinson (North Holland, 1979). [12] L. y. He, M. Jin and P. f. Zhuang, Phys. Rev. D 71 , 116001 (2005). [3] T. Kunihiro, T. Muto, R. Tamagaki, T. Tatsumi and T. Takatsuka, Prog. Theor. Phys. Suppl. 112 , 1 (1993). [4] H. Toki, S. Hirenzaki, T. Yamazaki and R. S. Hayano, Nucl. Phys. A 501 , 653 (1989); P. Kienle and T. Ya- mazaki, Prog. Part. Nucl. Phys. 52 , 85 (2004). [13] D. Ebert and K. G. Klimenko, arXiv:0911.1944 [hep-ph]. [14] M. Matsuzaki, arXiv:0909.5615 [hep-ph]; J. O. Ander- sen, L. T. Kyllingstad and K. Splittorff, arXiv:0909.2771 [hep-lat]; H. Abuki, R. Gatto and M. Ruggieri, Phys. Rev. D 80 , 074019 (2009); D. Ebert and K. G. Kli- menko, arXiv:0902.1861 [hep-ph]; H. Abuki, T. Brauner and H. J. Warringa, Eur. Phys. J. C 64 , 123 (2009). [15] J. O. Andersen and L. Kyllingstad, arXiv:hep-ph/0701033. [5] J. B. Hartle, R. F. Sawyer and D. J. Scalapino, Astro- phys. J. 199 , 471 (1975); A. B. Migdal, G. A. Sorokin, O. A. Markin and I. N. Mishustin, Phys. Lett. B 65 , 423 (1976); O. Maxwell, G. E. Brown, D. K. Campbell, R. F. Dashen and J. T. Manassah, Astrophys. J. 216 , 77 (1977); A. Ohnishi, D. Jido, T. Sekihara and K. Tsubak- ihara, Phys. Rev. C 80 , 038202 (2009). [6] C. Ishizuka, A. Ohnishi, K. Tsubakihara, K. Sumiyoshi and S. Yamada, J. Phys. G 35 (2008) 085201. [7] J. Zimanyi, G. I. Fai and B. Jakobsson, Phys. Rev. Lett. 43 , 1705 (1979); S. Krewald and J. W. Negele, Phys. Rev. C 21 , 2385 (1980). [16] D. Ebert and K. G. Klimenko, Eur. Phys. J. C 46 , 771 (2006). [17] T. Muto, Prog. Theor. Phys. Suppl. 153 , 174 (2004). [18] W. Bentz, T. Horikawa, N. Ishii and A. W. Thomas, Nucl. Phys. A 720 , 95 (2003). [8] T. Hatsuda and T. Kunihiro, Phys. Rept. 247 , 221 (1994); S. P. Klevansky, Rev. Mod. Phys. 64 (1992) 649. FIG. 3: Phase diagram in ( µ, µ e ) plane at m = 5 . 5 MeV.