Qcd phase diagram from finite energy sum rules
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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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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]


  • 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:


      chemical potential/temperature values for endpoint than models

  • Critical end point might not even exist!

Alternative signature: Melting of resonances

Im 




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

Correlator of axial currents

Quark – hadron duality

Finite energy sum rules

Operator product expansion

Non-pert part: dispersion relations

Pert part: imaginary parts at finite T and 

  • Twocontributions:

  • Annihilationchannel (availablealso at T==0)

  • Dispersionchannel (Landaudamping)

Imaginary parts at finite T and 

Annihilation term

Dispersion term

Pion pole

Threshold s0 at finite T and 

N=1, C2<O2> = 0



Need quark condensate at finite T and 

quark condensate T,   0

Poisson summation formula

quark condensate

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

Representation makes it easy to carry out integration





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 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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