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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

- 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)

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

- =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

- Lattices gives:
- Critical end point might not even exist!

Im

s0

s

pole

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

Finite energy sum rules

Operator product expansion

- Twocontributions:
- Annihilationchannel (availablealso at T==0)
- Dispersionchannel (Landaudamping)

Annihilation term

Dispersion term

Pion pole

N=1, C2<O2> = 0

2

GMOR

Need quark condensate at finite T and

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

2

_

8

- 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.