do we understand interactions of hard probes with dense matter ?
DESCRIPTION
Do We Understand Interactions of Hard Probes With Dense Matter ?. Joint EIC & Hot QCD Workshop on Future Prospects of QCD at High Energy BNL - 20 July 2006. Berndt Mueller (YITP Kyoto & Duke University). It’s all about “Matter”. What’s the Matter? Probing the Matter - PowerPoint PPT PresentationTRANSCRIPT
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Do We UnderstandInteractions of Hard Probes With Dense Matter ?
Joint EIC & Hot QCD Workshop on
Future Prospects of QCD at High EnergyBNL - 20 July 2006
Berndt Mueller (YITP Kyoto & Duke University)
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It’s all about “Matter”
What’s the Matter? Probing the Matter Understanding the Matter
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General comments
A young field: ~10 years of serious theory, 5 years of data! We are still in the conceptual phase.
A rich field – for theorists and experimentalists alike: Full of well defined questions and challenges.
An exciting field – new, unanticipated phenomena are discovered at a rapid pace in theory and experiment.
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Part I
What’s the Matter?
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QCD phase diagram
Saturation
Baryon density
Hadronicmatter
Critical end
point ?
Nuclei
Chiral symmetryrestored
Color SC
Neutron stars
Entropy
density Coexistence region
QGPRHIC
Color charge density
EIC
Chiral symmetrybroken
CEBAF
CGC
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Past and future of QCD
The first 30 years of QCD were concerned (at the perturbative scale Q2) with single parton distributions: PDF’s, FF’s, GPD’s.
The future - exploration of multi-parton (N 2) correlations. These are generally:
Higher-twist effects (suppressed by powers of Q2).
Substantial effects in perturbative Q2 range require high parton densities:
A 1, x 0, dN/dy large.
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Parton correlations
med( )
Initial-final state correlations
E.g., low opacity jet quenching
qq x FF ( )
Initial state correlations
E.g., double scatteri
')
n
(
g
qq x FF x
med med
Final state correlations
E.g., heavy quark recombination
qq qq
J/
x1
x1’
x2
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Part II
Probing the matter
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Theoretical tools: Factorization
1 2 1 22 2
ˆ ( )( ) ( )
ˆ
h cX hNN ab c h
a babcXT T h
d d D zdx dx f x f x
dy dp dy dp z
QCD factorization:
pp0
centralN
coll = 975 94
AuAu0
Medium modifies the fragmentation
function D(z)
“Higher twist”
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High-energy parton loses energy by
rescattering in dense, hot medium.q
q
“Jet quenching” = parton energy loss
Described in QCD as medium effect on parton fragmentation:
Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z:
2 (med) 2 2
1 /( , ) ( , ) ,p h p h p h
E E
zD z Q D z Q D Q
Important for controlled theoretical treatment in pQCD:
Medium effect on fragmentation process must be in perturbative q2 domain.
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Mechanisms
High energy limit: energy loss by gluon radiation. Two limits:
(a) Thin medium: virtuality q2 controlled by initial hard scattering (LQS, GLV)
(b) Thick medium: virtuality q2 controlled by rescattering in medium (BDMPS)
Trigger on leading hadron (e.g. in RAA) favors case (a).
Low to medium jet energies: Collisional energy loss is competitive!
Especially when the parent parton is a heavy quark (c or b).
q
q
L
q q
g
L
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Radiative energy loss:
2/ TdE dx L k
Radiative energy loss
Scattering centers = color chargesq q
g
L
2 22
2T
2
ˆf
dq kq dq
dq
Density of scattering centers
Range of color forceScattering power of the QCD medium:
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Higher twist formalism
2
2
22 2
122
2
med,A2 1
A
2
2
with 2 (1 )( , ) ( , )
'( / ', )
2 '
(0) ( ) ( ) ( )( , , )
( ) (0) (
Medium eff
( , , ,
ect
)
( , )
, ,)
s
Lq h q h
q qg L
q qg
Q
sq h
z
qg TL
L
q
q x p q z zD z Q D z Q
dq dzD z z q qg gqz x
q z
F y F y yT x x
x q
z x xx
f x y
d
q
y
11 1
0
Integrated gluon density in
( ) ( ) 1
the medium
1L L
Lix p y ix p ydy F y F y y e e
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Eikonal formalism
quark
x
x
- 0
( ) ( ; ) ( )
( ; ) exp ( , )L
q x W x L q x
W x L i dx A x x
P
Gluon radiation: + x = 0
x
Kovner Wiedemann
Radiation probablility ~ correlation function C along forward light cone
Gluonic energy density correlation length
†
2
2 †
0 0
2 2
Tr[ ( ; ) ( ; )]( , )
1
11 ( ) ( ) ( , ) ( ) ( , )
2
1ˆ
11 ( ) exp ( )
2 4
c
xLi
i
i
i F
W x L W y LC x y
N
x y dx dx F x W x x F x W x x
x y L xF F qy L
Nonperturbative definition of q-hat
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q-hat in AdS/CFT
214
cl
ˆ( ) exp ( )
e (xp )
AT TW C qL x y
S C
horizon
(3+1)-D
world0
1r
T
x
C
L
cl Area of extremal worldsheet bounded ( ) by CS C
3 34 2 3
SYM 54
3/ 4ˆ2
,cq g N T s
Liu, Rajagopal, Wiedemann, hep-ph/0605178
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Dynamic medium
(1) 12 s
2
2
2
4 2
(1) 12 s4 2
2ln
2l
Static medium:
1+1 dim boost inv. expansion:
n 9
f
gs
EE C
L
dN
L
LE
Ed
CLA y
Thin medium: opacity expansion (GLV) works well for leading hadron
22 9ˆ gs
f
dNq
A dy
assumes perturbative scattering and simplified evolution of the medium
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Modeling sensitivity
Surface emission of leading hadrons
2/3
2/3~ exp
~
AA part
gpart
dNE LN
E A dy
R N
I. Vitev, hep-ph/0603010
Renk & Ruppert
Details of modeling of the medium and probability distribution P(E) of energy loss are very important.
Average interaction length L is not appropriate. Value of q-hat is very sensitive to modeling details.
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Energy loss at RHIC
2ˆ 5 10 GeV /fmq Data suggest large energy loss parameter:
RHIC
Eskola et al.
pT = 4.5–10 GeV
Dainese, Loizides, Paic
Present calculations use simplified geometry and evolution models.
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q-hat at RHIC
Pion gas
QGP
Cold nuclear matter
sQGP? ??
RHIC dataCaveat:
Details of medium evolution are important for quantitative extraction of q-hat from data!
A. Majumder – HT formalism with realistic evolution 2ˆ 2 3 GeV /fmq
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The QGP is a “windy” place
Longitudinally and transversely flowing medium distorts jet cone
Along axis Off axis
T. Renk, J. Ruppert, PRC 72 (2005) 044901
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Flat or rising RAA ?
Vitev et al (GLV)
LHC
Armesto et al (ASW)
Extrapolations to LHC energy vary widely due to modeling differences:
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Charm energy loss
q_hat = 14 GeV2/fm
q_hat = 4 GeV2/fm
q_hat = 0 GeV2/fm
dNg/dy = 1000
Very surprising, b/c radiative energy loss of heavy quarks should be suppressed
Reconsider collisional energy loss mechanism (Mustafa & Thoma)
From “non-photonic” electrons:
S. Wicks et al nucl-th/0512076
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Reaction plane correlations
Quenching effect in non-central collisions depends on direction of jet relative to the collision plane:
Allows for limited (!) test of L dependence!
LE
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Back-to-back leading hadrons are quadratically suppressed!
Di-jet correlations
8 < pT(trig) < 15 GeV/c
Away-side jet
T. Renk
J. Ruppert
trigger
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Photon tagged jets
“Golden” channel: q + g q + . Photon tags pT (and flavor - u/d quark!) of scattered parton.
Can be used to perform jet tomography (RAA does not work)
Important baseline and calibration for (opposite side) di-hadron tomography.
T. Renk, hep-ph/0607166
RAA does not discriminate ? -jet discriminates models
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Medium-pT photons
Turbide, Rapp, Gale PRC 69 014903 (2004)0 = 0.33 fm/c, T = 370 MeV
Hard Probes 2006, June 15, 2006 – G. David, BNL
R.J. Fries, BM, D.K. Srivastava, PRL 90 (2003) 132301
2
2
s qed u s
dt s s u
gq
Jet induced contribution
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Part III
Understanding the Matter
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Where does the “lost” energy go?
p+p Au+Au
Lost energy of away-side jet is redistributed to rather large angles!
Trigger jetAway-side jet
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Angular correlations
STAR Preliminary
PHENIX
2.5 < pT,trigger < 4.0 GeV1.0 < pT,assoc < 2.5 GeV
Backward peak of correlated hadrons shifts sideways when pT window of associated hadrons is lowered!
Deflection of primary backward parton – or extended shower of secondary particles associated with quenched backward parton?
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Conical Flow vs Deflected Jets
Mediumaway
near
deflected jetsaway
near
Medium
mach coneJ. Ulery, Hard Probes 2006
STAR Data
* 0180
* 00.0
0110
Cent=0-5%
*
2
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Theorists’ concepts
(Colorless or colorful) sonic shockwave:H. Stöcker, Nucl. Phys. A 750:121-147 (2005),J. Casalderrey-Solana & E. Shuryak, hep-ph/0411315,J. Ruppert & B.M., Phys. Lett. B 618:123-130 (2005),T. Renk & J. Ruppert, hep-ph/0509036
Localized heating of medium:A. Chaudhouri, U. Heinz, nucl-th/0503028
Large Angle Gluon Emission:Ivan Vitev, Phys.Lett.B630:78-84,2005Cherenkov (-like) radiation:A. Majumder & X. N. Wang, nucl-th/0507062,V. Koch et. al., nuclt-th/0507063,I. Dremin, hep-ph/0507167
Trigger jet
Trigger jet
Trigger jet
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Collective QGP modes
Transverse modes
Signal: Cherenkov rings
“Colored” sound ?
Longitudinal (sound) modes
Normal sound
Signal: Mach cones
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Mach cone phenomenology
Trigger jet
Away side jet
Heating
Sound wave
Fraction f of isentropic energy deposition into sound mode
Fraction (1-f) of dissipative energy deposition into heat – requires viscous, turbulent flow behind leading parton.
Thermal spectrum
Spectrum of sonic matter
Casalderrey et al., hep-ph/0602183
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Dihadron correlations
Two-point velocity correlations among 1-2 GeV/c hadrons
away-side same-side
Parton correlations naturally translate into hadron correlations. Parton correlations likely to exist in the quasithermal regime,
created as the result of jet-medium interactions.
An explanation for compatibility dihadron correclations with recombination?
Fries, Bass, BM PRL 94, 122301 (2005)
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Mach cone phenomenology II
Dijet rapidity correlation Trigger vertex distribution
Rapidity cut effects Flow effects on correlation
Renk - Ruppert, hep-ph/0605330
Renk, nucl-th/0607035
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Wakes in the QGP
Mach cone requires collective mode with (k) < k.
Question: Is there a colored mode in this kinematic regime?
Or – can color field couple “superefficiently” to sound mode?
J. Ruppert and B. Müller, PLB 618 (2005) 123 Angular distribution depends
on energy fraction in collective mode and propagation velocity
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Mach cone in AdS/CFT
2
2 2
2 2 2 2
22 2
3 v 1 v cos( )
2 1 3v cos
3v cos 2 v 1 3cos( )
2 1 3v cos
E
iQ k
k
O k
J.J. Friess et al. hep-th/0607022
N = 4 SYM
1
2 22 v
tan
c
dpg N T
k k
dt
Mach angle
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The AdS5/CFT wake
Subsonic
Supersonic
Angular distributions for v = 0.95 and different k.
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Summary
Jets are rich and discriminative probes of the medium: Strong energy loss agrees semi-quantitatively with theory; Probes of a well defined transport coefficient: q-hat; Quantitative determination of q-hat requires sophisticated and realistic description of medium evolution (transport); Rigorous, nonperturbative calculation of q-hat in QCD ? Relative weight of radiative and collisional energy loss ? Dependence on primary parton flavor ? Interaction of radiated energy with medium probes dissipation mechanisms and collective QGP modes.
Jet studies at the LHC will complement and greatly extend the RHIC measurements, but a lot remains to be explored at RHIC (heavy quarks, photon-jet correl’s, di- and multi-hadron correl’s with particle ID, etc.)