QCD Phase Diagram from Finite Energy Sum Rules

Alejandro AyalaInstituto 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

• 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, 014504 (2009)

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!

Alternative signature: Melting of resonances

s

Im

s0pole

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 s0 at finite T and

GMOR

N=1, C2<O2> = 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, 014504 (2009)

Representation makes it easy to carry out integration

28 _

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 s0 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.