1. F. Scardina INFN-LNS Catania, University of Messina V. Greco, M. Di Toro Jet quenching Dynamics [Based on arXiv:1009.1261 (today) ]

2. Outline  Our simple model Our simple model  Quenching observables : Quenching observables : Nuclear modification factor R AA (quarks)/R AA (gluons) linked to the flavour linked to the flavour dependence of ΔE dependence of ΔE  Open questions Open questions Simultaneous description of both R AA and V 2 is yet theoretical challenge – “azimuthal puzzle” High P T protons less suppressed than pions - flavor puzzle High P T protons less suppressed than pions - flavor puzzle  Conclusion and future developments x y z Elliptic flow

3. Modelling jet quenching Our model is based on the approximation by which jets lose energy in a bulk medium that is expanding and cooling independently from the jets energy loss.  Initial condition  Hadronization with AKK fragmentation function D(z)  Density profile for the Bulk medium  Hard partons distributions in momenta coordinates (pQCD) in space (N coll )  Energy loss (gluon bremsstrahlung,GLV) Glauber Model (Wood Saxon) Sharp Ellipse Constant with

4. Application of the model to evaluate Integrated for p T > 6 GeV  For there are non-perturbative mechanisms (coalescence) π0π0 Au+Au at 200 AGeV

5. Open questions  Azimuthal puzzle Simultaneous description of both R AA and V 2 is yet a theoretical challenge The experimental data show V 2 above theoretical prediction High P T protons less suppressed than pions R AA Au+Au central 0-12% protons pions because they come more from gluons… …and gluons are more suppressed than quarks ΔE for gluons=9/4* ΔE for quarks But protons should be more suppressed R AA (q)/R AA (g)≤1 Flavor puzzle  Flavor puzzle R AA (q)/R AA (g)=9/4 Does it mean?

6. One solution to azimuthal puzzle: Energy loss near Tc Sharp EllipseWood Saxon Predominant energy loss at low T [Liao, Shuryak Phys. Rev. Lett. 102 (2009)] Solution of azimuthal puzzle? We analyze relation between T dependence of quenching and v 2,with R AA fixed on Data they are strongly related 20-30%

7. R AA (quark)/ R AA (gluon) and Temperature dependence of energy loss The ratio is related to temperature dependence of energy loss it is not necessarely 9/4 The ratio is lower if quenching mainly occur close to T c R AA fixed on experimental data for pions (R AA =0.2) Sharp Ellipse

8. R AA (quark)/ R AA (gluon) profile dependence Wood Saxon The two profiles show opposite behavior Rigid case is not adequate Sharp Ellipse

9. Over simplified case: all quarks lose the same amount of energy and all gluons lose ΔE gluon =9/4*ΔE quark Minimal realistic case: 2 classes of quarks quenched + unquenched, always with ΔE g =9/4*ΔE q The ratio is dominated by those particles which do not lose energy Sharp Ellipse: direct relation T τWood Saxon: No direct relation T τ (Surface -> low T also at early times) quenching at low T ( later tau) Many particles escape without E loss ; those in the inner part must be strongly quenched  (red dot dash line) quenching at low T  E is strong in a layer on the surface -> all particles must cross this layer so all particles lose energy ≠ R AA (quark)/R AA (gluon): profile and T dependence of energy loss

10. One solution to flavor puzzle:Jet conversion [Ko, Liu, Zhang Phys. Rev C 75] [Liu, Fries Phys. Rev C 77] We also have introduced this mechanism in our code: results confirmed To solve it inelastic collisions that cause a change of the flavor have been invoked [See Ko talk] The conversion rate is given by the collisional width R AA (q)/R AA (g)

11. without conversion Kc=0 conversion kc=6 E loss at high T GLVc GLV α(T) E loss at low T Exp Correlation R AA (quark)/R AA (gluon)-V 2 (Wood-Saxon) R AA (P T ) fixed on experimental data for pions Lattice QCD EoS state moves V 2 and RAA(q)/RAA(g) to the right To get close to experimental data:  DE stronger close to phase transition is need But If  E is stronger close to Tc deviations of  (T) from the free gas approximation become important - > use lQCD EoS a= 0.15; n=1.89  flavor conversion becomes more necessary E loss at low T EoS lattice QCD 20-30%

12. Conclusions and Perspective  If one goes beyond R AA, a realistic profile for the fireball is needed  Different ΔE(T) generate very different R AA (q)/R AA (g) and v 2  Observed v 2 and R AA (q)/R AA (g) seem to suggest a ΔE stronger near Tc + a strong flavor conversion  Sensitive to deviation from the free gas expansion (EoS) for Eloss (T~Tc)  What goes on for LHC conditions? Future Developments  transport code takes into account collisional and radiative energy loss joint to a dynamics consistent with the used EoS [Greiner Group][Catania]

14. Initial condition  Density profile for the bulk In longitudinal direction evolves according to the Bjorken expansion at the velocity of light 1.Glauber Model partecipant distribution 2.Sharp elliptic shape  Momenta space  High P T partons distribution  Coordinates space (N coll ) Dal profilo di densita otteniamo il profilo di T Ideal gas The initial transverse density profile can be modelled in two different way The spectra are calculated in the NLO pQCD scheme [Ko, Liu, Zhang Phys. Rev C 75][Liu, Fries Phys. Rev C 77] The value of the parameters A f,B f and n f are taken from Ref.

15. Glauber Model  The trasverse density profile for the bulk is proportional to the partecipant distribution  The hard parton distribution in space coordinates scales with the number of binary Nucleon collision Proiezione lungo l’asse x Density profile for the bulk Density profile for the jet

16. Hadronization z=p h /p p [S. Albino, B. A. Kniehl, and G. Kramer, Nucl. Phys B597] The parton distribution after the quenching are employed to evaluate the hadron spectrum by indipendent jet fragmentation using the AKK fragmentation function

18. Ratio R AA (q)/R AA (g) We consider a simplified case in which all quarks lose the the same amount of energy DE and all gluons lose their energy according to DE=9/4*DE Spectra are shifted by a quantity equal to the energy lost Partons that finally emerge with an energy pT Are those which before quenching had an energy pT+  e*η where η=1 for quarks and 9/4 for gluons There is no reason why this ratio must be 9/4

19. Over simplified case: all quark lose the the same amount of energy and all gluons lose ΔE g =9/4*ΔE quark Minimal realistic case: 2 classes of quarks undergoing different quenching, always with ΔE g =9/4*ΔE q The ratio is dominated by the way the energy loss is distributed among partons Sharp Ellipse: direct relation T τWood Saxon: No direct relation T τ (Surface -> low T also at early times) quenching at high T particles lose energy early; all particle lose energy (dotted line) quenching at high T No DE at the surface but only in the inner part of the fireball (strong DE); particles in the surface escape almost without Eloss quenching at low T ( later tau) Many particles escape without Eloss; those in the inner part must be strongly quenched  blue thin line) quenching at low T DE is strong in a layer on the surface -> all particles across this layer so all particles lose energy ≠ R AA (quark)/R AA (gluon): profile and T dependence of energy loss ≠