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XXXI Bienal de la RSEF, Granada, España, 10-14 septiembre 2007.

COEFICIENTES DE TRANSPORTE EN UN GAS DE PIONES. Angel Gómez Nicola. Universidad Complutense Madrid. XXXI Bienal de la RSEF, Granada, España, 10-14 septiembre 2007. t. (fm/c). T (MeV). 120-200. 300-400. HADRON GAS ( p, K , h, r,...). ¿QGP?. 50. 1. 5-10. PERTURBATIVE QCD

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XXXI Bienal de la RSEF, Granada, España, 10-14 septiembre 2007.

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  1. COEFICIENTES DE TRANSPORTE EN UN GAS DE PIONES Angel Gómez Nicola Universidad Complutense Madrid XXXI Bienal de la RSEF, Granada, España, 10-14 septiembre 2007.

  2. t (fm/c) T (MeV) 120-200 300-400 HADRON GAS (p, K, h, r,...) ¿QGP? 50 1 5-10 PERTURBATIVE QCD quarks and gluons EFFECTIVE LOW-ENERGY MODELS Light hadrons Heavy Ion Collisions: Hadronic matter at high Temperature and Density

  3. Heavy Ion Collisions: Hadronic matter at high Temperature and Density QCD phase diagram

  4. Chiral Symmetry of QCD: QCD with Nfmassless quarks is chiral invariant: Spontaneously Broken at T=0 (no chiral degeneracy of SU(Nf ) multiplets): (ISOSPIN FOR Nf =2) Nf = 2: p’s (3) Nf = 3: p’s (3), K’s (4),  “NGB” are the lightest pseudoscalars ( mq 0  mBG0) RELEVANT D.O.F AT LOW ENERGIES E<<L 1 GeV

  5. free energy density T similarly to a ferromagnet with Chiral Symmetry is restored at Tc 150-200 MeV The order parameter is the quark condensate:

  6. Chiral Perturbation Theory: Relevant for low and moderate temperatures below Chiral SSB Most general derivative and mass expansion of NGB mesons compatible with the SSB pattern of QCD model-independent low-energy predictions. NLSM Weinberg’s chiral power counting:

  7. TC measure the response of the system to restore equilibrium after the action of an external force coupled to a conserved current . Linear Response (Kubo formula) in terms of retarded correlators: In equilibrium at temperature T Diagramatically, nonperturbative corrections needed to account for the inverse collisional width dependence (“pinching poles”): Im as expected from Kinetic Theory  Transport coefficients of a pion gas in ChPT: D.Fernández-Fraile,AGN:PRD73:045025,2006, NPA785:166-169,2007, EPJA31:848,2007

  8. In the dilute gas regime: Exactly Unitary. Data up to 1 GeV. r(770), f0(600)

  9. In the dilute gas regime: Exactly Unitary. Data up to 1 GeV. r(770), f0(600)

  10. “Double lines” with equal momentum carryG≠0 propagators and carry a “nonperturbative” factor Y for chiral loops: Transport coefficients: revising chiral counting Identify diagrams with larger powers of Y: Ladders Bubbles

  11. Loop spectral function ~ Potentially large Detailed analysis of the effective ladder vertex T dependence factorizes PERTURBATIVE IN CHPT

  12. Unitarization is important ! Unitarity gives larger T-dependence. Ladders still formally ChPT perturbative.

  13. Gp 0 and resonances in pp scattering important near the origin ! W.Liu, R.Rapp nucl-th/0604031

  14. Results for shear and bulk viscosities Sound attenuation length (related to elliptic flow):

  15. Results for shear and bulk viscosities Sound attenuation length (related to elliptic flow):

  16. Transport coefficients in ChPT require a modification of the standard chiral power counting to account for O(1/Gp) collision effects. The leading order gives rigourously the T<<mpbehaviour, consistently with nonrelativistic Kinetic Theory. At higher temperatures, the LO agrees reasonably with KT analysis and phenomenological/theoretical results. Unitarity is crucial to ensure the correct high-T behaviour. As TTcladder-type diagrams may have to be sumed, although results suggest strong cancellations. Kaons, chemical potentials … CONCLUSIONS & OUTLOOK

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