Transcript Energy Loss: predictions and comparison

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
December 13-15, 2002
1
Ivan Vitev
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   L /  result
(including unitarity corrections )
High-pT azimuthal asymmetry (hydo + jet energy loss)
Suppression of hadron production (with Cronin + shadowing)
December 13-15, 2002
2
Ivan Vitev
Gluon Radiation and the LandauPomeranchuk-Migdal (LPM) Effect
•
In QCD:
a) Gyulassy-Wang: multiple interactions, arbitrary
medium, the transverse gluon dynamics is
neglected
M.Gyulassy and X.N.Wang,
Nucl. Phys. B 420 (1994).
b) Baier et al. (BDMPS): thick medium, large number
of scatterings, exclusively the LPM regime
- DE =
p
2
q L log
C AE
C R m2l
C R a s m2L2
L
- DE =
log
4
l
l
So long as:
R.Baier et al.,
Nucl.Phys. B 483, (1997).
E  50  100 GeV, L / 
(Also see: Zakharov; Wiedemann)
•
CRas
1
Linear otherwise
Motivation:
All approaches require:   1,  0.4  0.5 GeV
For a nucleus RA  1.2 A1/ 3 fm can be applicable
only if you have a few (3-5) scatterings. Does
leave the room for an improved calculation.
WA98, central versus peripheral
p0
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).
December 13-15, 2002
3
Ivan Vitev
Gluon Radiation, Scaling with ns
Consider only the direct diagrams:
q  0 in the | A |2

ns


ns




ns

M. Gyulassy, P. Levai, I.V.,
Nucl. Phys. B 571 (2000)
2
CR s 1 
ns
(1)  k  BH
 3  2 2 1  (1  CR / C A )  1 f  2 ,
d k
 k 
 
dN g( ns )
 1, 3 diagrams,
L

elastic scat. fact.
2
1L
 2, 7 diagrams,   elastic scat. fact.
2 
...
n
 n, 2
(n+1)
1 L
-1 diagrams,
  elastic scat. fact.
n!   



• Exponential sensitivity to ns – need for
unitarity conserving factors (here imposed
a posteriori with Z g )
• Insensitivity of the radiative spectrum to
the higher order correlations (orders in
opacity)
December 13-15, 2002
4
Log (k 2 /  2 )
Ivan Vitev
Quenching in a Toy Model Using JETSET
(Quark-Antiquark String Fragmentation)
B. Andersson et al., Phys. Rep. 97 (1983)
RAA ( pT )
dN / dpT all
What is now usually labeled
I.V.(S. Bass et al.),
Nucl.Phys. A 661, (1999).
RA
A
Focus on the typical
moderate pT
RAA=0.2-0.5
pT [GeV]
pT [GeV]
• 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 .
December 13-15, 2002
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Ivan Vitev
Virtual Corrections to the
Medium Induced Radiation
M. Gyulassy, P. Levai, I.V., Phys.Rev.Lett. 85 (2000),
M. Gyulassy, P. Levai, I.V., Nucl.Phys. B 594 (2001).
E
(1)
Power suppressed
2CR s


C 
 R s
2
qn , an
+
qn , an qn , an
December 13-15, 2002
xc
 1 dx  2
 x c  

(z)
(z

z
)

E
dx
log

0
0
 x 
  
xc x 4



dz 2
2E

(z)
(z

z
)
Log

O(1)


0
 g (z)
2 (z )(z  z 0 )


z0
2E
 ...
2
 L
dN g
2E
For Bjorken expansion: E 
L ln 2  ...
dy
 L
zn
zn
dz
z g (z)
0
Even for small E and thin media: E  L2 ln
GLV Reaction Operator approach:
zn

qn , an
6
ˆn V
ˆ n†
ˆ n†D
ˆ n V
Rˆ n  D
+
qn , an
zn
qn , an
Ivan Vitev
Induced Bremsstrahlung to All Orders in Opacity
E / 
Convergence:

n1,2,3
dI / dx [GeV ]
December 13-15, 2002
7
L / g
x
/E
Ivan Vitev
High-pT Azimuthal Asymmetry v2(pT)
Any jet correlations have been discarded:
perfect coupling to the reaction geometry
R(b,  ) 
E (b,  )
,
E (0,  )
E (b,  )   d 2 r

TATB
dz  ( z, r  ˆ z ) z
TAB 
M. Gyulassy, I.V. and X.N. Wang,
Phys.Rev.Lett. 86 (2001)
• In the limit of large energy loss the sharp
cylinder geometry applies.
See also: E. Shuryak, Phys.Rev. C 66 (2002).
Predicted: saturation, plateau and subsequent decrease.
December 13-15, 2002
8
Ivan Vitev
Comparison to Data
(and its Time Evolution)
• There is a quantitative difference
Calculations/fits with flat  v2  const  .
or continuously growing  v2  ln pT /   .
Check against high-pT data (200 AGeV)
b=7 fm
b~7 fm
Same for 0-50%
C. Adler et al. [STAR Collab.],
arXiv: nucl-ex/0206006
• The decrease with pT is now
supported by data
• For minimum bias this rate is
slightly slower
K. Filimonov [STAR Collab.],
arXiv: nucl-ex/0210027
December 13-15, 2002
See: N.Borghini, P.Dinh, J-Y.Ollitrault,
Phys.Rev. C 64 (2001)
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Ivan Vitev
Initial Parton Broadening via the GLV Elastic
Reaction Operator
zn zn
+
zn
qn , an qn , an
qn , an
¥
dN (b) =
å
n
dN (b) = e
qn , an
Elastic scattering case:
zn
+
qn , an
M.Gyulassy, P.Levai, I.V., Phys.Rev. D66, (2002)
qn , an
B. Kopeliovich et al., Phys.Rev.Lett. 88, (2002)
æ d s% (b )
ö÷
T (b0 )ççç4 p 2 el2
- s el tot ÷
÷
çè
dq
÷
ø÷
dN 0 (b)
n= 0
¥
n
cn
1 d s el
2
dN ( p) = å e
d
q
dN 0 ( p - q1 - ... - qn )
Õ
2
ò
i
n ! i= 1
s el d qi
n= 0
-c
Trivial application: d 2 N i ( p)   2 ( p), scale
dN (b) µ e c (bmK 1 (bm)- 1) » e
2
b2 m2
2
- c
ln
2
1.08bm
See e.g.: H. Bethe, Phys. Rev. 89 (1953)
RBA
0.5
Both enhancement and suppression are an integral
part of the Cronin effect. Understood in terms of
momentum and probability conservation and redistribution.
December 13-15, 2002
10
Y. Zhang et al., Phys.Rev. C65, (2002)
Ivan Vitev
SPS
d+Au:
250%
Predicted (Y=0)
Shadowing+Cronin
in d+Au and Au+Au
at 17, 200, 5500 AGeV
Au+Au:
400%
d+Au:
30%
RHIC
Au+Au:
60%
d+Au:
4%
LHC
December 13-15, 2002
Au+Au:
10%
1. At SPS the Cronin effect is large:
does leave room for small suppression
due to the non-Abelian energy loss.
2. At RHIC the Cronin effect is
comparable (~50% larger) to estimates
by X.N.Wang and B.Kopeliovich. In A+A
the effect has not been presented.
3. At LHC shadowing/antishadowing
dominate. Cronin effect is reduced due
to the much harder spectra.
11
Ivan Vitev
The Center of Mass Energy Systematics
of Mono-jet Tomography
1. At SPS s NN  17GeV Cronin
effect dominates. Even with energy
0
loss  exhibit noticeable
enhancement
2. Cronin effect, shadowing, and
jet quenching conspire to give flat
suppression pattern out to the
highest pT at RHIC s NN  200GeV
RAA ( pT )  0.2  0.3  N part / Nbin.
Feedback!
3. At LHC s NN  5500GeVthe
nuclear modification is completely
dominated by energy loss. Predicts
below N part .quenching, strong pT
dependence
I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002)
December 13-15, 2002
12
Ivan Vitev
Quenched Hadron Spectra:
Comparison to Data
The data at RHIC s NN  200 GeV
is still preliminary
1. There is qualitative agreement
between 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 R AA
will be confirmed at the LHC.
I.V. and M.Gyulassy, Phys.Rev.Lett. 89 (2002)
December 13-15, 2002
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Ivan Vitev
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.
Tomography results
Cold A
g  ?( 1 fm3 )
December 13-15, 2002
SPS
g
5 10 fm3
RHIC
g
30  55 fm3
14
LHC
g 130  275 fm3
Ivan Vitev
Why Tomography?
Positron emission tomography
 Conventional X-ray position tomography
X-ray
creates an image based on the attenuation
of the flux from a calibrated source:
e+e-
 Information about the shape of
the object

Calibrated
source
Image
Jet tomography
 Information about the density of
the object
Azimuthal tomography
g
L
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).
December 13-15, 2002
g
g
Lbig
g
g
Lsmall
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).
15
Ivan Vitev
Nuclear Effects on Hadron Production
(The Point of View of Relativistic Heavy Ions)
Nuclear shadowing, antishadowing, EMC effect

xP
P
…
Shadowing:
RHIC
X
Partonic model A.Mueller and J.Qiu
Generalized vector dominance model
Antishadowing:
Practical approach: EKS’98 parameterization
fa / A ( x, Q2 )  Sa / A ( x, Q2 ) fa / p ( x, Q2 )
K.Eskola,V.Kolhinen,and C.Salgado,
Eur.Phys.J. C9 (1999)
Constructive interference J.Qiu, S.Brodsky
Partonic model J.Qiu
EMC effect:
Nuclear swelling E.Predazzi, L.Frankfurt, M.Strikman Fermi motion:
Quark cluster models H.Pirner and J.Vary
Gain from the motion inside the nucleus
December 13-15, 2002
16
Ivan Vitev
The Cronin Effect
Faster than linear scaling of the p+A cross section
with the number of binary collisions
b
d p  A
d p  p  N coll  ,  = (p T )

Models of the Cronin effect
are based on multiple initial
state scattering – helps to
gain pT at moderate pT (and
compensates at small pT)
p
A
Glauber model
• Hadronic scattering • Gaussian approximation
• Partonic scattering • Deviations in the case of
few collisions
M.Gyulassy, P.Levai, and I.V., Phys.Rev. D66, (2002)
December 13-15, 2002
17
Ivan Vitev
Predicted Cronin Effect+Shadowing
at Forward and Backward Rapidities
I.V. and M.Gyulassy
• Note the scales: if Cronin effect
is detectable (20%-30%) at Y=0
then it should be detectable at Y=3
• For pT<2 GeV: suppression
comparable to standard Cronin
measurements. For pT>2 GeV –
a much broader enhancement
December 13-15, 2002
Qs
with Qs2=6.6 GeV2
Compared
A.Dumitru and J.Jalilian-Marian,
Phys.Rev.Lett. 89, (2002)
• Strong suppression below Qs
and RAB=1 above
18
Ivan Vitev
Suppression vs. Enhancement of High-pT Hadrons
,K,p…
Cronin
Effect
central
PHENIX
Binary scaling
Jet Quenching
peripheral
WA98, central versus peripheral
p0
STAR, nucl-exp/0206011, PRL
ATLAS
simulation
at LHC
December 13-15, 2002
19
Ivan Vitev