Transcript Ridges, Jets and Recombination in Heavy

Ridges, Jets and Recombination
in Heavy-ion Collisions
Rudolph C. Hwa
University of Oregon
Shandong University, Jinan, China
October, 2012
Outline
• Introduction
• Ridges
• Minijets
• Particle spectra and correlations
• Azimuthal anisotropy
• Large Hadron Collider
• Conclusion
2
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.
Yang Chunbin (Wuhan)
Zhu Lilin (Sichuan)
Charles Chiu (U. Texas)
An area of focus is about Ridges
which is an interesting phenomenon in its own right.
3
Ridge
4
Collision geometry
pT


pseudorapidity
azimuthal angle
transverse momentum
  ln(cot  / 2)

pT
5
p2
p1


6
Correlation on the near side
ridge R
Jet
J
Ridgeology
trigger
J+R

R


STAR
Putschke, QM06
J

Properties of Ridge Yield
Dependences on Npart, pT,trig, pT,assoc, trigger 
7
1.
Dependence on Npart
participants
2. on pT,trig
STAR preliminary
Jet+Ridge ()
Jet ()
pt,assoc. > 2 GeV
Putschke,
QM06
Jet)
R
Ridge yield
0
as Npart
0
 depends on medium
Ridges observed at any pT,trig
Ridge is correlated to jet production.
Surface bias of jet  ridge is due to
medium effect near the surface
Medium effect near surface
8
3. Dependence on pT,assoc
Putschke, QM06
STAR
Ridge
Ridge is exponential
in pT,assoc
slope
independent of pT,trig
Exponential behavior
implies thermal source.
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.
9
4. Dependence of jet
and
ridge yields
on trigger s
Feng, QM08
jet part, near-side
jet part, near-side
20-60%
top 5%
ridge part, near-side
Out-ofplane
ridge part, near-side
6 5
s
4
3
2
1
Inplane
3<pTtrig<4, 1.5<pTassoc<2.0 GeV/c
Different s dependencies for different
centralities --- important clues on the
properties of correlation and geometry
10
Effect of Ridge on two-particle correlation
without trigger
Auto-correlation
between p1 and p2
0.15<pt<2.0 GeV/c, ||<1.3,
at 130 GeV
STAR, PRC 73, 064907 (2006)
Ridges are present
with or without triggers.
11
From the data on ridge, we learn that
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.
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
Usual domains in pT at RHIC
low
Hydro
intermediate
2
TT
ReCo
TS
high
6
pQCD
pT
GeV/c
SS
Hadronization
CooperFrye
k1+k2=pT
lower ki
higher density
Fragmentation
k T > pT
13
Pion formation:
qq
distribution
Fqq  TT TSSS
Proton formation:
T
thermal
S
shower
uud distribution
Fuud  TTT TTS  TSS SSS
soft
component
soft semi-hard
components
usual
fragmentation
(by means of
recombination)
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In high pT jets it is necessary to determine the
shower parton distributions.
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.
h
fragmentation
S
D(z)
A
q
A
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In high pT jets it is necessary to determine the
shower parton distributions.
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.
h
Now, a new
component
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soft
TT
thermal
TS
hard
fragmentation
SS
Transverse momentum
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 production by TT, TS and SS recombination
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fragmentation
thermal
TS
Hwa & CB Yang, PRC70, 024905 (2004)
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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
Ridge is from enhanced
thermal source caused
by semi-hard scattering.
SS
trigger
ST peak (J)
TT ridge (R)

Recombination of
partons in the ridge
associated
particles
These wings are
useful to identify
the Ridge

At 0 it is mainly the  distribution that is of interest.
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Hard parton directed at s , loses energy along the way, and enhances
thermal partons in the vicinity of the path.
The medium expands during the successive
soft emission process, and carries the
enhanced thermal partons along the flow.
Flow direction  normal to the surface
s Reinforcement of emission effect leads to a
 cone that forms the ridge around the flow
direction .
s But parton direction s and flow direction
 are not necessarily the same.

Correlation between s and 
If not, then the effect of soft emission is
spread out over a range of surface area,
thus the ridge formation is weakened.
 ( s   (x, y))2 
C(x, y,  s )  exp  

2
2



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Correlated
emission model
(CEM)
STAR
Feng QM08
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3<pTtrig <4
1.5 <pTassoc
<2 GeV/c
CEM

Chiu-Hwa, PRC
79, 034901 (09)
 ; 0.33
s
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That was Ridge associated with a trigger
Single-particle distribution at low pT (<2 GeV/c)
Region where hydro claims relevance --requires rapid thermalization
0 = 0.6 fm/c
Something else happens even more rapidly
Semi-hard scattering
1<kT<3 GeV/c
Copiously produced, but not reliably calculated in pQCD
t < 0.1 fm/c
1. 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.
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Ridge can be associated with a semihard parton without a
trigger.
1 ( pT , ,b)  B( pT ,b)  R( pT , ,b)
Base is the background,
independent of 
Ridge, dependent on ,
hadrons formed by TT reco
How is this untriggered ridge related to the
triggered ridge on the near side of
correlation measurement?
Correlated part of two-particle distribution on the near side
2corr (1,2)  2J (1,2)  2R (1,2)
trigger
assoc part
JET
RIDGE
?
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1
2
2
1
Two events: parton 1 is undetected
thermal partons 2 lead to detected hadrons
with the same 2
R(2 )   d12R (1,2 )
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 (1 )   d2 2R (1,2 )
R(2 )
untriggered ridge
2R (1,2 )
Y R (1 )
triggered ridge yield
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Geometrical consideration for untriggered Ridge
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2  
Hwa-Zhu, PRC 81,
034904 (2010)
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.
S(,b) 

 dl  
arc
[w2 sin2   h2 cos2  ]1/2 d


 h E( ,1  w / h ) 
2
2
h
w
   tan 1[ tan(   )]

elliptical integral of the second kind
Top view: segment narrower at higher b
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Side view: ellipse (larger b) flatter than
circle (b=0) around =0.
Ridge due to enhanced thermal
partons near the surface
R(pT,,b)  S(,b)
b normalized to
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nuclear density D(b)
Asymmetry of S(,b)
=0
=/2
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=0
=/2
S(,b) converts the spatial
elliptical anisotropy to
momentum anisotropy --key step in calculating v2
without free parameters.
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
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Momentum asymmetry
py
Conventional hydro approach
y
higher pressure
gradient
px
x
v2  cos 2
d cos 2( )


 d( )
Good support for hydro at
pT<2 GeV/c
Assumption: rapid thermalization
Elliptic flow
Inputs: initial conditions, EOS, viscosity, freeze-out T, etc.28
Minijet approach
If 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 direction
Their effects on hadronization have
azimuthal anisotropy
 asymmetry can be expanded in harmonics:
( pT , ,b)  0 ( pT ,b)[1  2v2 ( pT ,b)cos(2 )  ...]
We can show agreement with v2 data in this approach also
--- with no more parameters used than in hydro
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and without assumption about rapid thermalization
Azimuthal anisotropy
 h ( pT ,,b)  Bh ( pT ,b)  Rh ( pT , ,b)
base
Bh ( pT ,b)  Nh ( pT ,b)e pT /T0
ridge
Rh ( pT , ,b)  S(,b)R h ( pT ,b)
v ( pT ,b)  cos 2
h
2
h



2
0
T0 to be determined
1
d cos 2 ( pT ,  ,b)
2

2
h
d

( pT ,  ,b)

h

2
0
d cos 2 S( ,b)R h ( pT ,b)
B h ( pT ,b)  R h ( pT ,b)
0
Rh ( pT ,b)
e pT /T  e pT /T0
pT /T '
Z( pT )  h


e
1
 pT /T0
B ( pT ,b)
e
Enhancement factor
T0 is the only parameter to
adjust to fit the v2 data
T'
T0T
T  T0

pT
cos 2
S
1
Z ( pT )  1
factorizable
Hwa-Zhu (12)
b
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STAR
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v2h ( pT ,b) 
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cos 2
S
Z 1 ( pT )  1
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Npart dependence is
independent of pT
Agrees with <cos2>S for Npart>100
No free parameters used for Npart dependence
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v ( pT ,b) 
h
2
cos 2
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S
Z 1 ( pT )  1
Z( pT )  e pT /T '  1
T’ determines pT dependence of v2
as well as the ridge magnitude (T=T-T0)
T'
T0T
T  T0
T0 = 0.245 GeV
One-parameter fit of pT dependence (Npart dependence already reproduced).
h
2
v ( pT ,b)
hydrodynamical elliptic flow
ridge generated by minijets without hydro
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When TS recombination is also taken into account,
we get better agreement with data
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R.Hwa - L. Zhu, Phys. Rev. C 86, 024901 (2012)
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pT dependence of Ridge
 h ( pT ,,b)  Bh ( pT ,b)  Rh ( pT , ,b)
S(,b)R h ( pT ,b)
 h ( pT ,b)  Bh ( pT ,b)  R h ( pT ,b)  Nh ( pT ,b)e p
T
Base
Ridge
/T
Inclusive
T=0.283 GeV
Nh ( pT ,b)e pT /T0 Nh ( pT ,b)[e pT /T  e pT /T0 ]
Base T0=0.245 GeV
Ridge TR=0.32 GeV
enhancement of
thermal partons
by minijets
Inclusive ridge
(inclusive)
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 dependence due to initial
parton momenta
v2 and ridge
are intimately related
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 h ( pT ,,b)  Bh ( pT ,b)  Rh ( pT , ,b)  M h ( pT , ,b)
B
Bridge ridge
TS recombination
dNTS
1
( pT ,  )  2
pT dpT
pT
Minijet
dq
Ž (q, p )
  q Fi (q,  )TS
T
i
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RHIC
At pT>2GeV/c, we must further include SS recombination.35
Large Hadron Collider (LHC)
ALICE
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.
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37
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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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Conclusion
Study of Ridge and Minijets gives us insight into the
dynamical process of hadronization:
Ridge in TT reco with enhanced T due to minijets
Azimuthal anisotropy (v2) can be well reproduced
without hydrodynamics.
As s is increased from RHIC to LHC, S is significantly higher.
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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42
Backup slides
43
Hadron production by parton recombination
p0
Pion
dN 
dk dk
  1 2 Fqq (k1 , k2 )R (k1 , k2 , pT )
dpT
k1 k2
Recombination function
R (k1 , k2 , pT ) 
k1k2 k1  k2
(
1)
2
pT
pT
q and qbar momenta, k1, k2, add to give pion pT
Proton
p
0
dN p
dpT

dk1 dk2 dk3
 k1 k2 k3 Fuud (k1, k2 , k3 )Rp (k1, k2 , k3 , pT )
At low pT thermal partons are most important
TT
TTT
F(ki )  Cki exp(ki / T )
pT2
 Np
exp(pT / T )
pT dpT
mT
dN 
C2

exp(pT / T )
pT dpT
6
dN p
phase space factor in
RF for proton formation
same T for partons, , p
empirical evidence
44
PHENIX, PRC 69, 034909 (04)
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Same T for , K, p --in support of recombination.
Proton production from recombination
pT2
 Np
exp(pT / T )
pT dpT
mT
dN p
T=0.283 GeV
Hwa-Zhu, PRC 86, 024901 (2012)
Slight dependence on centrality
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TS+SS recombination
TS  SS ( pT , ,b)  
1
dq
hadronization
Fi (q, ,b)H i (q, pT )

q i
Fi (q,,b)   dP(,,b)Fi (q,  )
geometrical factors
due to medium
q
k

probability of hard parton
creation with momentum k
TS
b
dN
1
( pT ,  )  2
pT dpT
pT
dNSS
1
( pT ,  )  2
pT dpT
pT
dN ihard
kdkdy
dq
Ž (q, p )
  q Fi (q,  )TS
T
i
dq
Ž (q, p )
  q Fi (q,  )SS
T
i
x  pT / q
only adjustable parameter 
Path length
Fi (q,  )   dkkfi (k)G(k,q,  )
 fi (k)
y 0
degradation
G(k,q,  )  q (q  ke )
Ž (q, p )  dq2 S j ( q2 ) dq Ce q1 /T R (q , q , p )
TS
T

1
2
T
 q2 i q  1
xDi (x)  
dx1 dx2  j
x2 
j'
S
(x
),S
(
) R (x1, x2 , x)
 i 1 i
x1 x2 
1  x1 
   l (x0 , y0 ,,b)
(x0 , y0 ,  , b) is calculable from geometry
46
Geometrical considerations
Nuclear medium that hard parton traverses

Geometrical path length
k
x0,y0
D(x(t),y(t))
density
(Glauber)
(x0 , y0 ,,b)  
t1 (x0 , y0 , ,b)
0
dtD[x(t), y(t)]
Dynamical path length
   l (x0 , y0 ,,b)
 to be
determined
Average dynamical path length
 (,b)    dx0 dy0 l (x0 , y0 ,,b)Q(x0 , y0 ,b)
Probability of hard parton
creation at x0,y0
TA (x0 , y0 ,b / 2)TB (x0 , y0 ,b / 2)
Q(x0 , y0 ,b) 
r r
r r
2r
 d sTA (s  b / 2)TB (s  b / 2)
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Higher harmonics
Conventional approach: fluctuations of initial configuration
Minijet approach: hadronization of minijets themselves outside the medium
--- plays the same role as fluctuations of initial state
R
J
S
T

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
2
 2
pT dpT pT
dp1 dp2
 p1 p2 T( p1 )S( p2 ,  )R ( p1, p2 , pT )
dq
Fi (q,  )Si ( p2 / q)


= A ( p ,b)
q i
3
T
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A3 ( pT , ,b)  J(,b)A3 ( pT ,b)
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Hwa-Zhu
a2=0.6, a3=1.6, a4=1.4
v2 arises mainly from
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cos 2
S
v3, v4 come only from
cos n
J
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