Jet Quenching in Thin Plasmas - the Prediction Before the Experiment

December 13-15, 2002 Ivan Vitev 1

Jet Quenching in Thin Plasmas -

the Prediction Before the Experiment

Ivan Vitev Iowa State University, Ames, IA 50011

First Two Years at RHIC: Theory vs. Experiments

December 13-14, 2002, INT-Seattle, WA


Outline of the Talk

The motivation: multipart on interaction PQCD program:

Focus on heavy ion reactions (L~5 fm, dynamical, evolution) The WA98 puzzle (RAA = 2-3, enhancement not suppression) Gluon radiation and hadron suppression, QM’99: Necessity for large probability corrections to dNg : (dominance of the lowest order in-medium correlations) Jet quenching with RAA= 0.2-0.5 (toy model using JETSET)

Predictions of the GLV approach vs experiment: Dominant lowest order in the opacity result (including unitarity corrections ) High-pT azimuthal asymmetry (hydo + jet energy loss) Suppression of hadron production (with Cronin + shadowing)

/L


Gluon Radiation and the Landau-Pomeranchuk-Migdal (LPM) Effect

• In QCD: a) Gyulassy-Wang: multiple interactions, arbitrary medium, the transverse gluon dynamics is neglected

b) Baier et al. (BDMPS): thick medium, large number of scatterings, exclusively the LPM regime

22

log4

sREC LLa m

l l- =D

22logsR A

R

Eq L

CE

CC a

p ml=- D

M.Gyulassy and X.N.Wang,Nucl. Phys. B 420 (1994).

R.Baier et al., Nucl.Phys. B 483, (1997).

(Also see: Zakharov; Wiedemann)

So long as: 50 100 GeV, / 1E L

Linear otherwise

WA98, central versus peripheral 0p

All approaches require:

• Motivation:1, 0.4 0.5 GeV

For a nucleus can be applicable only if you have a few (3-5) scatterings. Doesleave the room for an improved calculation.

1/31.2 fmAR A

The “apparent” lack of energy loss at the SPS.X.-N. Wang, Phys.Rev.Lett. 81, (1998).M.M. Aggarwal et al., Phys.Rev.Lett. 81, (1998).


Gluon Radiation, Scaling with ns

2 2( / )Log k

Consider only the direct diagrams:20 in the | |q A

2

n(n+1)

, 3 diagrams, elastic scat. fact.

, 7 diagrams, elastic scat. fact.

...

, 2 -1 diagrams,

L

1 L

2

1 L elastic scat. fact.n!

1

2

s

s

s

n

n

n n

M. Gyulassy, P. Levai, I.V.,Nucl. Phys. B 571 (2000)

(2

2 2

( )

3 21)1

1 (1 ) 1/ ,s

s

nn

gA

R s BHR

CdNC

k

kfC

d k

• Exponential sensitivity to ns – need for unitarity conserving factors (here imposeda posteriori with )

• Insensitivity of the radiative spectrum to the higher order correlations (orders in opacity)

gZ


Quenching in a Toy Model Using JETSET

(Quark-Antiquark String Fragmentation)

RAA

What is now usually labeled

Focus on the typical moderate pT

• Indications of 2-5 fold suppression (toy model results).

• The actual hadronic spectra are a superposition of the distributions like the above, leading to a flatter RAA .

RAA=0.2-0.5

B. Andersson et al., Phys. Rep. 97 (1983)

I.V.(S. Bass et al.),Nucl.Phys. A 661, (1999).

/ allTdN dp

( )AA TR p

[GeV]Tp [GeV]Tp


Virtual Corrections to theMedium Induced Radiation

c

0 c

0

x1(1) R s

z x 0

c0

0R

g

s

2

z

g

22

0

x(z)

(z)

(z)(z) (z

(z z )x

2E

2C dz dxE E dx log

x 4

C dzLog O(1)

2(z z )

( z )) z

M. Gyulassy, P. Levai, I.V., Phys.Rev.Lett. 85 (2000),

M. Gyulassy, P. Levai, I.V., Nucl.Phys. B 594 (2001).

nz

,n nq a

,n nq a

nz

,n nq a

,n nq a +

nz

+

nz

,n nq a

,n nq a

† †n n n n nR̂ ˆ ˆD D ˆ ˆV V GLV Reaction Operator approach:

Even for small E and thin media: For Bjorken expansion:

Pow

er su

ppre

ssed

22 2

ln ...E

E LL

2

2ln ...

g EE

dN

dy LL


Induced Bremsstrahlung to All Orders in Opacity

1,2,3n

Convergence:

/x E

/ [ ]dI dx GeV

/E

/ gL


High-pT Azimuthal Asymmetry v2(pT)

M. Gyulassy, I.V. and X.N. Wang, Phys.Rev.Lett. 86 (2001)

Predicted: saturation, plateau and subsequent decrease.

Any jet correlations have been discarded: perfect coupling to the reaction geometry

• In the limit of large energy loss the sharp cylinder geometry applies.See also: E. Shuryak, Phys.Rev. C 66 (2002).

( ,(

)

(0, ),, )

E bb

ER

2 ˆ( ,, )( ) A B

AB

T Td r d r zzE z z

Tb


Comparison to Data (and its Time Evolution)

C. Adler et al. [STAR Collab.], arXiv: nucl-ex/0206006

K. Filimonov [STAR Collab.],arXiv: nucl-ex/0210027

b=7 fmb~7 fm

• There is a quantitative difference Calculations/fits with flat or continuously growing

2 .v const 2 / .ln Tv p

Check against high-pT data (200 AGeV)

Same for 0-50%

• The decrease with pT is now supported by data• For minimum bias this rate is slightly slower

See: N.Borghini, P.Dinh, J-Y.Ollitrault, Phys.Rev. C 64 (2001)


Initial Parton Broadening via the GLV Elastic Reaction Operator

Elastic scattering case:nz

,n nq a

nznznz

,n nq a ++

,n nq a

,n nq a

,n nq a

,n nq a M.Gyulassy, P.Levai, I.V., Phys.Rev. D66,

(2002)

02

2(( )

-0

0

02 1

0

)

-

4

2

1

( ) ( ) ( )

( )1

- - ...!

( )-

el totel

d bT

n d q

n

eln

n ie

b

ii

n

l

n

dN dN dN

dN e dNn

b e bb

dp q q

dd q p

q

ps

s

c s

sc

æ ö÷ç ÷ç ÷ç ÷÷çç ÷è ø

=

¥

=

¥

=

= =

=

å

å Õò

%

B. Kopeliovich et al., Phys.Rev.Lett. 88, (2002)

Y. Zhang et al., Phys.Rev. C65, (2002)

Both enhancement and suppression are an integralpart of the Cronin effect. Understood in terms of momentum and probability conservation and redistribution.

0.5BAR

Trivial application: 2 2( ) ( ),id N p p scale 2

( )1

2 2 2ln( ) 1 2 1.08( )

bb bKbebdN e

mm m m

cc --µ »

See e.g.: H. Bethe, Phys. Rev. 89 (1953)


Predicted (Y=0) Shadowing+Cronin in d+Au and Au+Au

at 17, 200, 5500 AGeV

SPS

RHIC

LHC

d+Au:250%

Au+Au:400%

d+Au:30%

Au+Au:60%

d+Au:4%

Au+Au:10%

1. At SPS the Cronin effect is large:does leave room for small suppressiondue to the non-Abelian energy loss.

2. At RHIC the Cronin effect is comparable (~50% larger) to estimatesby X.N.Wang and B.Kopeliovich. In A+Athe effect has not been presented.

3. At LHC shadowing/antishadowing dominate. Cronin effect is reduced dueto the much harder spectra.


The Center of Mass Energy Systematics of Mono-jet Tomography

I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002)

17NNs GeV

0

200NNs GeV

5500NNs GeV

1. At SPS Cronin

effect dominates. Even with energy

loss exhibit noticeable

enhancement

2. Cronin effect, shadowing, and

jet quenching conspire to give flat

suppression pattern out to the

highest pT at RHIC

3. At LHC the

nuclear modification is completely

dominated by energy loss. Predicts

below quenching, strong

dependence

.0.2 0.3( ) /part bA inTA Np NR

.partN Tp

Feedback!


Quenched Hadron Spectra: Comparison to Data

I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002)

The data at RHIC is still preliminary

200 GeVNNs

1. There is qualitative agreementbetween data and theory.

2. There are some quantitative deviations but data has to be finalized before their evaluation.

3. The most interesting question is whether the systematics of will be confirmed at the LHC.

AAR


Conclusions

Perturbatively computable multi-parton processes in QCD matter (both cold nuclear matter and the quark-gluon plasma) present an exciting new frontier for theoretical studies.

At RHIC the observed large azimuthal anisotropy and the large suppression of the hadronic spectra signal of a strong radiative energy loss. The predicted pT-systematics is now supported by data.

We have shown how d+A data can help disentangle initial and final state nuclear effects. Cold A SPS RHIC LHC

3( 1? )g fm 35 10g fm 330 55g fm 3130 275g fm

Tomography results


Why Tomography?

X-ray

Calibrated source Image

Conventional X-ray position tomography creates an image based on the attenuation of the flux from a calibrated source:

Information about the shape of the object

Information about the density of the object

g

gL

I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002);M.Gyulassy, P.Levai,and I.V.,Nucl.Phys. B 583 (2002);Phys.Rev.Lett. 85 (2000).

M.Gyulassy, I.V.,and X.N.Wang,Phys.Rev.Lett. 86 (2001);M.Gyulassy, I.V.,X.N.Wang, and P.Huovinen,Phys.Lett. B526 (2002).

Azimuthal tomographyJet tomography

gg

Lbig

g

Lsmall

e+e-

Positron emission tomography


Nuclear Effects on Hadron Production(The Point of View of Relativistic Heavy

Ions) Nuclear shadowing, antishadowing, EMC effect

PxP

X

…

Shadowing:Partonic model A.Mueller and J.Qiu

Generalized vector dominance model

Practical approach: EKS’98 parameterizationK.Eskola,V.Kolhinen,and C.Salgado,Eur.Phys.J. C9 (1999) /

2/

2 2/( , ) ( , ) ( , )a paA Aaf x Q x Q f x QS

EMC effect:Nuclear swelling E.Predazzi, L.Frankfurt, M.StrikmanQuark cluster models H.Pirner and J.Vary

Fermi motion:

Antishadowing: Constructive interference J.Qiu, S.BrodskyPartonic model J.Qiu

Gain from the motion inside the nucleus

RHIC


The Cronin Effect

Faster than linear scaling of the p+A cross section with the number of binary collisions

p A

Glauber model

T, = (p )collp A p pd d N

b

Models of the Cronin effect are based on multiple initial state scattering – helps to gain pT at moderate pT (andcompensates at small pT)

• Hadronic scattering

• Partonic scattering

• Gaussian approximation

• Deviations in the case of few collisions

M.Gyulassy, P.Levai, and I.V., Phys.Rev. D66, (2002)


Predicted Cronin Effect+Shadowing at Forward and Backward

Rapidities

• Note the scales: if Cronin effect is detectable (20%-30%) at Y=0then it should be detectable at Y=3

• For pT<2 GeV: suppressioncomparable to standard Croninmeasurements. For pT>2 GeV –a much broader enhancement

A.Dumitru and J.Jalilian-Marian,Phys.Rev.Lett. 89, (2002)

with Qs2=6.6 GeV2

Qs

• Strong suppression below Qs

and RAB=1 above

Compared

I.V. and M.Gyulassy


Suppression vs. Enhancement of High-pT Hadrons

ATLASsimulation

at LHC

WA98, central versus peripheral 0p

STAR, nucl-exp/0206011, PRL

central

peripheral

,K,p…

Binary scalingPreliminary

Jet Quenching

CroninEffect

PHENIX

Jet Quenching in Thin Plasmas - the Prediction Before the Experiment

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