Transcript "Jets and Ridges at RHIC and LHC"

Ridges and Jets at RHIC and LHC
Rudolph C. Hwa
University of Oregon
Quantifying Hot QCD Matter
INT UW
June, 2010
What is common between RHIC and LHC:
Partons have to hadronize at the end when density is low,
no matter what the initial state may be.
Universal approach: parton recombination at all pT
at any initial energy
What is different:
Which partons recombine? Jet-jet reco at LHC.
Key point of this talk:
Late-time physics can affect our assumption
about the nature of early-time physics
Have to understand RHIC data well, before projecting to LHC.
1
Introduction
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
kT > pT
2
Regions in time
1
8
0.6
rapid thermalization
 (fm/c)
hadronization
hydro
Initial state scattering occurs even earlier.
An example of late-time physics affecting thinking about early-time physics:
Cronin effect: --- initial-state or final-state effect?
Cronin effect in pA is larger for proton than for ; it implies
final-state effect (in ReCo), not hard-scattering+frag, not hydro.
Early-time physics: CGC, P violation, …
Pay nearly no attention to hadronization at late times.
3
Large  structure of Ridge ---
PHOBOS
PHOBOS, PRL104,062301(10)
 ~ 4, pTtrig>2.5GeV/c
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Before understanding that, we
should understand single-particle
distribution, summed over all
charged and integrated over all pT
Simpler
scenario
BRAHMS has dN/dy at
fixed pT =0.4 GeV/c
Referred to as
“long-range”
correlation on the near
side
PRL 91, 052303 (03)
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PHOBOS
4
y is commonly identified with 
BRAHMS PLB 684,22(10)
PHOBOS
all charged
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BRAHMS
 only
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How is this difference to be
understood?
Proton contribution should
not be ignored.
How much does it contribute
to the  distribution?
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5
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Early-time
physics:
CGC
Dusling, Gelis, Lappi, Venugopalan
arXiv: 0911.2720
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how one goes
from initialstate to final
state in one
step
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6
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Ridge without detailed input on early-time physics
7
First, we need to understand single-particle
distribution in pT, , Npart, and  ---before correlation.
Topics to be covered:
Hadronization
Ridges with or without trigger
Jets
8
Hadron production at low pT in the recombination model
Pion at y=0
p0
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
It doesn’t work with transverse rapidity yt
At low pT
TT
Proton at y=0
TTT
dN p
F(ki )  Cki exp(ki / T )
p0
dN p
dpT

dk1 dk2 dk3
 k1 k2 k3 Fuud (k1, k2 , k3 )Rp (k1, k2 , k3 , pT )
pT2
 Np
exp(pT / T )
pT dpT
mT
phase space factor in
RF for proton formation
dN 
C2

exp(pT / T )
pT dpT
6
same T for partons, , p
empirical evidence
9
PHENIX, PRC 69, 034909 (04)
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went on to mT plot
Proton production from recombination
dN p
pT2
 Np
exp(pT / T )
pT dpT
mT
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Same T for , K, p --in support of recombination.
Slight dependence on centrality --to revisit later
10
Ridge formation
SS
trigger
ST peak (J)
TT ridge (R)
associated
particles


Mesons:
Baryons: TTT in the ridge
Suarez
QM08
B/M in ridge even higher than in inclusive distr.
11
Feng, QM08
Jet and Ridge Yield
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
12
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



13
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
14
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.
15
Ridge can be associated with a semihard parton without a
trigger.
1 ( pT , ,b)  B( pT ,b)  R( pT , ,b)
Base, independent of ,
not hydro bulk
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
?
Putschke, Feng (STAR)
Wenger (PHOBOS)
16
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
17
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
18
nuclear density D(b)
Single-particle distribution at low pT with Ridge
1 ( pT , ,b)  B( pT ,b)  R( pT , ,b)  N(b)[e p
T
After average over ,
1 ( pT ,b)  N(b)[e p
T
/T0
 D(b)S(,b)r( pT ,b)]
/T0
 D(b)S (b)r( pT ,b)]
Compare with data that show exponential behavior
1 ( pT ,b)  N(b)e p
T
/T (b)
T (b)  0.3(1  0.03b 2 ) GeV
T0  T (b  2)
r(pT,b) can be determined;
 dependence comes only from
S(,b); v2 can be calculated.
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19
Ridge yield with trigger at 1
R
R
d


(

,

)

Y
(1 )
 2 2 1 2
 S(1 ,b)
Feng QM08
 s  1
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Normalization
adjusted to fit,
since yield
depends on
exp’tal cuts
s dependence is calculated
Normalization is
not readjusted.
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S(,b) correctly
describes the 
dependence of
correlation
20
RAA(pT, , b) can be calculated with the  dependence arising entirely from the ridge.
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Hwa-Zhu, PRC 81,
034904 (2010)
art
Summary
 dependencies in
Ridge R(pT,,b)
v2(pT,b)=<cos 2 >
yield YR()
RAA(pT,,b)
are all inter-related --- for pT<2 GeV/c
21
Jets
Dependence on  and Npart
PHENIX 0903.4886
pT>2 GeV/c
pT
Npart
Need some organizational simplification.
Clearly,  and b are related by geometry.
22

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)
23
Define
P(,,b)   dx0 dy0Q(x0 , y0 ,b) [   l (x0 , y0 ,,b)]
It contains all the information on the relationship between  and b.
 (,b)   dP(,,b)
centrality
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 ( , c) looks universal, except for c=0.05 (no  dep at c=0)
It suggests that P(,,c) may depend on fewer variables.
24
Define
KNO scaling
 (z)   (, c)P(, , c)
z   /
 dz (z)  1
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For every pair of  and c:
 dzz (z)  1
• we can calculate
 ( , c)
• PHENIX data gives
 We can plot the exp’tal data
RAA ( , c)
RAA ( )
25
Scaling behavior in 
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5 centralities and 6 azimuthal angles () in one universal curve for each pT
Lines are results of calculation in RM.
Complications to
take into account:
Hwa-Yang, PRC 81, 024908 (2010)
• details in geometry
• dynamical effect of medium
• hadronization
26
TS+SS recombination
TS  SS ( pT , ,b)  
1
geometrical factors
due to medium
q
k

probability of hard parton
creation with momentum k
TS
b
dq
hadronization
Fi (q, ,b)H i (q, pT )

q i
Fi (q, ,b)   dP(, ,b)Fi (q,  )
dN
1
( pT ,  )  2
pT dpT
pT
dNSS
1
( pT ,  )  2
pT dpT
pT
Fi (q,  )   dkkfi (k)G(k,q,  )
dN ihard
kdkdy
dq
Ž (q, p )
  q Fi (q,  )TS
T
i
Nuclear modification factor
only adjustable parameter 
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
dq
Ž (q, p )
  q Fi (q,  )SS
T
i
x  pT / q
 fi (k)
xDi (x)  
dx1 dx2  j
x2 
j'
S
(x
),S
(
) R (x1, x2 , x)
 i 1 i
x1 x2 
1  x1 

dN AA
/ dpT d
RAA ( pT ,  , c) 
N coll dN pp / dpT

   l (x0 , y0 ,,b)
27
Result of calculation in terms of 
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exp(2.6 )
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 is dimensionless
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Two-jet recombination at LHC
At LHC, the densities of hard partons is high.
At kT not too large, adjacent jets can
be so close that shower partons from
two parallel jets can recombine.
Two hard
partons
2j
dN AA
 12 j ( pT , ,b)
pT dpT d
dq dq'

Fi (q, ,b)Fi ' (q', ,b)H ii ' (q,q', pT )

q q' ii '
1
H ii ' (q, q ', pT )  2
pT
dq1 dq2 j q1 j ' q2 
 q1 q2 Si ( q )Si ' ( q ' )R (q1, q2 , pT )
Fi (q, ,b)   dP(, ,b)Fi (q,  )
12 j ( pT ,,b)   dd ' P(,,b)P( ',,b)12 j ( pT , ,  ')
12 j ( pT , ,  ')  
dq dq'
Fi (q,  )Fi ' (q',  ')H ii ' (q,q', pT )

q q' ii '
29
Recombination of two shower partons from two jets
H ii ' (q, q ', pT ) 
1
pT2
dq1 dq2 j q1 j ' q2 
 q1 q2 Si ( q )Si ' ( q ' )R (q1, q2 , pT )
Overlap of two jet cones
R (q1,q2 , pT )  R (q1,q2 , pT )
 - probability for overlap of two shower partons
from adjacent jets
=10-m, m=1, 2, 3
=10-3: 1-jet (S1S’1)
same jet 1
=10-1: 2-jet (S1S2)
different jets
30
Go back to
12 j ( pT ,,b)   dd ' P(,,b)P( ',,b)12 j ( pT , ,  ')
12 j ( pT , ,  ')  
dq dq'
Fi (q,  )Fi ' (q',  ')H ii ' (q,q', pT )

q q' ii '
, b are the same for the two jets,
but  and ’ are independent

For given , b there is only one (,b)
KNO scaling implies
’
12 j ( pT ,,b)   dz dz' (z) (z')12 j ( pT , z, z',  (,b))
Inclusive distribution

dN AA
(b)  1TS  SS ( pT , ,b)  12 j ( pT , ,b)
pT dpT d

dN AA
/ pT dpT d (b)
RAA ( pT ,  ,b) 
N coll (b)dN pp / pT dpT

31
Pion production at LHC
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1 jet
Hwa-Yang, PRC 81, 024908 (2010)
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>1 !
2 jet
Scaling

dN AA
/ pT dpT d (b)
RAA ( pT ,  ,b) 
N coll (b)dN pp / pT dpT

Scaling badly broken
 N coll for 1-jet
2
 N coll
for 2 jets
modest increase
at 50-60%
2
scales
12 j ( pT , ,b) / N coll
1j
2j
The admixture of 1  1 ruins the scaling behavior.
Observation of large RAA at pT~10 GeV/c will
be a clear signature of 2-jet recombination.
32
Recombination (2 jets) vs fragmentation (1 jet)
pT~10 GeV/c

gluon
k1
pT=k’1+k’2
k’i
kT~20 GeV/c
(1-j
fragmentation)
(2-j recombination)
k2
more probable
pT~10 GeV/c
p
gluon
k1
pT=k’1+k’2 +k’3
k’i
k2
kT>20 GeV/c
(1-j
fragmentation)
(2-j recombination)
even more probable
If pT>20 GeV/c, 2-j requires higher ki, whose density is lower;
thus smaller  reduces probability of recombination.
33
Production rates of p and  are separately reduced, as pT is
increased, but the p/ ratio is still >1 even up to pT~20 GeV/c
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5-20
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Hwa-Yang, PRL97,042301 (2006)
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Ridge
2j

If 2-jet 1 ( pT ,  ( , c))
dominates single-particle
inclusive at pT~10 GeV/c, then there are many such
hadrons ( and p) at that pT at all .
Using trigger at pTtrig ~ 10 GeV/c to find ridge would
involve subtraction of a huge background.
1j

If higher pT ( > 30 GeV/c), then 1-jet 1 ( pT ,  ( , c))
dominates, and ridge is not expected (from
RHIC).
It probably will be hard to find detectable ridge at LHC.
trig
 ~ 4 correlation at RHIC
35
Jet peak
TS reco
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Single-particle distribution

h
1B R
h
dN B
J h (, pT ) h
h
R
(, pT ) 

L
(

,
p
)V
T
B
R ( pT )
2
d pT dpT
pT
Longitudinal:
TransVerse:
L (, pT )   dzz(1 z)F(zX)F((1 z)X)
V  ( pT )  C 2 pT2 e pT /T
factorizble
z  k1 / pT
X
pT
cosh 
s /2
similarly for h=p
BRAHMS, PRL
94,162301(05)
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<pT> essentially
independent of y
37
Chiu-Hwa (preliminary)
Two-particle distribution
2h h (1, pt ;2 , pa )  1h (1, pt )1h (2 , pa )  C2h h (1, pt ;2 , pa )
1 2
1
2
1 2
2h h (1, pt ;2 , pa )  1h (trig) (1, pt )1h (2 , pa )
1 2
1
2
BR
h2


J
(2 , pa ) h2
h1 h2
h1 (trig)
h2
h2
C2 (1, pt ;2 , pa )  1
(1, pt ) 
L (2 , pa )[VB R ( pa )  VB ( pa )]
2
p
a


ridge
Ridge distribution per trigger
VRh2 ( pa )
dN Rh2
1
1
( pa ) 
C2h1h2 (1 , pt ; 2  1  , pa )  2 J h2 (2 , pa )Lh2 (2 , pa )VRh2 ( pa )
d
N trig
pa
1.5
dN Rch
dN Rh2
dN ch
  dpa pa
( pa )   d1
0
d h2 
d
d2
correlation in transverse
component --- ridge
2  1  
no correlation in 
38
Correlation is in the transverse component,
(ridge being TT+TTT reco)
with negligible correlation between trigger
1 and associated 2
1.5
map 1(2) to dN/d: dN /   0 d11ch (  1 )
ch
PHOBOS
PHOBOS

QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
1(trig)
Where is the long-range
correlation that requires
early-time physics?
39
Conclusion
Hadronization and initial geometry are important to
understanding RHIC and LHC physics
pT<2GeV/c
semihard partons  ridge (TT reco)   dependence
pT>2GeV/c (RHIC): TS+SS reco  scaling
pT~10GeV/c (LHC): 2j-SS reco  scaling broken
Probably no ridge at higher pTtrig and pTassoc at LHC.
1 and dN/d are related with no need for long-range
correlation between (trig) and (ridge).
40