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Ridges, Jets and Recombination in Heavy-ion
CollisionsRudolph C. Hwa
University of Oregon
Shandong University, Jinan, China
October, 2012
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Outline• Introduction• Ridges• Minijets• Particle spectra and correlations• Azimuthal anisotropy• Large Hadron Collider• Conclusion
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The conventional method to treat heavy-ion collisions is relativistic hydrodynamics---- which can be tuned to reproduce data.
There is no proof that it is the only way (necessary)---- can only demonstrate that it is a
possible way (sufficient).
We propose another possible way---- minijets and recombination.
An area of focus is about Ridgeswhich is an interesting phenomenon in its own right.
Yang Chunbin (Wuhan) Zhu Lilin (Sichuan) Charles Chiu (U. Texas)
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Ridge
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Collision geometry
azimuthal angle φ
φ
transverse momentum pT
pT
pseudorapidity
η =ln(cotθ / 2)
θ
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η
p1p2
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Ridgeology
η
J+R
ridge R Jet J
R
J
Correlation on the near side
Properties of Ridge YieldDependences on Npart, pT,trig, pT,assoc, trigger
Putschke, QM06STAR
trigger
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Jet+Ridge () Jet ()Jetη)
Putschke, QM06
R
1. Dependence on Npart on pT,trig2.pt,assoc. > 2 GeVSTAR preliminary
Medium effect near surface
Ridges observed at any pT,trig
Ridge yield 0as Npart 0
depends on medium
Ridge is correlated to jet production. Surface bias of jet ridge is due to medium effect near the surface
participants
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Ridge
Putschke, QM06
3. Dependence on pT,assoc
Yet Ridge is correlated to jet production; thermal does not mean no correlation.
Ridge is from thermal source enhanced by energy loss by semi-hard partons traversing the medium.
Ridge is exponential in pT,assoc slope independent of pT,trigExponential behavior
implies thermal source.
STAR
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4. Dependence of jet and ridge yields on trigger s
20-60% top 5%jet part, near-side
ridge part, near-side
jet part, near-side
ridge part, near-side
STAR
3<pTtrig<4, 1.5<pT
assoc<2.0 GeV/c
Feng, QM08
In-plane
Out
-of-
plan
e
1
43
2
56s
Different s dependencies for different centralities --- important clues on the properties of correlation and geometry
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Effect of Ridge on two-particle correlation without trigger
Ridges are present with or without triggers.
STAR, PRC 73, 064907 (2006)
Auto-correlation between p1 and p2
0.15<pt<2.0 GeV/c, |η|<1.3, at 130 GeV
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From the data on ridge, we learn that1. Ridge is correlated to jets (detected or
undetected).2. Ridge is due to medium effect near the surface.3. Ridge is from the thermal source enhanced by
energy loss by semihard partons traversing the medium.
4. Geometry affects the ridge yield.On the basis of these phenomenological properties we build a theoretical treatment of the ridge.But first we outline the theoretical framework that describes the formation of hadrons from quarks.
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Theoretical treatment
Fragmentation
kT > pT
Hadronization Cooper-Frye k1+k2=pT
lower ki higher density
TT TS SS
Usual domains in pT at RHIC
pQCDHydro
low high
ReCo
intermediate
2 6 pTGeV/c
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Pion formation: qq distributionthermal
shower
soft component
soft semi-hard components
usual fragmentation(by means of recombination)
TSFqq =TT+TS+SS
Proton formation: uud distribution
Fuud =TTT +TTS +TSS +SSS
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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.The recombination of thermal partons with shower partons becomes conceptually unavoidable.
A AqD(z)
hfragmentation
In high pT jets it is necessary to determine the shower parton distributions.
S
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hNow, a new component
Once the shower parton distributions are known, they can be applied to heavy-ion collisions.The recombination of thermal partons with shower partons becomes conceptually unavoidable.
In high pT jets it is necessary to determine the shower parton distributions.
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thermal
fragmentation
soft
hard
TS Pion distribution (log scale)
Transverse momentum
TT
SS
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production by TT, TS and SS recombination
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Hwa & CB Yang, PRC70, 024905 (2004)
thermal
fragmentation
TS
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Now, back to Ridge.How do we relate ridge to TT, TS, SS recombination?
Recall what we have learned from the ridge data:1. Ridge is correlated to jets (detected or
undetected).2. Ridge is due to medium effect near the surface.3. Ridge is from the thermal source enhanced by
energy loss by semihard partons traversing the medium.
4. Geometry affects the ridge yield.
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Medium effect near surface
SS
trigger
TT ridge (R)
η
associated particles
These wings are useful to identify the Ridge
At η0 it is mainly the distribution that is of interest.
Ridge is from enhanced thermal source caused by semi-hard scattering.
Recombination of partons in the ridge
ST
peak (J)
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The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow.
Hard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path.
s
But parton direction s and flow direction are not necessarily the same.
s
Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction .
If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened.
Flow direction normal to the surface
Correlation between s and
C(x, y,φs)=ex −φs−x,))
2
2s 2
⎡⎣⎢
⎤⎦⎥
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CEM
s
Correlated emission model (CEM)
Chiu-Hwa, PRC 79, 034901 (09)
s ; 0.33
STAR
Feng QM08
3<pTtrig <4
1.5 <pTassoc
<2 GeV/c
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Single-particle distribution at low pT (<2 GeV/c)
Region where hydro claims relevance --- requires rapid thermalization
0 = 0.6 fm/cSomething else happens even more rapidlySemi-hard scattering 1<kT<3 GeV/cCopiously produced, but not reliably calculated in pQCD t < 0.1 fm/c1. If they occur deep in the interior, they get absorbed and become a part of the bulk.2. If they occur near the surface, they can get out. --- and they are pervasive.
That was Ridge associated with a trigger
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Base is the background, independent of
Ridge, dependent on , hadrons formed by TT reco
Correlated part of two-particle distribution on the near side ρ2
corr (1,2) = ρ2J (1,2) + ρ2
R (1,2)
trigger
assoc part
JET RIDGE
How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement?
Ridge can be associated with a semihard parton without a trigger.
ρ1(pT ,φ,b) = B(pT ,b) + R(pT ,φ,b)
?
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1
2
1
2Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2
R(φ2 )∝ dφ1∫ ρ2R φ1,φ2 )
Ridge is present whether or not 1 leads to a trigger.
Semihard partons drive the azimuthal asymmetry with a dependence that can be calculated from geometry. (next slide)
If events are selected by trigger (e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles 2.
Y R (φ1)∝ dφ2∫ ρ2R φ1,φ2 )
R(φ2 ) ρ2R (φ1,φ2 ) Y R (φ1)
untriggered ridge triggered ridge yield
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Geometrical consideration for untriggered Ridge
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Ridge due to enhanced thermal partons near the surfaceR(pT,,b) S(,b)
nuclear density D(b)
For every hadron normal to the surface there is a limited line segment on the surface around 2 through which the semihard parton 1 can be emitted.
2 S(φ,b)= dl
aρc∫ = [w2 sin2a + η2
a−
a+
∫ cos2a]1/2da
=h E(α ,1− w2 / h2 )α −
α + a±=tan−1[
hwtan(φ ± σ )]
elliptical integral of the second kind
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b normalized to RA
Top view: segment narrower at higher b
Side view: ellipse (larger b) flatter than circle (b=0) around =0.
Hwa-Zhu, PRC 81, 034904 (2010)
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Asymmetry of S(,b)
=0
=/2
S(,b) converts the spatial elliptical anisotropy to momentum anisotropy --- key step in calculating v2 without free parameters.
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=/2
=0
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Momentum asymmetryConventional hydro approach
x
ypx
py
higher pressure gradient
Good support for hydro at pT<2 GeV/c
Inputs: initial conditions, EOS, viscosity, freeze-out T, etc.
Assumption: rapid thermalization
v2 = cos2φ =dφcos2φρφ)∫
dφρφ)∫
Elliptic flow
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Minijet approachIf minijets are created within 1 fm from the surface, they get out before the medium is equilibrated.More in the x
direction than in the y directionTheir effects on hadronization
have azimuthal anisotropy
We can show agreement with v2 data in this approach also--- with no more parameters used than in hydro
and without assumption about rapid thermalization
asymmetry can be expanded in harmonics:ρ(pT ,φ,b) = ρ0 (pT ,b)[1+ 2v2 (pT ,b)cos(2φ) + ...]
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Azimuthal anisotropy
=cos2φ S
Z −1(pT ) +1
factorizable
bpT
T0 is the only parameter to adjust to fit the v2 data
Hwa-Zhu (12)
T '=T0TT −T0
=e− pT /T − e− pT /T0
e− pT /T0= epT /T ' −1
ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)
T0 to be determinedbase B
h (pT ,b)=NηT ,b)e−T /T0
ridge
Rh (pT ,φ,b)=Sφ,b)RηT ,b)
v2h (pT ,b)= cos2φ ρ
η =dφcos2φρηT ,φ,b)0
2
∫dφρηT ,φ,b)0
2
∫=
12
dφcos2φSφ,b)R ηT ,b)0
2
∫BηT ,b)+ R
ηT ,b)
Enhancement factor
Z(pT )=RηT ,b)BηT ,b)
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STAR
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Npart dependence is independent of pTv2
h (pT ,b)=cos2φ S
Z−1T )+1
No free parameters used for Npart dependence
Agrees with <cos2>S for Npart>100
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T0 = 0.245 GeV
One-parameter fit of pT dependence (Npart dependence already reproduced).
v2h (pT ,b)=
cos2φ S
Z−1T )+1Z(pT )=e
T /T '−1 T '=T0TT −T0
v2h (pT ,b)
hydrodynamical elliptic flowridge generated by minijets without hydro
T’ determines pT dependence of v2 as well as the ridge magnitude (T=T-T0)
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R.Hwa - L. Zhu, Phys. Rev. C 86, 024901 (2012)
When TS recombination is also taken into account, we get better agreement with data
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η dependence due to initial parton momenta
Nh (pT ,b)[e−T /T −e−T /T0 ]
Base Ridge =Nh (pT ,b)e
− pT /T Inclusive T=0.283 GeV
Nh (pT ,b)e−T /T0
v2 and ridge are intimately related
Base T0=0.245 GeV
enhancement of thermal partons by minijets
Ridge TR=0.32 GeV
pT dependence of Ridge
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(inclusive)
Inclusive ridge
ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)
S(φ,b)R ηT ,b)
ρ h (pT ,b) = Bh (pT ,b) + Rh (pT ,b)
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ρh (pT ,φ,b) = Bh (pT ,b) + Rh (pT ,φ,b)B ridg
e Bridge
+ M h (pT ,φ,b)Minijet
dN
TS
TdTT ,x)=
1T2
dθθ∫i
∑ Fiθ,x)TS∂ θ, T )TS recombination
At pT>2GeV/c, we must further include SS recombination.
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RHIC
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Large Hadron Collider (LHC)
Using the same recombination model applied to Pb-Pb collisions at 2.76 TeV, we get T=0.38 GeV
and good fits of all identified particle spectra.
ALICE
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R.H.-L.Zhu, PRC84,064914(2011)
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We learn about the dependence of T and S on collision energy.
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quarks pions
The pT range is too low for reliable pQCD, too high for hydrodynamics.Shower partons due to minijets are crucial in understanding the nature of hadronic spectra. TS and TTS recombination provides a smooth transition from low to high pT --- from exponential to power-law behavior.
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ConclusionStudy of Ridge and Minijets gives us insight into the dynamical process of hadronization:
Ridge in TT reco with enhanced T due to minijetsAzimuthal anisotropy (v2) can be well reproduced without hydrodynamics.
As is increased from RHIC to LHC, S is significantly higher.
s
Spectra of all species of hadrons are well explained by TT, TTT, TS, TTS, TSS, SS, SSS recombination.
Minijets at LHC cannot be ignored --- even at low pT.
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At LHC the Higgs boson may have been found.But in Pb-Pb collisions, nothing so spectacular has been discovered.
Most observables seem to be smooth extrapolations from RHIC in ways that have been foreseen.Can we think of anything that is really extraordinary? --- unachievable at lower energies
e.g., a strange nugget? solid evidence against something?
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Backup slides
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Hadron production by parton recombination
TT F(ki )=Cki ex−ki / T)dN
TdT=C
2
6ex−T / T)
TTTdN p
pT dpT
=NT2
m T
ex−T / T) same T for partons, , p
empirical evidence
At low pT thermal partons are most important
phase space factor in RF for proton formation
Pion p0dN
dT=
dk1k1∫
dk2k2
Fθθ k1, k2 )R k1, k2 , T )
Proton p0dN p
dpT
=dk1k1∫
dk2k2
dk3k3
Fuud k1, k2 , k3)Rk1, k2 , k3, T )
Recombination function
R k1, k2 , T )=k1k2T2dk1 +k2
T−1)
q and qbar momenta, k1, k2, add to give pion pT
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p
PHENIX, PRC 69, 034909 (04)
dN p
pT dpT
=NT2
m T
ex−T / T)
Proton production from recombination
Slight dependence on centrality
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Same T for , K, p --- in support of recombination.T=0.283
GeVHwa-Zhu, PRC 86, 024901 (2012)
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q
b
Fi (q,φ,b)= dxPx∫ ,φ,b)Fiθ,x)geometrical factors due to medium
TS+SS recombination
G(k,q,x)=θdθ−ke−x )degradation
ρ1
TS+SS (pT ,φ,b) =dqq∫ Fi
i∑ (q,φ,b)H i (q, pT ) hadronization
dNihard
kdkdy y=0
=ik)
Fi (q,x)= dkki∫ k)G k,θ,x)
k probability of hard parton creation with momentum k
only adjustable parameter x =l(x0 , y0 ,φ,b)
xDi x)=
dx1x1∫
dx2x2
Siφx1),Si
φ'x2
1−x1)
⎧⎨⎩
⎫⎬⎭R x1, x2 , x)x =T / θ
TS∂ (q, pT )=
dθ2θ2∫ Si
φθ2θ) dθ1∫ Ce−θ1 /TR θ1,θ2 , T )
dN
TS
TdTT ,x)=
1T2
dθθ∫i
∑ Fiθ,x)TS∂ θ, T )
dN
SS
TdTT ,x)=
1T2
dθθ∫i
∑ Fiθ,x)SS∂ θ, T )
is calculable from geometry l (x0 , y0 ,φ,b)Path
length
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Nuclear medium that hard parton traverses
x0,y0
k
Dynamical path length
x =l(x0 , y0 ,φ,b) to be determined
Geometrical considerations
Average dynamical path length
x (φ,b) = γ dx0dy0∫ l (x0 , y0 ,φ,b)Q(x0 , y0 ,b)
Q(x0 , y0 ,b)=
TAx0 , 0 ,−b / 2)TBx0 , 0 ,b / 2)d 2ρsTA
ρs+ρb / 2)TB
ρs−ρb / 2)∫
Probability of hard parton creation at x0,y0
Geometrical path length
l (x0 , y0 ,φ,b)= d[x),)]0
1 x0 ,0 ,φ,b)
∫D(x(t),y(t))density (Glauber)
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Higher harmonicsConventional approach: fluctuations of initial configurationMinijet approach: hadronization of minijets themselves outside the medium --- plays the same role as fluctuations of initial state
J stays close to the semihard parton, whose angle is erratic; thus additional contribution to azimuthal anisotropy. pT dependence of TS component is known
Hwa-Yang PRC(04),(10)
dN
TS
TdT=2T2
d11
∫d22
T1)S2 ,x)R 1, 2 , T )
S
R J
T
A3(pT ,φ,b)=Jφ,b)A3T ,b)
A3(pT ,b)=dqq
Fi (q,x)Si2 / θ)i∑∫ QuickTime™ and a
decompressorare needed to see this picture.
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QuickTime™ and a decompressor
are needed to see this picture.QuickTime™ and a
decompressorare needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
a2=0.6, a3=1.6, a4=1.4
v3, v4 come only from cosnφ J
v2 arises mainly from cos2φ S
Hwa-Zhu