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)
It’s all about “Matter”
What’s the Matter? Probing the Matter Understanding the Matter
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.
Part I
What’s the Matter?
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
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.
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
Part II
Probing the matter
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”
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.
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
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:
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
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
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
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
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.
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.
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
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
Flat or rising RAA ?
Vitev et al (GLV)
LHC
Armesto et al (ASW)
Extrapolations to LHC energy vary widely due to modeling differences:
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
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
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
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
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
Part III
Understanding the Matter
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
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?
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
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
Collective QGP modes
Transverse modes
Signal: Cherenkov rings
“Colored” sound ?
Longitudinal (sound) modes
Normal sound
Signal: Mach cones
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
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)
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
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
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
The AdS5/CFT wake
Subsonic
Supersonic
Angular distributions for v = 0.95 and different k.
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.)