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QCD in Medium

Thomas Klähn. QCD in Medium. Quark Matter in Neutron Stars . Image: PSR B1509-58 NASA/CXC/SAO/P.Slane, et al. . 4/3/2009. Why Quark Matter in Compact Stars?. The QCD Phase Diagram. At high T and n a phase transition from nuclear to quark matter is predicted.

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QCD in Medium

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  1. Thomas Klähn QCD in Medium Quark Matter in Neutron Stars ... Image: PSR B1509-58 NASA/CXC/SAO/P.Slane, et al.

  2. 4/3/2009 Why Quark Matter in Compact Stars? • The QCD Phase Diagram At high T and n a phase transition from nuclear to quark matter is predicted • Heavy Ion Collisions (HICs) • hot, „dilute“, symmetric matter • Neutron Stars • cold, dense, asymmetric matter • superconducting phases www.gsi.de

  3. Quark Matter What is so special about the quarks: Confinement: No isolated quark has ever been observed Quarks are confined in baryons and mesons Dynamical Mass Generation: Proton 940 MeV, 3 constituent quarks with each 5 MeV → 98.4% from .... somewhere? and look at this: eff. quark mass in proton: 940 MeV/3 ≈ 313 MeV eff. quark mass in pion : 140 MeV/2 = 70 MeV quark masses generated by interactions only ‚out of nothing‘ interaction in QCD through (self interacting) gluons dynamical chiral symmetry breaking (DCSB) is a distinct nonperturbative feature! Confinement and DCSB are connected. Not trivially seen from QCD Lagrangian. Investigating quark-hadron phase transition requires nonperturbative approach.

  4. Quark Matter Confinement and DCSB are features of QCD. Wouldn‘t it be nice to account for these phenomena when describing QM in Compact Stars? Bag-Model: While Bag-models certainly account for confinement (constructed to do exactly this) they do not exhibit DCSB (quark masses are fixed). NJL-Model While NJL-type models certainly account for DCSB (applied, because they do) they do not (trivialy) exhibit confinement. Modifications to address these shortcomings exist (e.g. PNJL) Still holds: Inspired by, but not based on QCD. Lattice QCD still fails at T=0 and finite μ Dyson-Schwinger Approach Derive gap equations from QCD-Action. Self consistent self energies. Successfuly applied to describe meson and hadron properties Extension from vacuum to finite densities desirable → EoS within QCD framework

  5. 4/3/2009 Dyson Schwinger Approach in Medium • Inverse Quark Propagator: • Renormalised Self Energy: • Loss of Poincaré covariance increases complexity • → technically and numerically more challenging → no surprise, though • General Solution: • Similar structured equations in vacuum and medium, but in medium: • 1. one more gap • 2. gaps depend on (4-)momentum, energy and chemical potential Divide and Conquer! revokes Poincaré covariance Louis XI the Prudent Vacuum: and Medium: and Solve this and get EoS from T-Dynamics Easier said, than done

  6. Deconfinement and chiral phase transition • For μ < 0.53 GeV: • A = C • M= B/A increases monotonically • What happens at 0.53 GeV ? H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  7. Deconfinement and chiral phase transition Schwinger Function Mass pole expansion μ = 0, 0.4, 0.5 GeV • For μ < 0.53 GeV: • A = C • M= B/A increases monotonically • What happens at 0.53 GeV ? H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  8. Deconfinement and chiral phase transition Schwinger Function Mass pole expansion • For μ < 0.53 GeV: • A = C • M= B/A increases monotonically • What happens at 0.53 GeV ? H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  9. Deconfinement and chiral phase transition Schwinger Function Mass pole expansion • For μ < 0.53 GeV: • A = C • M= B/A increases monotonically • What happens at 0.53 GeV ? inverse lifetime → deconfinement H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  10. Deconfinement and chiral phase transition Gap equations have 2nd, deconfined and masslesssolution (Wigner-Phase) Compare Pressure in both phases: μ > 0.38 GeV: Wigner phase favored (B=0) Confinement for μ < 0.53 GeV H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  11. Deconfinement and chiral phase transition Gap equations have 2nd, deconfined and masslesssolution (Wigner-Phase) Compare Pressure in both phases: μ > 0.38 GeV: Wigner phase favored (B=0) Confinement for μ < 0.53 GeV 1st order chiral and deconfinement phase transition H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  12. Deconfinement and chiral phase transition • Promising: • 1. chiral symmetry breaking • 2. confinement/deconfinement • 3. a framework that • starts from the QCD-Action • But: the way to the EoS is • numerically nontrivial • andnot fully explored yet • up to now there exists • (to my best knowledge) • not a single, high density EoS • with 1.,2. and 3. • Possible ways to the QM - EoS: • Another Framework (NJL, Bag, etc) • A friendlier model • Try harder 1st order chiral and deconfinement phase transition H. Chen, W. Yuan, L. Chang, Y.-X. Liu, T.K., C.D. Roberts, Phys.Rev.D78:116015,2008

  13. An algebraic EoS Reminder on what needs to be solved: Ansatz for self energy Specify behaviour of Infrared strength running coupling for large k (zero width + finite width contribution) Previous results started from 2nd term Will proceed with the 1st one → Munczek/Nemirowsky (1983)

  14. An algebraic EoS general solution of the gap equations in medium results in propagator: In this model, the gap equations have algebraic solutions: Chirally broken and confined (Nambu-Goldstone) phase: Chirally restored and unconfined (Wigner-Weyl) phase: ... at finite Temperatures: Matsubara Frequencies

  15. Results Wigner Phase to obtain .2 .4 2 GeV fits π and ρ masses

  16. Results Wigner Phase to obtain approaching ideal Fermi gas behavior with increasing chemical potential 2 GeV 10 GeV .2 .4 2 GeV fits π and ρ masses

  17. Results Wigner Phase to obtain approaching ideal Fermi-gas with increasing chemical potential ‚small‘ chem. Potential: ← 2 GeV 10 GeV .2 .4 2 GeV

  18. Results Wigner Phase to obtain model is scale invariant regarding μ/η well satisfied up to ‚small‘ chem. Potential: ← ~μ 5 ~μ 4 .2 .4 2 GeV

  19. Results Wigner Phase to obtain model is scale invariant regarding μ/η well satisfied up to ‚small‘ chem. Potential: ← Basically have a QM-EoS, but need to determine ~μ 5 ~μ 4 .2 .4 2 GeV

  20. The EoS Calculate Pressure Difference at μ=0 with and get 3 quarks in a nucleon:

  21. The EoS Calculate Pressure Difference at μ=0 with and get decreases 3 quarks in a nucleon:

  22. The EoS Calculate Pressure Difference at μ=0 with and get 3 quarks in a nucleon:

  23. The EoS Calculate Pressure Difference at μ=0 with and get 3 quarks in a nucleon: Substract

  24. (Danielewicz et al., 2002) Flow Constraint in Symmetric Matter This looks rather soft but is within the constrained domain at meaningfull densities. Hybrid stars like it harder...

  25. Phase transition under compact star conditions Soft QM + Large transition density

  26. Neutron Stars nostable hybrid stars found in this model .

  27. Neutron Stars • X This is a fairly simple model • Results can change • They don‘t have to, though • X Caveats: • Mixed phase? • d-quark-drip scenario? • bound states • (B-S, Fadeev) • X However ... • This is the first in-mediuim EoS (I know) obtained within • a framework based on the QCD-action (proof of principle) and might indicate trouble for • the idea of hybrid stars.

  28. Conclusions • Obtained a QM - EoS in the QCD-action based non-perturb. Dyson-Schwinger-Formalism • with a simple Ansatz for the effective interaction (Munczek/Nemirovsky) • algebraic results for distribution function and Bag-Pressure • structure of distribution function has interesting features • the obtained EoS is soft, but reasonable (Meson masses, Flow ok, standard NSs) • found no stable hybrid star configurations • interesting & necessary work ahead: Diquarks, Mesons, Nucleons in Medium • - Fermi edge develops with • increasing chemical potential • - • Therefore • For Bag-Model/polytrope modellers: • Might be a good idea to consider • with 4 (this model), at least > 3 (ideal gas)

  29. The End Thank you!

  30. Neutron Stars And really: In this model no stable hybrid star configurations are found.

  31. Why Neutron Stars?

  32. Why Neutron Stars? ‚same constituents‘ can mean very different things: (not to forget: leptons) However: Meson and Baryon are Quark bound states QuantumChromoDynamics Successfull theory in Vacuum: Meson and Nucleon properties Neutron Stars: In mediumQCD Credit: F. Weber

  33. 4/3/2009 Dyson Schwinger Approach based on QCDaction, in terms of local Lagrangian density Defines generating functional ... partition function + source terms

  34. 4/3/2009 Dyson Schwinger Approach Problem is attacked in vacuum Mesons and Baryons as composites of confined quarks (and diquarks) q-propagator, d-propagator, Bethe-Salpeter-Ampl., Faddeev Ampl. Meson, Diquark → Bethe Salpeter Equations P. Maris (2002) Effective masses of diquarks. Bhagwat et al. (2007) Flavour symmetry breaking and meson masses Nucleon →Faddeev Equations Cloet et al. (2008) Current quark mass dependence of nucleon magnetic moments and radii Eichmann et al. (2008) The nucleon as a QCD bound state in a Faddeev approach.

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