Jets in Nuclear Collisions
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Transcript of Jets in Nuclear Collisions
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Jets in Nuclear Collisions
Why jets in nuclear collisions? How do we find jets in nuclear collisions? Is hard scattering different in nuclear collisions than in
e+e- or pp collisions? What happens in the nuclear medium?
Is jet transport & fragmentation changed? What do we still want to know?
Barbara JacakStony Brook UniversityJune 29, 2004
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Why collide nuclei at s=200 GeV/A?
high energy nuclear collisions should create quark gluon plasma
At high temperature and density: T~170 MeV and/or ~50 Debye screening by produced color-chargesexpect transition to “free” gas of quarks and gluons
Attractive potentialConfinement at large distance
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pressure builds up
how to probe the plasma?
PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
Kpnd,
Hadrons reflect (thermal) properties when inelastic collisions stop (chemical freeze-out).
, e+e-, +Real and virtual photons emitted as thermal radiation.
Hard scattered or heavyq,g probes of plasma formed
System expands & cools
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Hard quarks & gluons jets
Hard scattering happens early
affected by initial state nucleus
Hard partons propagatefast quarks, gluons traverse
the interesting stuffradiate gluonsinteract with QGP partons
Fragmentation is last step - outside the medium
coneRFragmentation:
z hadron
parton
p
p
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Plasma physics of the quark gluon plasma?
Want to knowpressure, viscosity, energy gradients, equation of state,thermalization time & extent
determine from collective behavior
Other plasma parametersradiation rate, collision frequency, conductivity, opacity, Debye screening length?
what is interaction of q,g in the medum? need short wavelength strongly interacting
probe
high momentum q,g provide just this!
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What is the effect of the medium?
hadrons
q
q
hadronsleadingparticle
leading particle
schematic view of jet production
decreases their momentum fewer high momentum particles beam “jet quenching”
before they create jets, the scattered quarks radiate energy (~ GeV/fm) in the colored medium
Approach:calculate jet rate, test in pp, compare jets in A+A to p+p
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QCD and EM Radiation
EM
BUT radiated gluons also interact with gluons in the medium! Energy loss depends on gluon density along the path.
EM Radiation by scattering:Interference between initialand final state radiation
gluon quark
QCD
Radiation interferestoo
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Energy Loss in Dense QCD MatterEnergy Loss in Dense QCD Matter Ivan Vitev,Ivan Vitev, ISUISU
• Elastic energy loss
J.D.Bjorken, SLAC preprint (1982) unpublished
2 2 /2
46 1 ln jetelastic T
s
E TE T e
TL
• Inelastic (radiative) energy loss
QCD is very differentfrom QED in the
ability of the gluon to reinteract
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Energy loss expected
Since QCD is non-abelian, even 1 scattering in final state is sufficient to generate energy loss
Remember that radiated gluon couples to medium!
formation length of max E gluon: lF ~ 2E/2 ( = pT kick )
E ~ E x L/ x L 2/2E ~ 2 L 2 /2 standard radiationwith no interference
formation time of radiated gluon( gluon interaction probability)
So:
In normal, cold nuclei dE/dx ~ 0.5 GeV/fm
Prediction for RHIC: 10x E of cold nuclei
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A closer look at the calculation
• Radiative energy loss
(1) R s
3(1)
2
2g
g
2R s
2CE Log ... ,
4
Static medium
9 C 1E Log ... ,
4 A
(L)
dNdy (L
1+1D
)
L 2E
Bjo
L
2EL
L
rken
• Significantly larger than the elastic for static nuclear matter
• Can be related to the density of gluons/quarks in the system or T
• Takes into account geometry, the small number of scatterings, finite kinematics
M.Gyulassy, P.Levai, I.V., Nucl.Phys.B594, (2001); Phys.Rev.Lett.85, (2000)
But medium is not static!Expands density drops
2 ,zV R LzL ct
0exp
2anding static
tE E
R
0
152
R
t
2
1desnity:
dN
dy R t
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How do we find jets in nuclear collisions?
In p+p can look for hadrons in the characteristic “cone” pattern
How to find the jet?
s=200 GeV energy is modest; jet not large
Central Au+Au collision
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3 Ways to “Skin a Cat Jet”
1) Single Particle Spectra:High pT dominantly from jets
d/dpT RAA, RdA
nuclear modification factor
2) 2-Particle Correlations:dN/d()
3) Jet Reconstruction:d/dET, Fragmentation function
trigger
“Trigger” = 0
Adler et al., PRL90:082302 (2003), STAR
near-side
away-sideNice work if you can get it!
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Jet physics in Au+Au
Trigger:hadron with pT > 2.5 GeV/cBiased, low energy, high z jets!
of associated partners
Count associated lower pT
particles for each trigger “conditional yield”Near side yield: number of jet associated particles from same jet in specified pT binAway side yield: jet fragments from opposing jet
triggernear side < 90°Partner from same jet
away side > 90° opposing jet
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Subtract the underlying event
CARTOON
flow
flow+jet dN
Ntrig d
includes ALL triggers(even those with no
associated particles inthe event)
jetUnderlying event isbig! Collective flow causes another correlation in them:
B(1+2v2(pTtrig)v2(pT
assoc)cos(2))
associated particles with non-flow angular
correlations -> jets!
Treat as 2 Gaussians
1
combinatorial background large in Au+Au
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Benchmark calculation of probe rate on a simple system: p+p collisions
p-p PRL 91 (2003) 241803
Good agreementwith NLO pQCD
2
/( , )
a Nf x Q
2
/( , )ch a
D z Q
Parton distribution functions
Fragmentation functions
0
0 rates:dN/dpT
2dy1dy2 ~ dxa dxb dzc dzd
fa/N(xa,Q2) . fb/N(xb,Q2) . Dh1(zc,Q2) . Dh2(zd,Q2) .
dab /dQ2dy
To generalize for nuclei:fa/N(xa,Q2,r) fa/N(xa,Q2) .
Sa/A(xa,r) .
tA(r)
Nuclear modification to structure function (shadowing, saturation, etc.)
Nuclear thickness function
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Now check that it works in Au+Au
Not so easy – cannot use anything that should be affected by the medium!
Try QCD direct photons
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pQCD in Au+Au? direct photons
[w/ the real suppression]
( pQCD x Ncoll) / background Vogelsang/CTEQ6
[if there were no suppression]
( pQCD x Ncoll) / ( background x Ncoll)
Au+Au 200 GeV/A: 10% most central collisions
[]measured / []background = measured/background
Preliminary
Probe calculation works!
pT (GeV/c)
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Is the message in the medium?
Is there “jet quenching” as predicted from energy loss? count high pT particles (AA vs. pp) look at back-to-back jets
How much energy do fast partons lose?What does it tell us about the medium?
Where does the “lost” energy go?
What does the presence of q and q in the QGP do to jet fragmentation?
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Technique to search for jet quenching
Compare to baseline: nucleon-nucleon collisions at the same energy
To 0’th order: Au + Au collisions start with collisions of quarks & gluons in the individual N-N reactions(+ effects ofnuclear binding andcollective excitations)
Hard scattering (p transfer > few GeV) processes scale as the number of N-N binary collisions <Nbinary>
so for pT> 2 GeV/c expect: YieldA-A = YieldN-N . <Nbinary>
nucleons
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Nuclear Modification of Hadron Spectra?
ddpdT
ddpNdpR
TNN
AA
TAA
TAA /
/)(
2
2
<Nbinary>/inelp+p
nucleon-nucleon cross section
1. Compare Au+Au to nucleon-nucleon cross sections2. Compare Au+Au central/peripheral
Nuclear Modification Factor:
If no medium effect: RAA < 1 in regime of soft physics RAA = 1 at high-pT where hard scattering dominates Jet quenching: RAA < 1 at high-pT
AA
AA
AA
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pp
AuAubinaryAuAuAA Yield
NYieldR
/
Au-Au s = 200 GeV: high pT suppressed!
PRL91, 072301(2003)
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look for the jet on the other sideSTAR PRL 90, 082302 (2003)
Central Au + Au
Peripheral Au + Au
near side
away side
peripheral central
22 2 2( ) ( ) (1 cos(2 ))D Au Au D p p B v
Medium is opaque!
Trigger 4-6 GeV/c pT
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Suppression larger out-of-plane
Path Length Dependence
nGLVE L
di-hadron, 20-60% Central Background SubtractedSee J. Bielcikova et al., (nucl-ex/0311007) for background derivation
STAR Preliminary
s =200 GeVNN
Measured
ReflectedIn-plane
Out-of-plane
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Suppression: a final state effect?
Hadronic absorption of fragments: Gallmeister, et al. PRC67,044905(2003)Fragments formed inside hadronic medium
Hadron source is soft, after allRecombination of flowing partonsFries, Muller, Nonaka, Bass nucl-th/0301078Lin & Ko, PRL89,202302(2002), Hwa, et al.
Energy loss of partons in dense matterGyulassy, Wang, Vitev, Baier, Wiedemann…
PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
Hadron gas
1AuAuR But absent in d+Au collisions! d+Au is the “control” experiment
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Suppression: an initial state effect?
Gluon Saturation (color glass condensate)
Wavefunction of low x gluons overlap; the self-coupling gluons fuse, saturating the density of
gluons in the initial state. (gets Nch right!)
Levin, Ryshkin, Mueller, Qiu, Kharzeev, McLerran, Venugopalan,
Balitsky, Kovchegov, Kovner, Iancu …
probe rest frame
r/ggg
dAu AuAuR R RdAu~ 0.5D.Kharzeev et al., hep-ph/0210033
1dAuR Broaden pT :•Multiple elastic scatterings
(Cronin effect) Wang, Kopeliovich, Levai, Accardi
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PHENIX Preliminary 0
PHOBOS Preliminary
STAR Preliminary
Experiments show NO suppression in d+Au!
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Centrality Dependence
Dramatically different and opposite centrality evolution of AuAu experiment from dAu control.
Jet Suppression is clearly a final state effect.
Au + Au Experiment d + Au Control
PHENIX preliminary
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Are back-to-back jets there in d+Au?
Pedestal&flow subtracted
hadronsleadingparticle suppressed
q
q
?
Yes!
So this is the rightpicture for Au+Au
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Property probed: density
Au-Au
d-AudAu
Agreement with data:Vitev, Gyulassy, Wang, others say dE/dx ~ 7.5 GeV/fm get dAu right too!
initial gluon density=
dNg/dy ~ 1100
~ 15 GeV/fm3
hydro initial state same 5-10 x critical
NB: Lowest energy radiation sensitive to infrared cutoff.
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Recap
Hard partons are excellent probes of QGP Can calculate their production rate with pQCD in Au+Au (surprisingly) Can do jet physics in heavy ion collision See jet quenching in single particles & back-to-back
correlationsInfer:dE/dx ~ 7.5 GeV/fmdNg/dy ~ 1100 ~ 15 GeV/fm3
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Turn to the fragmentation function
coneRFragmentation:
z hadron
parton
p
p
Standard picture
If true:
fragmentation independent of medium
Baryon/meson at high pT same in Au+Au and p+p
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Formation time of fragmentation hadrons
Uncertainty principle relates hadron formation time to hadron size, Rh and mass, mh
In laboratory frame: f ~ Rh (Eh /mh)consider 2.5 GeV pT hadrons
f ~ 9-18 fm/c for pions; Rh~0.5-1 fm
f ~ 2.7 fm/c for baryons (Rh~1 fm) Alternatively, consider color singlet dipoles from
combination of q & q from gluon splittingUsing gluon formation time, can estimatef ~ 2Eh (1-z)/(kT
2+mh2)
for z = 0.6-0.8 and kT ~ QCD (f baryons) ~ 1-2 fm/c R(Au nucleus) ~ 7 fm Baryon formation is NOT outside the medium!
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We observe a puzzle
h/0 ratio shows that p is enhanced only < 5 GeV/c
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Hydro. expansion at low pT + jet quenching at high pT.
Coalesce (recombine) boosted quarks hadrons enhances mid pT hadrons baryons especially
pQCD spectrum shifted by 2.2 GeV
Teff = 350 MeV
R. Fries, et al
Are extras from the (soft) underlying event?
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Phase space filled with partons:coalesce into hadrons
ReCo of hadrons: convolution of Wigner functions
Where does ReCo win?
),()2
,2
;2
,2
()2()2( 3
33
,3
3
3qrq
PrRq
PrRW
rqddRd
Pd
dNMab
ba
M Wab(1;2) = wa(1)wb(2)
fragmenting parton:ph = z p, z<1
recombining partons:p1+p2=ph
Power law:
Exponential: TpTAew /~
DAeDwN TzPT /frag ~
TPTeAwwN /2reco ~
Tpw ~
TPN ~frag
2reco ~
TPN
Use lowest Fock state, i.e. valence quarks
R. Fries
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Coalescence Model results
Fries et al: Phys.Rev. C68 (2003) 044902Greco, Ko, Levai: PRC 68 (2003)034904
•particle ratios and spectra OK
•intermediate pT hadrons from
coalescence of flowing partons NOT from jets, so no jet-like associated particles
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But baryons show jet-like properties too…
Baryons at 2-4 GeV/c pT scale with Ncoll !
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So baryons seem jet-like!
baryons & antibaryons not suppressed!? parton E depends upon what fragmentation WILL be???
baryon excess due to fragmentation function modification?Step 1: determine if baryons are from jets
do we see hadronic partners from the same jet?Step 2: calculate effect of q,q in surrounding medium upon
(soft part of) fragmentation function
Rcp
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Step 1: use 2 particle correlations
Select particles with pT= 2.5-4.0GeV/c
Identify them as mesons or baryons viaTime-of-flight
Find second particle with pT = 1.7-2.5GeV/c
Plot distribution of the pair opening angles
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Jets in PHENIX
Large multiplicity of charged particles--solution: find jets in a statistical manner using angular correlations of particles
mixed events give combinatorial background 2 x 90 degree acceptance in phi and ||<0.35
--solution: correct for azimuthal acceptance,
but not for acceptance Elliptic flow correlations
--solutions: use published strength values and subtract (could integrate over 90° to integrate all even harmonics to zero)
PHENIX PRL 91 (2003) 182301
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Subtracting combinatorial background
CARTOON
flow
flow+jet dN
Ntrig d
includes ALL triggers(even those with no
associated particles inthe event)
jetAssociated particles from the underlying event. Collective flow causes another correlation in them:
B(1+2v2(pTtrig)v2(pT
assoc)cos(2))
associated particles with non-flow angular
correlations -> jets!
Treat as 2 Gaussians
1
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• jet partner equally likely for trigger baryons & mesons
• Same side: only slight decrease with centrality
•Away side: partner rate as in p+p confirms jet source of baryons!
• See disappearance of away-side jet for both baryons and mesons
Identify Trigger: Source of intermediate pT baryons?
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pions
only soft protons
partners expected from recombination
•Yield of partners per trigger expected from recombination of purely thermal (soft) constituent quarks
(dilutes jets)
Many baryons ARE from jets, but medium modifies those jets
Allow fast quark to combine with quarks from medium
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pT spectra of same jet associated particles
Spectra in lab, rather than jet, frame
Allows to compare with inclusive spectra
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Compare slope to inclusive hadron spectra
Generally higher
Perhaps thermalized in most central collisions?Calculations (step 2) desperately needed!
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Conclusion about fragmentation function
It’s modified in the medium!Au+Au jets richer in soft hadrons than p+p or d+AuAu+Au jets baryon yield increases with medium volume
Maybe some evidence that jet fragments are beginning to thermalize in the medium
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What do we still want to know?
Quantitative information on medium modification of jet fragmentation
Where does the energy radiated by fast partons go?Many soft gluons – no (per observed multiplicity)A few semi-hard gluons? … could be
How is the lost energy propagated in the medium?Infer energy, color transport properties of QGP basic plasma physics!Is the lost energy thermalized in the medium?
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values
B
(fm)
Npart R/R+F
R/R+F
p
Partner yield
Partner yield p
12 24 0.45 0.95 0.027 0.0047
0.0014 0.0007
7.5 156 0.65 0.97 0.0172 0.0030
0.0008 0.0004
0 390 0.8 0.98 0.0098 0.04017
0.0005 0.0003
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kT, jT at RHIC from p+p Data
J. Rak, Wed.
J. Rak, DNP03
s=200 GeV
di-hadron
Statistical Errors Only
near-side away-side
nearfar
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Moment Analysis of QCD Matter2 ( )
( )
T g
g
k x dx
E x x dx
I. Vitev, nucl-th/0308028
Induced Gluon Radiation ~collinear gluons in cone “Softened” fragmentation
in je
i j t
t
n e
: increases
z : decreases
chn
Gyulassy et al., nucl-th/0302077
coneRFragmentation:
z hadron
parton
p
p
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Collective effects? Pressure: a barometer called “elliptic flow”
Origin: spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system spatial anisotropy momentum anisotropy
v2: 2nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane
Almond shape overlap region in coordinate space 2cos2 v
x
y
p
patan
y2 x2 y2 x2
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Hydro. CalculationsHuovinen, P. Kolb,U. Heinz
v2 reproduced by hydrodynamics
STARPRL 86 (2001) 402
• see large pressure buildup • anisotropy happens fast • early equilibration !
central
Hydrodynamics assumes early equilibrationInitial energy density is inputEquation of state from lattice QCDSolve equations of motion
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But at forward rapidity reach smaller x
y = 3.2 in deuteron direction x 10-3 in Au nucleus
Strong shadowing, maybe even saturation?
d Au
Phenix Preliminary
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Pions in 3 detectors in PHENIX
Charged pions from TOF
Neutral pions from EMCAL
Charged pions from RICH+EMCAL
Cronin effect gone at pT ~ 8 GeV/c
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Centrality dependence of Cronin effect
Probe response of cold nuclear matter with increased number of collisions.
See larger Cronin effect for baryons than for mesons (as at Fermilab)
Qualitative agreement with model by Accardi and Gyulassy. Partonic Glauber-Eikonal approach: sequential multiple partonic collisions. nucl-th/0308029
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Does Cronin enhancement saturate?
A different approach:
Intrinsic momentum broadening in the excited projectile proton:
hpA: average number of collisions:
X.N.Wang, Phys.Rev.C 61 (2000): no upper limit.
Zhang, Fai, Papp, Barnafoldi & Levai, Phys.Rev.C 65 (2002): n=4 due to proton d dissociation.