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QCD Phase Diagram from Finite Energy Sum Rules

QCD Phase Diagram from Finite Energy Sum Rules. Alejandro Ayala Instituto de Ciencias Nucleares , UNAM (In collaboration with A. Bashir , C. Domínguez , E. Gutiérrez , M. Loewe, and A. Raya) arXiv:1106.5155  [ hep-ph ]. Outline. Deconfinement and chiral symmetry restoration

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QCD Phase Diagram from Finite Energy Sum Rules

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  1. QCD Phase Diagram from Finite Energy Sum Rules Alejandro Ayala Instituto de CienciasNucleares, UNAM (In collaboration with A. Bashir, C. Domínguez, E. Gutiérrez, M. Loewe, and A. Raya) arXiv:1106.5155 [hep-ph]

  2. Outline • Deconfinement and chiral symmetry restoration • Resonance threshold energy as phenomenological tool to study deconfinement • QCD sum rules at finite temperature/chemical potential • Results

  3. Deconfinement and chiral symmetry restoration • Driven by same effect: • With increasing density, confining interaction gets screened and • eventually becomes less effective (Deconfinement) • Inside a hadron, quark mass generated by confining • interaction. When deconfinement occurres, generated • mass is lost (chiral transition)

  4. Critical end point?

  5. Lattice quark condensate and Polyakov loop A. Bazavov et al., Phys. Rev. D 90, 014504 (2009)

  6. Status of phase diagram • =0: Physical quark masses, deconfinement and chiral symmetry restoration coincide. Smooth crossover for 170 MeV < Tc < 200 MeV • Analysis tools: • Lattice (not applicable at finite ) • Models (Polyakov loop, quark condesate) • Lattice vs. Models: • Lattices gives: smaller/larger chemical potential/temperature values for endpoint than models • Critical end point might not even exist!

  7. Alternative signature: Melting of resonances Im  s0 s pole For increasing T and/or B the energy threshold for the continuum goes to 0

  8. Correlator of axial currents

  9. Quark – hadron duality Finite energy sum rules Operator product expansion

  10. Non-pert part: dispersion relations

  11. Pert part: imaginary parts at finite T and  • Twocontributions: • Annihilationchannel (availablealso at T==0) • Dispersionchannel (Landaudamping)

  12. Imaginary parts at finite T and  Annihilation term Dispersion term Pion pole

  13. Threshold s0 at finite T and  N=1, C2<O2> = 0 2 GMOR Need quark condensate at finite T and 

  14. quark condensate T,   0 Poisson summation formula quark condensate

  15. A. Bazavov et al., Phys. Rev. D 90, 014504 (2009) Lose of Lorentz covariance means that Parametrize S-D solution in terms of “free-like” propagators Parameters fixed by requiring S-D conditions and description of lattice data

  16. Representation makes it easy to carry out integration 2 _ 8

  17. Susceptibilities

  18. QCD Phase Diagram

  19. Summary and conclusions • QCD phase diagram rich in structure: critical end point? • Polyakov loop, quark condensate analysis can be supplemented with other signals: look at threshold s0as function of T and  • Finite energy QCD sum rules provide ideal framework. Need calculation of quark condesnate. Use S-D quark propagator parametrized with “free-like” structures. • Transition temperatures coincide, method not accurate enough to find critical point, stay tuned.

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