1 Jamie Nagle

University of Colorado

GLV

ASW

AMY

BDMPSPQ

MZO

WW

DGLV

AdS/CFT

Hard Probes 2008Illa da Toxa, Galacia-Spain

Medium Parameters Medium Parameters in Jet Quenchingin Jet Quenching

WHDG

2

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:0801.4020arXiv:0801.1665

Focus on published data in this talk

I view preliminary data with a healthy skepticism

Every RHIC published result on which a full quantitative analysis is to be performed needs to explicitly quote these

uncertainty contributions !

0

3

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.

Developed by Mike Tannenbaum and JLN

4

PQM (ASW w/ BDMPS Weights)

22

ˆ L

kq

T

q̂

Quenching Factor

Extra thanks to Constantin Loizides for providing the input curves

5

fm

2 GeV6.35.2

1.22.3 2.13ˆ q

Clear minimum in modified 2

1 std. dev.2 std. dev.

~

6

4~ˆˆ gqq pertfitted

RHIC

fm

GeV 0.9 3.1 n ˆ

2322

sscatters

22

TNL

kq c

mfp

DebyeT

MeV 300 T ,3N ,5.0 cs

PQM result implies very strong coupling (non-perturbative)

Even used to motivate AdS/CFT calculation

ˆ q SYM 3 / 2 3

4 5

4 T 3 26.68 SYM Nc T 3

Liu, Rajagopal, Wiedemann

MeV) 300(T 5.4ˆfm

GeV2 SYMq

RHIC data

sQGP

fm

2 GeV6.35.2

1.22.3 2.13ˆ q

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…”

4~ˆˆ gqq pertfitted

RHIC

8

q̂/75.0R AA

AA

AA

R

R2

ˆ

ˆ

q

q

If one measures RAA within ±10%, one determines q within ±20%, regardless of the q !

Surprised !?

^^

9

G-Y Qin et al., PRL 100, 072301 (2008)

“Once temperature evolution is fixed by the initial conditions and evolution [by 3+1 dimensional hydrodynamics], s is the only quantity which is not uniquely determined.”

AMY + Hydro

Note that within AMY, the coupling s is not just for the probe-medium, but also within the medium itself !

s

10

Clear minimum in modified 2

1 std. dev.2 std. dev.

Assuming AMY+Hydro is perfectly correct, then this is the constraint on s from the experimental

statistical and systematic uncertainties.

Coupling Constraint~

280.0 AMY 0.0330.024

016.0012.0s

MeV) 300(T 1ˆfm

GeV2 q

11

PQM <q> = 13.2 GeV2/fm +2.1- 3.2

^

GLV dNg/dy = 1400 +270- 150

WHDG dNg/dy = 1400 +200- 375

ZOWW 0 = 1.9 GeV/fm +0.2- 0.5

AMY s = 0.280 +0.016- 0.012

Constraints

Each constraint is assuming a perfect model with only one unknown parameter. Uncertainty is from experimental sources only !

RHIC data

sQGP?

RHIC data

QGP?

12

PQM <q> = 13.2 GeV2/fm +2.1- 3.2

^

GLV dNg/dy = 1400 +270- 150

WHDG dNg/dy = 1400 +200- 375

ZOWW 0 = 1.9 GeV/fm +0.2- 0.5

AMY s = 0.280 +0.016- 0.012

Constraints

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.

ZOWW has hard sphere geometry.

13

Strongly or Weakly Coupled ?

v2

pT (GeV/c)

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).

Perturbative parton cascade (MPC) and analytic results unable to describe bulk flow.

Does that contradict underlying AMY assumption with s = 0.28 ?

BAMPS with ggggg and s = 0.6 (but incorrect angular distribution)

Does this mean anything?

Jet quenching problem is critical to resolve, in particular, because of the

implications on the bulk medium itself.

Z. Xu, C. Greiner, H. Stöcker, arXiv: 0711.0961 [nucl-th]

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

GLV

ASW

WHDG

AMY

BDM

PS

PQM

ZOW

W

DGLV

AdS/CFT

Data

What is an experimentalist to do?

16PHENIX: Phys. Rev. C76, 034904 (2007)

0

0

When preliminary data with higher statistics and better systematics are published, this should be much more constraining.

PQM calculations indicate steeper dependence with larger q

Somewhat smaller dependence. Most quenching models underpredict high pT v2.

Reaction Plane Dependence

^

PQM Calculation

17

Nagle Toy Energy Loss Model (NTELM)

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.

h

h

BDMPS – many soft scatteringsGLV – fewer harder scatterings

Dijet Observables

Parton 2 Path (fm)

Larger dE/dx

18

IAA fit has “sharper 2 concavity” than RAA, thus more sensitive.

Does it matter that the plot has a mis-label?

2 /d.o.f.

ZOWW Calculation (Jets and Dijets)

Yes it does !

19

However, IAA has steeper dependence on 0 than RAA.If equal data uncertainties, IAA should be more constraining.

2 /d.o.f.

This only utilizes statistical uncertainties. Re-do with full 2.~

20

Private Communication Peter Jacobs Estimated Type C Uncertainty ~ 7%

ZOWW Calculation

STAR PRL 97 (2006) 162301

std.) (2 std.) (1 9.2 ???0.9

???6.00

Constraint using zT > 0.4

std.) (1 9.1 1.03.00 Why is this different from ZOWW paper?

21

In the ZOWW paper, they only use the DAuAu as the constraint !

d-Au

Au-Au

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 constraintDAA constraintDAA + scale uncertainty

23

~

0 [GeV/fm]

RA

A o

r I A

A 2 (total) –

2 (min)

~~

ZOWW Au-Au 0-5% CentralRAA (0 pT = 8 GeV), IAA (pTtrig = 8-15 GeV, zT = 0.75)

std.) (2 std.) (1 9.2 ???0.9

???6.00

std.) (2 std.) (1 1.9 0.70.6

2.05.00

24

PQM IAA Calculations

<q> [GeV2/fm]^

q̂

PQM Calculation

STAR PRL 97 (2006) 162301

25

~

<q> [GeV2/fm]^

RA

A o

r I A

A 2 (total) –

2 (min)

~~

PQM Au-Au 0-5% CentralRAA (0 pT = 8 GeV), IAA (pTtrig = 8-15 GeV, zT = 0.75)

std.) (2 std.) (1 2.13ˆ 6.35.2

1.22.3 q

std.) (2 std.) (1 9.5ˆ 3.21.7

3.19.0 q

26<q> [GeV2/fm]^

2 (total) –

2 (min)

~~

0 [GeV/fm]

RA

A o

r I A

A

2 (total) –

2 (min)

~~

RA

A o

r I A

A

Imagine there is one true parameter in-between.

The probability of the two measurements being offset from the expectations by 1.5 (or more), is 1.7%

Discriminating ? What do we learn ?

27

PQM <q> = 13.2 GeV2/fm +2.1- 3.2

^

GLV dNg/dy = 1400 +270- 150

WHDG dNg/dy = 1400 +200- 375

ZOWW 0 = 1.9 GeV/fm +0.2- 0.5

AMY s = 0.280 +0.016- 0.012

Serious Proposal (?):

Collect set of calculations from all of these models for RAA, IAA, RAA(), and IAA. Probably with data in hand most will be ruled out – or at least significant insights will be gained. Part of TECHQM?

AdS/CFT qSYM = 4.5 GeV2/fm ^

28

SummaryExperimental observations….

- Well understood method for inclusion of uncertainties

- Large p-p and d-Au data sets will improve IAA

- Publication of high precision RAA() and IAA 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

30

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.