1. 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]

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 < T c < 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 s Im  s0s0 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 Operator product expansion Finite energy sum rules

10. Non-pert part: dispersion relations

11. Pert part: imaginary parts at finite T and  Two contributions: 1)Annihilation channel (available also at T=  =0) 2)Dispersion channel (Landau damping)

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

13. Threshold s 0 at finite T and  GMOR N=1, C 2 = 0 2 Need quark condensate at finite T and 

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

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

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 s 0 as 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.