QCD Phase Diagram and Finite Energy Sum Rules

Alejandro AyalaInstituto de Ciencias Nucleares, UNAM

(In collaboration with A. Bashir, C. Domínguez, E. Gutiérrez, M. Loewe, and A. Raya, )

Outline

• Status of QCD phase diagram

• Resonance threshold energy as phenomenological tool to study deconfinement

• QCD sum rules at finite temperature/chemical potential

• Non-perturbative quark propagator

Lattice at B=0

Deconfinement and chiral symmetry restoration

Driven by same effect:

• 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)

Possible scenarios for QCD phase diagram

Zooming in: Heavy ion experiments

Lattice quark condensate and Polyakov loop

Critical end point

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 values for endpoint chemical potential/temperature than Models

• Critical end point might not even exist!

Alternative signature: Melting of resonances

s

Im

s0pole

For increasing T and/or B the energy threshold for the continuum goes to 0

Quark – hadron duality

Operator product expansion

Finite energy sum rules

Dispersion relations

s

s0

Dispersion relations

Imaginary parts at finite T and

Imaginary parts at finite T and

Annihilation term

Dispersion term

Pion pole

Threshold s0 at finite T and

GMOR

N=1, C2<O2> = 0

Need quark condensate at finite T and

• At T==0, general structure:

Parametrize S-D solution in terms of “free-like” propagators

Parameters fixed by requiring S-D conditions on the above functions

T0, Lorentz covariant is lost

Strategy: Add an extra “free-like” propagator

Find extra parameters fitting, for example,

to quark condensate and pressure at T0

+

quark condensate T, 0

Poisson summation formula

quark condensate

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.

• Results… stay tuned!