1. W. A. Horowitz Quark Matter 2005 A Promising Solution to the Elliptic Quench Puzzle at RHIC William A. Horowitz Columbia University August 4-5, 2005

2. W. A. Horowitz Quark Matter 2005 What is the Puzzle?–Data Naïvely combine published R AA (p T ) and v 2 (p T ) data Preliminary PHENIX  0 data Data centrality classes: –STAR 1,2 charged hadron 0-5%, 10-20%, 20-30%, 30-40%, 40-60% –PHENIX 3,4 charged hadron 0-20%, 20-40%, 40-60% –PHENIX 5  0 10-20%, 20-30%, …, 50-60% Note: error regions are only a rough estimate

3. W. A. Horowitz Quark Matter 2005 What is the Puzzle?–Theory Can’t fit the RHIC phenomena Hydrodynamics –Not applicable at intermediate and higher p T Parton Cascade and Energy Loss –Don’t work: jet quenching and anisotropy anti- correlated –Models over-suppress R AA in order to reproduce large observed v 2

4. W. A. Horowitz Quark Matter 2005 GLV Energy Loss A geometric approximation: the gGLV Fractional energy loss: Integral through the 1D expanding medium that captures the L 2 dependence of energy loss in a static medium:

5. W. A. Horowitz Quark Matter 2005 The gGLV Use Glauber, factorization, and power law spectrum to yield: –10% difference between n=4 and n=5, use n=4 To calculate R AA and v 2, generate this at multiple values of  and find the Fourier modes Use hard sphere nuclear geometry –Systematically enhances v 2 6

6. W. A. Horowitz Quark Matter 2005 Model Failures Models can’t match intended data point for any value of their free parameter (opacity of the medium) –MPC 7 : calculated for 25- 35% centrality –gGLV: 40-50% centrality

7. W. A. Horowitz Quark Matter 2005 Modify gGLV Absorption model: add thermal absorption and stimulated emission 8, –Integral through 1D expanding medium that captures linear in L dependence of energy gain in static media: Punch model: add a momentum boost (  p T ) to the parton in the direction normal to the edge of emission

8. W. A. Horowitz Quark Matter 2005 Fixing the Parameters As in Drees, et al. 6, gGLV (  ) model fit to PHENIX most central R AA gGLV+abs ( , k) and gGLV+punch   p T ) parameters uniquely determined by a single (R AA,v 2 ) point: –20-30% centrality  0

9. W. A. Horowitz Quark Matter 2005 Success! Having fixed the parameters for a single centrality, allow the impact parameter to vary

10. W. A. Horowitz Quark Matter 2005 But! For radiative energy loss and thermal absorption, asymptotic expansions 7 give: where

11. W. A. Horowitz Quark Matter 2005 Failure of Absorption Too high a multiplicity required for absorption part of gGLV+absorption  5 and k =.25): –For E = 6 GeV, L = 5 fm, l 0 =.2 fm, and  s =.4: –For E = 10 GeV, L = 5 fm, l 0 =.2 fm, and  s =.4:

12. W. A. Horowitz Quark Matter 2005 Success of the Punch Reasonable multiplicity required for energy loss part of gGLV+punch (  ) –For E = 10 GeV, L = 5 fm, and  s =.3: Punch needed (  p T =.5 GeV) is on the order of the energy boost (~1 GeV) expected from deflagration, latent heat, or the effect of the bag constant

13. W. A. Horowitz Quark Matter 2005 Cu+Cu Predictions –Cu+Cu v 2 vs. R AA :–Centrality-binned Results: Use parameters for Au+Au, apply models to Cu+Cu

14. W. A. Horowitz Quark Matter 2005 Conclusions Previous theories don’t follow the elliptic quench pattern at RHIC Energy loss modified with either absorption or a punch agrees with the R AA and v 2 data Absorption ruled out by the multiplicity results Possible punch sources exist, with effects on the same order of magnitude –Smallness of punch (.5 GeV) should allow for necessary scaling when a more realistic nuclear density geometry is used and v 2 enhancement is lost

15. W. A. Horowitz Quark Matter 2005 References