Transcript QCD Phase Diagram and Finite Energy Sum Rules

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
• 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
Im 
pole
s0
s
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 
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 
N=1, C2<O2> = 0
2
GMOR
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
8
_
2
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 “freelike” structures.
• Transition temperatures coincide, method not
accurate enough to find critical point, stay tuned.