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

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]


Outline

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

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

Critical end point?


Lattice quark condensate and polyakov loop

Lattice quark condensate and Polyakov loop

A. Bazavov et al., Phys. Rev. D 90, 014504 (2009)


Status of phase diagram

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

Alternative signature: Melting of resonances

Im 

s0

s

pole

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


Correlator of axial currents

Correlator of axial currents


Quark hadron duality

Quark – hadron duality

Finite energy sum rules

Operator product expansion


Non pert part dispersion relations

Non-pert part: dispersion relations


Pert part imaginary parts at finite t and

Pert part: imaginary parts at finite T and 

  • Twocontributions:

  • Annihilationchannel (availablealso at T==0)

  • Dispersionchannel (Landaudamping)


Imaginary parts at finite t and

Imaginary parts at finite T and 

Annihilation term

Dispersion term

Pion pole


Threshold s 0 at finite t and

Threshold s0 at finite T and 

N=1, C2<O2> = 0

2

GMOR

Need quark condensate at finite T and 


Quark condensate t 0

quark condensate T,   0

Poisson summation formula

quark condensate


Qcd phase diagram from finite energy sum rules

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

Representation makes it easy to carry out integration

2

_

8


Susceptibilities

Susceptibilities


Qcd phase diagram

QCD Phase Diagram


Summary and conclusions

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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