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: [hep-ph]

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

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)

Critical end point?

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

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!

Alternative signature: Melting of resonances s Im  s0s0 pole For increasing T and/or  B the energy threshold for the continuum goes to 0

Correlator of axial currents

Quark – hadron duality Operator product expansion Finite energy sum rules

Non-pert part: dispersion relations

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

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

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

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

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, (2009)

Representation makes it easy to carry out integration 2 8 _

Susceptibilities

QCD Phase Diagram

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.