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Published: 2011-12-30
Abstract Views: 68
DOI: https://doi.org/10.53747/nst.v1i4.316
Issue
Vol. 1 No. 4 (2011)
Section
Articles
How to Cite
TRAN , H. P., NGUYEN , V. T., & NGUYEN , V. L. (2011). PHASE STRUCTURE OF THE LINEAR SIGMA MODEL WITH ELECTRIC NEUTRALITY CONSTRAINT. Nuclear Science and Technology, 1(4), 22-32. https://doi.org/10.53747/nst.v1i4.316

PHASE STRUCTURE OF THE LINEAR SIGMA MODEL WITH ELECTRIC NEUTRALITY CONSTRAINT

TRAN HUU PHAT1, NGUYEN VAN THU2,3, NGUYEN VAN LONG4
1 Vietnam Atomic Energy Commission, 59 Ly Thuong Kiet, Hanoi, Vietnam.
2 Department of Physics, Hanoi University of Education II Hanoi, Vietnam.
3 Institute of Nuclear Science and Technique, 5T 130, Hoang Quoc Viet, Hanoi, Vietnam.
4 Gialai Junior College of Education, 126 Le Thanh Ton, Pleiku, Gialai, Vietnam.

Main Article Content

Abstract

The phase structure of the linear sigma model with the electric neutrality is systematically studied by means of the Cornwall-Jackiw-Tomboulis  effective potential. The latter quantity is calculated in the improved Hartree – Fock (IHF) approximation  which  preserves the Goldstone theorem and the thermodynamic consistency.  It results that in the chiral limit, as function of T , the pion condensate undergoes a second order phase transition and, as function of μ, it undergoes a first order phase transition. In the physical world, where the chiral symmetry is explicitly broken, the chiral symmetry gets partial restoration as T ( or μ ) grows and the pion condensation is a first order phase transition occurring at μ = μc < μm , the pion mass in vacuum.

Article Details

Keywords

linear sigma model, chiral symmetry, pion condensation, electric neutrality

References

[1] A. B. Migdal, Sov. Phys. JETP 36, 1052 (1973).
[2] R. F. Sawyer, Phys. Rev. Lett. 29, 382 ( 1972).
[3] D. J. Scalapino, Phys. Rev. Lett. 29, 386 (1972).
[4] D. B. Kaplan and A. E. Nelson, Phys. Lett. B 175, 57 (1986).
[5] M. G. Alford, K. Rajagopal, and F. Wiczek, Nucl. Phys. B 537, 443 (1999).
[6] J. B. Kogut and D. K. Sinclair, Phys. Rev. D 64, 034508 (2001); ibid D 70, 094501 (2004).
[7] P. de Forcrand, M. A. Stephanov, and U. Wenger, PoS Lat 2007, 237 (2007).
[8] S.Gupta (2002), Critical Behavior in QCD at Finite Isovector Chemical Potential, hep-lat/0202005.
[9] D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86, 592 (2001).
[10] L. He, Phys. Rev. D 82, 096003 ( 2010).
[11] A. Barducci, R. Casalbuoni, G. Pettini, and L. Ravagli, Phys. Rev. D 71, 016011 (2005).
[12] L. He, M. Jin, and P. Zhuang, Phys. Rev. D 71, 116001 (2005).
[13] L. He and P. Zhuang, Phys. Lett. B 615, 93(2005).
[14] M. Frank, M. Buballa, and M. Oertel, Phys. Lett. B 562, 221 (2003).
[15] J. O. Andersen and T. Brauner, Phys. Rev. D 78, 014030 (2008).
[16] J. O. Andersen, Phys. Rev. D 75, 065011 (2007).
[17] O. Scavenius, A. Mocsy, I. N. Mishustin, and D. H. Rischke, Phys. Rev. C 64, 045202 (2001).
[18] M. C. Birse, T. D. Cohen, and J. A. McGovern, Phys. Lett. B 516, 27 (2001).
[19] J. B. Kogut and D. Toublan, Phys. Rev. D 64, 034007 (2001).
[20] M. Loewe and Villavicencio, Phys. Rev. D 70, 074005 (2004).
[21] T. H. Phat, N. V. Long, N. T. Anh, and L. V. Hoa, Phys. Rev. D 78, 105016 (2008).
[22] J. Cornwall, R. Jackiw, and E. Tomboulis, Phys. Rev. D 10, 2428 (1974).
[23] G. Amelia-Camelia and S. Y. Pi, Phys. Rev. D 47, 2356 (1993).
[24] S. Wolfram, The Mathematica Book, 5th edition, Wolfram Media/Cambridge University Press, Cambridge, UK, 2003.
[25] Tran Huu Phat and Nguyen Van Thu, Eur. Phys. J. C 71, 1810 (2011).
[26] D. K. Campell, R. F. Dashen, and J. T. Manassah, Phys. Rev. D 12,979 (1975).
[27] Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 10, 5016 (2005).
[28] M. G. Alford, M. Braby, and A. Schnitt, J. Phys. G: Nucl. Part. Phys. 35 , 025002 (2008).
[29] Tran Huu Phat and Nguyen Van Thu, in preparation.
[30] D. Ebert and K. G. Klimenko, Eur. Phys. J. C 46, 771 (2006).
[31] J. O Anderson and L. Kyllingstad , J. Phys. G: Part. and Nucl. Phys. 37 , 015003 (2010).