Jamie Nagle University of Colorado

1. Medium Parameters in Jet Quenching AMY GLV AdS/CFT BDMPS PQM WHDG ZOWW DGLV Jamie Nagle University of Colorado Hard Probes 2008 Illa da Toxa, Galacia-Spain ASW

2. p0 Focus on published data in this talk I view preliminary data with a healthy skepticism  Uncertainties: Type A = point-to-point uncorrelated [statistics dominated] Type B = point-to-point correlated [energy scale, shower merging] Type C = globally correlated (i.e. common multiplicative factor) [Glauber nuclear thickness, p-p absolute normalization]  Hard to reduce… arXiv:0801.4020 arXiv:0801.1665 Every RHIC published result on which a full quantitative analysis is to be performed needs to explicitly quote these uncertainty contributions !

3. Methodology for inclusion of statistical and systematic uncertainties Calculate the modified c2 as a function of the theory parameters set (p) for the optimal eb (systematic Type B offset) and ec (systematic Type C offset). If the type A uncertainties scale the same as the data under systematic offsets, then one needs to rescale si. Developed by Mike Tannenbaum and JLN

4. PQM (ASW w/ BDMPS Weights) Quenching Factor Extra thanks to Constantin Loizides for providing the input curves

5. ~ Clear minimum in modified c2 1 std. dev. 2 std. dev.

6. RHIC data sQGP PQM result implies very strong coupling (non-perturbative) Even used to motivate AdS/CFT calculation Liu, Rajagopal, Wiedemann

7. “The fragility of high pT hadron spectra as a hard probe” “The interaction of the hard parton with the medium appears to be much stronger than expected for perturbative interactions…”

8. ^ If one measures RAA within ±10%, one determines q within ±20%, regardless of the q ! Surprised !? ^

9. AMY + Hydro “Once temperature evolution is fixed by the initial conditions and evolution [by 3+1 dimensional hydrodynamics], as is the only quantity which is not uniquely determined.” G-Y Qin et al., PRL 100, 072301 (2008) Note that within AMY, the coupling as is not just for the probe-medium, but also within the medium itself !

10. Coupling Constraint ~ Clear minimum in modified c2 1 std. dev. 2 std. dev. Assuming AMY+Hydro is perfectly correct, then this is the constraint on as from the experimental statistical and systematic uncertainties.

11. RHIC data RHIC data QGP? sQGP? Constraints ^ +2.1 - 3.2 PQM <q> = 13.2 GeV2/fm +270 - 150 GLV dNg/dy = 1400 +200 - 375 WHDG dNg/dy = 1400 +0.2 - 0.5 ZOWW e0 = 1.9 GeV/fm +0.016 - 0.012 AMY as = 0.280 Each constraint is assuming a perfect model with only one unknown parameter. Uncertainty is from experimental sources only !

12. Constraints ^ +2.1 - 3.2 PQM <q> = 13.2 GeV2/fm Puzzling since WHDG has GLV radiative e-loss, but also collisional e-loss. However, WHDG has no initial state scattering, and GLV has fixed single representative path length. +270 - 150 GLV dNg/dy = 1400 +200 - 375 WHDG dNg/dy = 1400 +0.2 - 0.5 ZOWW e0 = 1.9 GeV/fm +0.016 - 0.012 AMY as = 0.280 ZOWW has hard sphere geometry.

13. v2 pT (GeV/c) Strongly or Weakly Coupled ? Perturbative parton cascade (MPC) and analytic results unable to describe bulk flow. R. Baier, A.H. Mueller, D. Schiff, D. Son, Phys. Lett. B539, 46 (2002). MPC 1.6.0, D. Molnar, M. Gyulassy, Nucl. Phys. A 697 (2002). Does that contradict underlying AMY assumption with as = 0.28 ? BAMPS with ggggg and as = 0.6 (but incorrect angular distribution) Does this mean anything? Z. Xu, C. Greiner, H. Stöcker, arXiv: 0711.0961 [nucl-th] Jet quenching problem is critical to resolve, in particular, because of the implications on the bulk medium itself.

14. 5 models with 5 different assumptions about properties of the medium (which are not known a priori). If after removing smoke screen from differing incorrect models of the geometry, etc., they all give equal agreement to RAA Conclusion - We do not need more sensitive observables We do need more discriminating observables - that already exist (!) - that can be measured in the future However, the above summary is incomplete. Theorists should be more discriminating (IMHO). Sometimes assumptions can be checked for self-consistency or by an extended calculation (e.g. of a term ignored). I am surprised by the lack of discussion of these details (e.g. Baier’s critique of PQM/ASW hep-ph/0605183).

15. WHDG AMY GLV AdS/CFT PQM ASW Data BDMPS ZOWW DGLV What is an experimentalist to do?

16. Reaction Plane Dependence p0 p0 PQM Calculation PQM calculations indicate steeper Df dependence with larger q Somewhat smaller dependence. Most quenching models underpredict high pT v2. ^ When preliminary data with higher statistics and better systematics are published, this should be much more constraining. PHENIX: Phys. Rev. C76, 034904 (2007)

17. Dijet Observables h h Nagle Toy Energy Loss Model (NTELM) Larger dE/dx Parton 2 Path (fm) Glauber geometry for parton paths. Constant dE/dx (varied in steps of +0.2 GeV/fm) Parton 2 path biased by high pT trigger particle 1 Thus, perhaps IAA (away side per trigger) will be more sensitive that RAA. Might also discriminate on fluctuations. BDMPS – many soft scatterings GLV – fewer harder scatterings

18. ZOWW Calculation (Jets and Dijets) c2 /d.o.f. IAA fit has “sharper c2 concavity” than RAA, thus more sensitive. Does it matter that the plot has a mis-label? Yes it does !

19. ~ This only utilizes statistical uncertainties. Re-do with full c2. However, IAA has steeper dependence on e0 than RAA. If equal data uncertainties, IAA should be more constraining. c2 /d.o.f.

20. STAR PRL 97 (2006) 162301 ZOWW Calculation Constraint using zT > 0.4 Private Communication Peter Jacobs Estimated Type C Uncertainty ~ 7% Why is this different from ZOWW paper?

21. d-Au Au-Au In the ZOWW paper, they only use the DAuAu as the constraint ! Extra thanks to X.N. Wang for providing the input curves

22. What are the constraints? Note the extremely low p-value. However, if you only use DAuAu shouldn’t we include the NLO pQCD scale uncertainty? If this theory uncertainty is included then magenta constraint Does the scale uncertainty cancel in IAuAu (or RAuAu)? IAA constraint DAA constraint DAA + scale uncertainty

23. ~ ~ c2 (total) – c2 (min) ZOWW Au-Au 0-5% Central RAA (p0 pT = 8 GeV), IAA (pTtrig = 8-15 GeV, zT = 0.75) RAAorIAA ~ e0 [GeV/fm]

24. PQM IAA Calculations STAR PRL 97 (2006) 162301 PQM Calculation ^ <q> [GeV2/fm]

25. ~ ~ c2 (total) – c2 (min) PQM Au-Au 0-5% Central RAA (p0 pT = 8 GeV), IAA (pTtrig = 8-15 GeV, zT = 0.75) RAA or IAA ~ ^ <q> [GeV2/fm]

26. ~ ~ ~ ~ c2 (total) – c2 (min) c2 (total) – c2 (min) Imagine there is one true parameter in-between. The probability of the two measurements being offset from the expectations by 1.5 s (or more), is 1.7% Discriminating ? What do we learn ? RAAorIAA RAAorIAA e0 [GeV/fm] ^ <q> [GeV2/fm]

27. Serious Proposal (?): Collect set of calculations from all of these models for RAA, IAA, RAA(Df), and IgAA. Probably with data in hand most will be ruled out – or at least significant insights will be gained. Part of TECHQM? ^ +2.1 - 3.2 PQM <q> = 13.2 GeV2/fm +270 - 150 GLV dNg/dy = 1400 +0.2 - 0.5 ZOWW e0 = 1.9 GeV/fm +200 - 375 WHDG dNg/dy = 1400 ^ AdS/CFT qSYM = 4.5 GeV2/fm +0.016 - 0.012 AMY as = 0.280

28. Summary Experimental observations…. - Well understood method for inclusion of uncertainties - Large p-p and d-Au data sets will improve IAA - Publication of high precision RAA(Df) and IgAA are key - Experiments need to quantify Type A, B, C uncertainties Theoretical observations…. - Need to resolve fundamental disconnect about whether perturbative calculations describe parton energy-loss - All calculations need realistic geometry, fluctuations, and running coupling - theorists need to critically evaluate other theorists work

29. EXTRAS

31. STAR PRL 97 (2006) 162301

32. WHDG GLV

33. Straight Line Model (SLM) Data is consistent with completely flat RAA inside the one standard deviation contour. Better fit than any current theory calculation. All have somewhat steeper pT dependence than the data.