Vấn đề dấu hiệu qua chuyển tiếp pha QCD

Journal of High Energy Physics - Tập 2010 - Trang 1-17 - 2010
Jens O. Andersen1,2, Lars T. Kyllingstad2, Kim Splittorff3
1Niels Bohr International Academy, Copenhagen, Denmark
2Department of Physics, Norwegian University of Science and Technology, Trondheim, Norway
3Niels Bohr Institute, Copenhagen, Denmark

Tóm tắt

Giá trị trung bình của yếu tố pha của định thức fermion QCD cho thấy mức độ nghiêm trọng của vấn đề dấu hiệu trong lý thuyết QCD. Chúng tôi tính toán giá trị trung bình của yếu tố pha như một hàm của nhiệt độ và tiềm năng hóa học baryon bằng cách sử dụng mô hình NJL hai hương vị. Điều này cho phép chúng tôi nghiên cứu mức độ nghiêm trọng của vấn đề dấu hiệu tại và trên ngưỡng chuyển tiếp tịnh sắc. Chúng tôi thảo luận về cách mà sự bất thường U(1)A ảnh hưởng đến vấn đề dấu hiệu. Cuối cùng, chúng tôi nghiên cứu sự tương tác giữa vấn đề dấu hiệu và điểm cuối của chuyển tiếp tịnh sắc.

Từ khóa

#Vấn đề dấu hiệu #lý thuyết trường lượng tử #chuyển tiếp pha #mô hình NJL #bất thường U(1)A

Tài liệu tham khảo

I.R. Klebanov, Nuclear matter in the Skyrme model, Nucl. Phys. B 262 (1985) 133 [SPIRES]. A.D. Jackson and J.J.M. Verbaarschot, Phase structure of the Skyrme model, Nucl. Phys. A 484 (1988) 419 [SPIRES]. R. Rapp, T. Schafer, E.V. Shuryak and M. Velkovsky, Diquark Bose condensates in high density matter and instantons, Phys. Rev. Lett. 81 (1998) 53 [hep-ph/9711396] [SPIRES]. M.G. Alford, K. Rajagopal and F. Wilczek, QCD at finite baryon density: nucleon droplets and color superconductivity, Phys. Lett. B 422 (1998) 247 [hep-ph/9711395] [SPIRES]. L. McLerran and R.D. Pisarski, Phases of cold, dense quarks at large-N c , Nucl. Phys. A 796 (2007) 83 [arXiv:0706.2191] [SPIRES]. K. Rajagopal and F. Wilczek, The condensed matter physics of QCD, hep-ph/0011333 [SPIRES]. J.B. Kogut and D.K. Sinclair, The finite temperature transition for 2-flavor lattice QCD at finite isospin density, Phys. Rev. D 70 (2004) 094501 [hep-lat/0407027] [SPIRES]. J.B. Kogut and D.K. Sinclair, Lattice QCD at finite temperature and density in the phase-quenched approximation, Phys. Rev. D 77 (2008) 114503 [arXiv:0712.2625] [SPIRES]. P. de Forcrand, M.A. Stephanov and U. Wenger, On the phase diagram of QCD at finite isospin density, PoS(LATTICE 2007)237 [arXiv:0711.0023] [SPIRES]. M.G. Alford, A. Kapustin and F. Wilczek, Imaginary chemical potential and finite fermion density on the lattice, Phys. Rev. D 59 (1999) 054502 [hep-lat/9807039] [SPIRES]. P. de Forcrand and O. Philipsen, The curvature of the critical surface (m ud , m s )crit(μ): a progress report, PoS(LATTICE 2008)208 [arXiv:0811.3858] [SPIRES]. P. de Forcrand and O. Philipsen, The chiral critical point of N f = 3 QCD at finite density to the order (μ/T)4, JHEP 11 (2008) 012 [arXiv:0808.1096] [SPIRES]. P. de Forcrand and O. Philipsen, The QCD phase diagram for small densities from imaginary chemical potential, Nucl. Phys. B 642 (2002) 290 [hep-lat/0205016] [SPIRES]. M. D’Elia and M.-P. Lombardo, Finite density QCD via imaginary chemical potential, Phys. Rev. D 67 (2003) 014505 [hep-lat/0209146] [SPIRES]. P. de Forcrand and O. Philipsen, The QCD phase diagram for three degenerate flavors and small baryon density, Nucl. Phys. B 673 (2003) 170 [hep-lat/0307020] [SPIRES]. R.V. Gavai and S. Gupta, Pressure and non-linear susceptibilities in QCD at finite chemical potentials, Phys. Rev. D 68 (2003) 034506 [hep-lat/0303013] [SPIRES]. C.R. Allton et al., The QCD thermal phase transition in the presence of a small chemical potential, Phys. Rev. D 66 (2002) 074507 [hep-lat/0204010] [SPIRES]. C.R. Allton et al., The equation of state for two flavor QCD at non-zero chemical potential, Phys. Rev. D 68 (2003) 014507 [hep-lat/0305007] [SPIRES]. C.R. Allton et al., Thermodynamics of two flavor QCD to sixth order in quark chemical potential, Phys. Rev. D 71 (2005) 054508 [hep-lat/0501030] [SPIRES]. I.M. Barbour, S.E. Morrison, e.g. Klepfish, J.B. Kogut and M.-P. Lombardo, Results on finite density QCD, Nucl. Phys. B Proc. Suppl. 60 (1998) 220 [hep-lat/9705042] [SPIRES]. Z. Fodor and S.D. Katz, Lattice determination of the critical point of QCD at finite T and mu, JHEP 03 (2002) 014 [hep-lat/0106002] [SPIRES]. Z. Fodor and S.D. Katz, Critical point of QCD at finite T and μ, lattice results for physical quark masses, JHEP 04 (2004) 050 [hep-lat/0402006] [SPIRES]. F. Karsch and H.W. Wyld, Complex Langevin simulation of the SU(3) spin model with nonzero chemical potential, Phys. Rev. Lett. 55 (1985) 2242 [SPIRES]. J. Flower, S.W. Otto and S. Callahan, Complex Langevin equations and lattice gauge theory, Phys. Rev. D 34 (1986) 598 [SPIRES]. J. Ambjørn, M. Flensburg and C. Peterson, The complex Langevin equation and Monte Carlo simulations of actions with static charges, Nucl. Phys. B 275 (1986) 375 [SPIRES]. G. Aarts and I.-O. Stamatescu, Stochastic quantization at finite chemical potential, JHEP 09 (2008) 018 [arXiv:0807.1597] [SPIRES]. G. Aarts, Can stochastic quantization evade the sign problem? — The relativistic Bose gas at finite chemical potential, Phys. Rev. Lett. 102 (2009) 131601 [arXiv:0810.2089] [SPIRES]. G. Aarts, Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas, JHEP 05 (2009) 052 [arXiv:0902.4686] [SPIRES]. E.S. Fraga and C. Villavicencio, Phase of the complex functional determinant in QCD at small chemical potential, arXiv:0806.2869 [SPIRES]. K.N. Anagnostopoulos and J. Nishimura, New approach to the complex-action problem and its application to a nonperturbative study of superstring theory, Phys. Rev. D 66 (2002) 106008 [hep-th/0108041] [SPIRES]. J. Ambjørn, K.N. Anagnostopoulos, J. Nishimura and J.J.M. Verbaarschot, The factorization method for systems with a complex action — A test in random matrix theory for finite density QCD-, JHEP 10 (2002) 062 [hep-lat/0208025] [SPIRES]. J. Ambjørn, K.N. Anagnostopoulos, J. Nishimura and J.J.M. Verbaarschot, Non-commutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems, Phys. Rev. D 70 (2004) 035010 [hep-lat/0402031] [SPIRES]. Z. Fodor, S.D. Katz and C. Schmidt, The density of states method at non-zero chemical potential, JHEP 03 (2007) 121 [hep-lat/0701022] [SPIRES]. S. Ejiri, On the existence of the critical point in finite density lattice QCD, Phys. Rev. D 77 (2008) 014508 [arXiv:0706.3549] [SPIRES]. K. Splittorff and J.J.M. Verbaarschot, The QCD sign problem for small chemical potential, Phys. Rev. D 75 (2007) 116003 [hep-lat/0702011] [SPIRES]. K. Splittorff and J.J.M. Verbaarschot, The approach to the thermodynamic limit in lattice QCD at μ ≠ 0, Phys. Rev. D 77 (2008) 014514 [arXiv:0709.2218] [SPIRES]. J.C.R. Bloch and T. Wettig, Random matrix analysis of the QCD sign problem for general topology, JHEP 03 (2009) 100 [arXiv:0812.0324] [SPIRES]. M. D’Elia and F. Sanfilippo, Thermodynamics of two flavor QCD from imaginary chemical potentials, Phys. Rev. D 80 (2009) 014502 [arXiv:0904.1400] [SPIRES]. A. Barducci, R. Casalbuoni, G. Pettini and L. Ravagli, A calculation of the QCD phase diagram at finite temperature and baryon and isospin chemical potentials, Phys. Rev. D 69 (2004) 096004 [hep-ph/0402104] [SPIRES]. C. Ratti and W. Weise, Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model, Phys. Rev. D 70 (2004) 054013 [hep-ph/0406159] [SPIRES]. L.-y. He, M. Jin and P.-f. Zhuang, Pion superuidity and meson properties at finite isospin density, Phys. Rev. D 71 (2005) 116001 [hep-ph/0503272] [SPIRES]. D. Ebert and K.G. Klimenko, Gapless pion condensation in quark matter with finite baryon density, J. Phys. G 32 (2006) 599 [hep-ph/0507007] [SPIRES]. S. Lawley, W. Bentz and A.W. Thomas, The phases of isospin asymmetric matter in the two flavor NJL model, Phys. Lett. B 632 (2006) 495 [nucl-th/0504020] [SPIRES]. J.O. Andersen and L. Kyllingstad, Pion condensation in a two-flavor NJL model: the role of charge neutrality, J. Phys. G 37 (2010) 015003 [hep-ph/0701033] [SPIRES]. H. Abuki, R. Anglani, R. Gatto, M. Pellicoro and M. Ruggieri, The fate of pion condensation in quark matter: from the chiral to the real world, Phys. Rev. D 79 (2009) 034032 [arXiv:0809.2658] [SPIRES]. M. Buballa, NJLS model analysis of quark matter at large density, Phys. Rept. 407 (2005) 205 [hep-ph/0402234] [SPIRES]. J. Han and M.A. Stephanov, A random matrix study of the QCD sign problem, Phys. Rev. D 78 (2008) 054507 [arXiv:0805.1939] [SPIRES]. K. Splittorff and J.J.M. Verbaarschot, Factorization of correlation functions and the replica limit of the Toda lattice equation, Nucl. Phys. B 683 (2004) 467 [hep-th/0310271] [SPIRES]. J.M. Moller, On the phase diagram of QCD with small isospin chemical potential, arXiv:0908.1642 [SPIRES]. R.D. Pisarski and F. Wilczek, Remarks on the chiral phase transition in chromodynamics, Phys. Rev. D 29 (1984) 338 [SPIRES]. J.-W. Chen, K. Fukushima, H. Kohyama, K. Ohnishi and U. Raha, U A (1) anomaly in hot and dense QCD and the critical surface, Phys. Rev. D 80 (2009) 054012 [arXiv:0901.2407] [SPIRES]. J. Danzer, C. Gattringer, L. Liptak and M. Marinkovic, A study of the sign problem for lattice QCD with chemical potential, Phys. Lett. B 682 (2009) 240 [arXiv:0907.3084] [SPIRES]. B. Klein, D. Toublan and J.J.M. Verbaarschot, The QCD phase diagram at nonzero temperature, baryon and isospin chemical potentials in random matrix theory, Phys. Rev. D 68 (2003) 014009 [hep-ph/0301143] [SPIRES]. K. Splittorff, The sign problem in the ϵ-regime of QCD, PoS(LAT2006)023 [hep-lat/0610072] [SPIRES]. K. Splittorff, Lattice simulations of QCD with μ(B) ≠ 0 versus phase quenched QCD, hep-lat/0505001 [SPIRES]. M.A. Stephanov, Non-gaussian fluctuations near the QCD critical point, Phys. Rev. Lett. 102 (2009) 032301 [arXiv:0809.3450] [SPIRES]. M.A. Stephanov, QCD phase diagram: an overview, PoS(LAT2006)024 [hep-lat/0701002] [SPIRES].