Collisional energy loss in a finite size QCD medium revisited
QCD Phase Diagram and Finite Energy Sum Rules
Transcript of QCD Phase Diagram and Finite Energy Sum Rules
![Page 1: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/1.jpg)
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, )
![Page 2: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/2.jpg)
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
![Page 3: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/3.jpg)
Lattice at B=0
![Page 4: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/4.jpg)
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)
![Page 5: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/5.jpg)
Possible scenarios for QCD phase diagram
![Page 6: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/6.jpg)
Zooming in: Heavy ion experiments
![Page 7: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/7.jpg)
Lattice quark condensate and Polyakov loop
![Page 8: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/8.jpg)
Critical end point
![Page 9: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/9.jpg)
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!
![Page 10: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/10.jpg)
Alternative signature: Melting of resonances
s
Im
s0pole
For increasing T and/or B the energy threshold for the continuum goes to 0
![Page 11: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/11.jpg)
Quark – hadron duality
Operator product expansion
Finite energy sum rules
![Page 12: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/12.jpg)
Dispersion relations
s
s0
![Page 13: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/13.jpg)
Dispersion relations
![Page 14: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/14.jpg)
Imaginary parts at finite T and
![Page 15: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/15.jpg)
Imaginary parts at finite T and
Annihilation term
Dispersion term
Pion pole
![Page 16: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/16.jpg)
Threshold s0 at finite T and
GMOR
N=1, C2<O2> = 0
![Page 17: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/17.jpg)
Need quark condensate at finite T and
• At T==0, general structure:
![Page 18: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/18.jpg)
Parametrize S-D solution in terms of “free-like” propagators
Parameters fixed by requiring S-D conditions on the above functions
![Page 19: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/19.jpg)
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
+
![Page 20: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/20.jpg)
quark condensate T, 0
Poisson summation formula
quark condensate
![Page 21: QCD Phase Diagram and Finite Energy Sum Rules](https://reader036.fdocuments.us/reader036/viewer/2022071602/613d722c736caf36b75d6cbf/html5/thumbnails/21.jpg)
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!