Jamie Nagle University of Qolorado, Boulder Winter Workshop on Nuclear Dynamics 2008 South Padre Island, Texas

Acknowledging fruitful collaboration with Mike Tannenbaum. Useful theory input and discussions with W. Horowitz, P. Jacobs, C. Loizides, G-Y Qin, I. Vitev, X.N. Wang. QuasiParticles versus the Perfect Fluid. Quarkonia. Quixotical Queries into Quicksand Quandaries ? Quantitative Constraints on the Quark Gluon Plasma. Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma. L.A. Linden Levy, J.L. Nagle, C. Rosen, P. Steinberg. e-Print: arXiv: [nucl-th] L.A. Linden LevyJ.L. NagleC. RosenP. Steinberg

Uncertainties: Type A = point-to-point uncorrelated (e.g. statistical) [shown as error lines] Type B = point-to-point correlated [shown as gray bars] Type C = globally correlated (i.e. all points move by multiplicative factor) [text] arXiv: arXiv:

Example Case: Type A: Dominated by Statistical Uncertainties Type B: Dominated by energy scale uncertainties and some contribution from photon shower merging for p T ~ GeV/c Type C: +/- 12% is roughly equal contributions from nuclear thickness uncertainty (T AA ) and proton-proton cross section absolute normalization. Every RHIC published result on which a full quantitative analysis is to be performed needs to explicitly quote these uncertainty contributions !

Methodology for inclusion of statistical and systematic uncertainties…. Calculate the modified  2 as a function of the theory parameters set (p) for the optimal  b (systematic Type B offset) and  c (systematic Type C offset). If the type A uncertainties scale the same as the data under systematic offsets, then one needs to rescale  i.

First example comparison… Wicks-Horowitz-Djordjevic-Gyulassy (WHDG) model Generalized GLV formalism + collisional energy loss. Realistic transverse geometry + Bjorken time expansion. No modified PDF’s or initial state multiple scattering.

Clear minimum in modified  2. dN g /dy = std. dev. 2 std. dev. What does this p-value mean? What does the whole result mean?

p-value Assume a particular hypothesis is true. If you did an infinite number of experiments, given a set of statistical and systematic uncertainties, what fraction of these experiments would have a worse modified  2 than the real experiment. Note that a p-value = 60% does not mean there is a 60% probability the hypothesis is correct.

Quiz on p-values…. Consider this example experiment with a very good  2 /dof = 10.5/19. A hypothesis with a level=0.56 has a p-value of 74%. Thus, 74% of the time (doing multiple experiments) just from statistical fluctuations we would get a worse  2. However, from a relative  2 analysis with a best value at 0.51, the level=0.56 is excluded at more than 3 standard deviations. How to resolve?

dN g /dy = std. dev. 2 std. dev. If we assume that all of the physics in WHDG is correct and there is only unknown parameter (dN g /dy), then this is the constraint on that parameter from the experimental statistical and systematic uncertainties. If the above assumption is incorrect, then this is not the constraint (i.e. theoretical uncertainties are not included) !

PQM GLV WHDG ZOWW

LionsTigersBears

G-Y Qin et al., PRL 100, (2008) “Once temperature evolution is fixed by the initial conditions and evolution [by 3+1 dimensional hydrodynamics], the  s is the only quantity which is not uniquely determined.” AMY + Hydro, oh my! AMY  s =

Straight Line Model (SLM) Data is consistent with completely flat R AA inside the one standard deviation contour.

PQM = 13.2 GeV 2 /fm ^ GLV dN g /dy = WHDG dN g /dy = ZOWW  0 = 1.9 GeV/fm AMY  s = Constraints Each constraint is assuming a perfect model with only one unknown parameter. Uncertainty is from experimental sources only ! Pion gas Cold nuclear matter RHIC data sQGP QGP Baier’s plot

“The fragility of high p T 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…” Implied qhat is effectively an order of magnitude stronger interactions than implied by other model extracted parameters. MUST be resolved ….

Thus, for a given fractional uncertainty on R AA, one always gets the same fractional uncertainty on qhat ! Surprised !?

WHDG GLV

What does “fragility” really mean? [if not in the statistical sense] Imagine a beam of partons aimed here… One could say that one has no sensitivity to the core density. Unless one has a model to relate the skin to the core density. This claim is somewhat odd since the “fragility” paper uses a uniform cylinder geometry ! Glauber Cylinder

Nagle Toy Energy Loss Model (NTELM) Glauber geometry for paths (L1 and L2) of partner partons. Constant dE/dx (varied in steps of +0.2 GeV/fm), L2 distribution biased by high p T trigger particle #1. Thus, perhaps I AA (away side per trigger) will be more sensitive that R AA.

STAR PRL 97 (2006)

I AA has a steeper dependence on  0 than R AA. Thus, if one had identical experimental uncertainties, then I AA should be more constraining.

I AA fit has “sharper  2 concavity” than R AA, thus more sensitive. Does it matter that the plot has a mis-label? Yes it does !  2 /d.o.f.

Private Communication Peter Jacobs Estimated Type C Uncertainty ~ 7%  0 = 2.9 +???  0 = ??? [I AA ] [R AA ] ZOWW Calculation STAR PRL 97 (2006)

In the ZOWW paper, they only use the D AuAu as the constraint ! d-Au Au-Au

What are the constraints? Note the extremely low p-value. However, if you only use D AuAu shouldn’t we include the NLO pQCD scale uncertainty? If this theory uncertainty is included then magenta constraint. Does the scale uncertainty cancel in I AuAu (or R AuAu )? I AA constraint D AA constraint D AA + scale uncertainty

Hydrodynamic Calculation Quantitative Comparison Statistical  2 ~ infinity Can we apply detailed quantitative analyses elsewhere? Can one eventually use viscous hydrodynamics to match the data and constrain the viscosities and relaxation times?

Q Summary Experimental observations…. - Well understood method for inclusion of uncertainties - Large p-p and d-Au data sets will improve I AA - Experiments need to quantify Type A, B, C uncertainties - Limits are getting close to Glauber limits (future improvements?) Theoretical observations…. - Need to resolve fundamental disconnect about whether perturbative calculations describe parton energy-loss - All calculations need realistic geometry, fluctuations, and running coupling

Some feel (strongly) that these comparisons are premature. If you feel this way, just consider storing the knowledge of this constraint method away until you believe it is useful !

Viscosity Quiz As one increases the strength of interactions (  ↑), the shear viscosity (  ) does what?  ↑,  increases ↑  ↑,  decreases ↓

Case I Thermal velocity << Flow velocity. No interactions (  =0) Larger interactions (  ↑) top region bottom region * In this case,  ↑   ↑

Case II Thermal velocity ~ Flow velocity No interactions (  =0) Larger interactions (  ↑) top region bottom region * In this case,  ↑   ↓

For a (nearly) ideal gas…. Kinetic Theory of Gases: Not only does viscosity decrease with stronger interactions, but Viscosity increases with larger temperature. Opposite to honey example…

Region of Brain containing higher intellect. Stimulate that part of your brain for this talk on quantitative statistics!