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Isospin Matter in the NJL Model

Isospin Matter in the NJL Model. ● Phase Diagram at finite μ I ● BCS-BEC Crossover in pion superfluid. Pengfei Zhuang (zhuangpf@mail.tsinghua.edu.cn) Tsinghua University, Beijing. QCD Phase Diagram.

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Isospin Matter in the NJL Model

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  1. Isospin Matter in the NJL Model ● Phase Diagram at finite μI ● BCS-BEC Crossover in pion superfluid Pengfei Zhuang (zhuangpf@mail.tsinghua.edu.cn)Tsinghua University, Beijing Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  2. QCD Phase Diagram Questions: 1) What is the phase of quark matter at finite μI ? 2) Is μI effect similar to μB effect? • D. T. Son and M. A. Stephanov, Phys. Rev. Lett. 86, 592(2001) • J. B. Kogut, D. K. Sinclair, Phys. Rev. D 66, 034505(2002) • K. Splittorff, D. T. Son, and M. A. Stephanov, Phys. Rev. D64, 016003 (2001) • M. Loewe and C. Villavicencio, Phys. Rev. D 67, 074034(2003) • Michael C. Birse, Thomas D. Cohen, and Judith A.McGovern, Phys. Lett. B 516, 27 (2001) • D. Toublan and J. B. Kogut, Phys. Lett. B 564, 212 (2003) • Barducci, R. Casalbuoni, G. Pettini, and L. Ravagli, Phys. Rev. D 69, 096004 (2004) • M. Frank, M. Buballa and M. Oertel, Phys. Lett. B 562, 221 (2003) • L. He and P. Zhuang, Phys. Lett. B 615, 93 (2005) Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  3. BCS and BEC Pairing in BCS, Tc is determined by thermal excitation of fermions, in BEC, Tc is controlled by thermal excitation of collective modes. Is there a similar BCS-BEC structure for QCD condensed matter ? Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  4. NJL Model ●there is reliable lattice QCD result at finite T, but not yet precise lattice simulation at finite μ, we have to consider effective models. ● the physics at finite T is vacuum excitation, but the physics at at finite μ is vacuum condensation. ●the BCS inspired Nambu-Jona-Lasinio (NJL) model successfully describes the chiral condensation and color condensation. chiral thermodynamics chiral and color condensate Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  5. NJL at Finite μI He, Jin and PZ, PRD71, (2005)116001 NJL with isospin symmetry breaking quark chemical potentials chiral and pion condensates with finite pair momentum quark propagator in MF gap equations: Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  6. Phase Structure of PionSuperfluid He and PZ, PRD74, (2006)036005 Jiang and PZ, PRCC83 (2011) 038201 μB μI Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  7. Quantum Fluctuations (Mesons) in RPA He, Jin, and PZ, PRD71, (2005)116001 meson propagator at RPA considering all possible channels in the bubble summation meson polarization functions mixing among normal in pionsuperfluid phase pole of the propagator determines meson masses the new eigen modes are linear combinations of Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  8. Meson Mixing and Goldstone Mode Hao and PZ, PLB652, (2007)275 mixing angles α between σ and π+ , β between σ and π_, and γ between π+ and π_ Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  9. Meson Spectral Functions Sun, He and PZ, PRD75, (2007)096004 meson spectra function between the temperatures Tc and T* BEC BCS Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  10. π – π scattering and BCS-BEC Crossover BEC BCS Normal Phase BEC BCS PionSuperfluid Mao and Zhuang: arXiv:1202.3490 BCS: overlapped molecules, large π – π cross section BEC: identified molecules, ideal Boson gas limit Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  11. Yukawa Potential in Quark Matter Mu and PZ, Eur. Phys. J C58, (2008)271 meson exchange in nucleon scattering (1934-1935) p p U n n meson exchange in NJL at quark level stable quark potential screen mass Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  12. Meson Screening Mass Jiang and PZ, Eur.Phys.J. C71 (2011) 1822 corresponding to the global isospin symmetry breaking, there is a Goldstone mode in the pion superfluid, which leads to a long range force between two quarks ! Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  13. Quark Potential in PionSuperfluid Jiang and PZ, Eur.Phys.J. C71 (2011) 1822 1) the maximum potential is located at the phase boundary . 2) the potential in pion superfluid is non-zero at extremely high isospin density, totally different from the temperature and baryon density effects ! Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  14. Conclusion and Outlook 1)There exists a pion superfluid at high isospin density, and the Goldstone mode controls the thermodynamics of the system. 2) There exists a BCS-BEC crossover in the pion superfluid. 3) The maximum coupling is located at the phase transition boundary, similar to the temperature and baryon density effects. 4) The coupling is non-zero even at extremely high isospin density, totally different from the temperature and baryon density effects. Heavy Ion Collisions at the LHC Era, July 2012，Quy Nhon, Vietnam

  15. July, 2008 Summer School on Dense Matter and HI Dubna

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