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A Promising Solution to the Elliptic Quench Puzzle at RHIC

Exploring the puzzle of fitting RHIC phenomena, discussing energy loss theories, model failures, parameter fixing, and successful modifications to solve the puzzle.

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A Promising Solution to the Elliptic Quench Puzzle at RHIC

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

  2. What is the Puzzle?–Data • Naïvely combine published RAA(pT) and v2(pT) data • Preliminary PHENIX p0 data • Data centrality classes: • STAR1,2 charged hadron • 0-5%, 10-20%, 20-30%, 30-40%, 40-60% • PHENIX3,4 charged hadron • 0-20%, 20-40%, 40-60% • PHENIX5p0 • 10-20%, 20-30%, …, 50-60% • Note: error regions are only a rough estimate

  3. What is the Puzzle?–Theory • Can’t fit the RHIC phenomena • Hydrodynamics • Not applicable at intermediate and higher pT • Parton Cascade and Energy Loss • Don’t work: jet quenching and anisotropy anti-correlated • Models over-suppress RAA in order to reproduce large observed v2

  4. GLV Energy Loss • A geometric approximation: the gGLV • Fractional energy loss: • Integral through the 1D expanding medium that captures the L2 dependence of energy loss in a static medium:

  5. The gGLV • Use Glauber, factorization, and power law spectrum to yield: • 10% difference between n=4 and n=5, use n=4 • To calculate RAA and v2, generate this at multiple values of f and find the Fourier modes • Use hard sphere nuclear geometry • Systematically enhances v26

  6. Model Failures • Models can’t match intended data point for any value of their free parameter (opacity of the medium) • MPC7: calculated for 25-35% centrality • gGLV: 40-50% centrality

  7. Modify gGLV • Absorption model: add thermal absorption and stimulated emission8, • Integral through 1D expanding medium that captures linear in L dependence of energy gain in static media: • Punch model: add a momentum boost (DpT) to the parton in the direction normal to the edge of emission

  8. Fixing the Parameters • As in Drees, et al.6, gGLV (k) model fit to PHENIX most central RAA • gGLV+abs (k, k) and gGLV+punch (k,DpT) parameters uniquely determined by a single (RAA,v2) point: • 20-30% centrality p0

  9. Success! • Having fixed the parameters for a single centrality, allow the impact parameter to vary

  10. But! • For radiative energy loss and thermal absorption, asymptotic expansions7 give: where

  11. Failure of Absorption • Too high a multiplicity required for absorption part of gGLV+absorption (k = .5 and k = .25): • For E = 6 GeV, L = 5 fm, l0 = .2 fm, and as = .4: • For E = 10 GeV, L = 5 fm , l0 = .2 fm, and as = .4:

  12. Success of the Punch • Reasonable multiplicity required for energy loss part of gGLV+punch (k = .18) • For E = 10 GeV, L = 5 fm, and as = .3: • Punch needed (DpT = .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. Cu+Cu v2 vs. RAA: Centrality-binned Results: Cu+Cu Predictions Use parameters for Au+Au, apply models to Cu+Cu

  14. Conclusions • Previous theories don’t follow the elliptic quench pattern at RHIC • Energy loss modified with either absorption or a punch agrees with the RAA and v2 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 v2 enhancement is lost

  15. References

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