QCD Phase Diagram and Finite Energy Sum Rules
Transcript of QCD Phase Diagram and Finite Energy Sum Rules
QCD Phase Diagram and Finite Energy Sum Rules
Alejandro AyalaInstituto de Ciencias Nucleares, UNAM
(In collaboration with A. Bashir, C. Domínguez, E. Gutiérrez, M. Loewe, and A. Raya, )
Outline
• Status of QCD phase diagram
• Resonance threshold energy as phenomenological tool to study deconfinement
• QCD sum rules at finite temperature/chemical potential
• Non-perturbative quark propagator
Lattice at B=0
Deconfinement and chiral symmetry restoration
Driven by same effect:
• 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)
Possible scenarios for QCD phase diagram
Zooming in: Heavy ion experiments
Lattice quark condensate and Polyakov loop
Critical end point
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 values for endpoint chemical potential/temperature 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
Quark – hadron duality
Operator product expansion
Finite energy sum rules
Dispersion relations
s
s0
Dispersion relations
Imaginary parts at finite T and
Imaginary parts at finite T and
Annihilation term
Dispersion term
Pion pole
Threshold s0 at finite T and
GMOR
N=1, C2<O2> = 0
Need quark condensate at finite T and
• At T==0, general structure:
Parametrize S-D solution in terms of “free-like” propagators
Parameters fixed by requiring S-D conditions on the above functions
T0, Lorentz covariant is lost
Strategy: Add an extra “free-like” propagator
Find extra parameters fitting, for example,
to quark condensate and pressure at T0
+
quark condensate T, 0
Poisson summation formula
quark condensate
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.
• Results… stay tuned!