Considerations for Distinguishing Between Soft- and Hard-Component
by Multiplicity Correlation
Na Li
Huazhong University of Science and Technology
7th International Workshop on CPOD, 7 - 11 November 2011
Na Li, CPOD, 2011. 11. 7-11 2
Motivation
Particleproduction
soft particles:• from hot dense medium
jets: • beginning of the collision• hard process
Mixed when measured in experiment
Particles produced in different processes carry different information of the collisions. It is important to distinguish the contribution of hydro part and non-hydro part, especially in the intermediate pT region.
2 2
2 2
F B
FB F B
V VC
V V
F-B Elliptic Correlation Function
g->0, (hydro dominance) CFB->1g->1, (jet dominance) CFB->0
J. Liao and V. Koch, Phys. Rev. Lett. 103, 042302 (2009)
η
… forwardbackward
Assumption: • the multiplicity of flow particle in each side fluctuate independently -> <ηFηB>=0
j
j f
MgM M
222 2 2
2
2 2
(1 ) 2 (1 )
(1 )
f f j
FBf j
g v g g v vC
g v g v
Requirement: ● Jet randomly falls into one region in a single event.
Na Li, CPOD, 2011. 11. 7-11 3
12
F f jFdM dM dM
d d d
1 12
B f jBdM dM dM
d d d
Unsolved Problem22
2 2 22
2 2
(1 ) 2 (1 )
(1 )
f f j
FBf j
g v g g v vC
g v g v
2 2 2(1 ) f jv g v g v
2 equations with 3 unknown variables!
Na Li, CPOD, 2011. 11. 7-11 4
More measurement needed!
The effect of <ηFηB> is small when g is relative large.
Multiplicity Correlation Function
1F B
MFB F B
M MC
M M
Definition:j
j f
MgM M
… forwardbackward
η
Na Li, CPOD, 2011. 11. 7-11 5
2MFBC g
jet contribution FB correlation of flow multiplicity
24 (1 )F B g
12
F F f jM M M
1 12
B B f jM M M
In A Multi-phase Transport Model (I)
6Na Li, Hangzhou, 2011. 7. 18-21
AMPT string melting model
With the assumption of no jet contribution at low pT, we may obtain
Na Li, CPOD, 2011. 11. 7-11 6
2 24 (1 )M F BFBC g g
4 0.06
0.0125
M F BFB
F B
C
Although the flow multiplicity exponentially decreases with pT , little pT dependence has been observed for <ηFηB>.
At low pT :
7Na Li, Hangzhou, 2011. 7. 18-21
The tail of hydro particle distribution may also caused the decreasing of FB multiplicity correlation function.
Na Li, CPOD, 2011. 11. 7-11 7
At intermediate pT :
The data points from AMPT are lower than the hydro-only simulation.
The jet contribution can not be neglect in intermediate pT range.
In A Multi-phase Transport Model (II)
2
2 22 22 2 2 2
2 2
2 2 2 2
(1 ) 2 (1 ) 4 (1 )
(1 ) (1 )
f f j F B fVFB
f j f j
g v g g v v g vC
g v g v g v g v
Non-hydro Contribution in v2
2 2 2(1 ) f jv g v g v
jet contribution correlation of flow multiplicity fluctuation
Na Li, CPOD, 2011. 11. 7-11 8
22 2
2 2
F BVFB F B
V VC
V V
0F B
L. X. Han, Phys.Rev.C 83, 047901 (2011)
If: the multiplicity of flow particle in each side fluctuate correlated
Elliptic Correlation in AMPTL. X. Han, Phys.Rev.C 83, 047901 (2011)
CFB is about 2 in central collisions. <ηFη B> is close to 0.25 at low pT.
Inconsistent with the result from multiplicity correlation ?
Results of AMPT model
Na Li, CPOD, 2011. 11. 7-11 9
0.0125F B
22
22 2 22 2 2
2 2
2 2 2 2
(1 ) 2 (1 ) 4(1 )
(1 ) (1 )
f f j fvV
FBf j f j
g v g g v v gC
g v g v g v g v
v2 fluctuation
12
1 12
F f jF
B f jB
dN dN dNd d d
dN dN dNd d d
Particles produced inin-plane and out-of-plane may fluctuate, thus ηF and ηB are the functions of φ, which may cause the fluctuation of v2!
10
For the flow dominate case: 22
2
22
4 1fvV
FBCv
0g
10
Larger v2 fluctuation in central collision causes the larger CFB at low pT.
Observables
Na Li, CPOD, 2011. 11. 7-11 11
Pure flow and jet v2 are expected to be extracted!
222 2 2
2
2 2
(1 ) 2 (1 )
(1 )
f f j
FBf j
g v g g v vC
g v g v
2 2 2(1 ) f jv g v g v 2 2 2(1 ) f jv g v g v
2 24 (1 )M F BFBC g g
22
22 2 222 2
2 2
4(1 )j fvV
FB
g v gC
v v
1
F B
FB F B
X XC
X X
Constant at low pT
Neglectable at large g
12Na Li, CPOD, 2011. 11. 7-11Na Li, CPOD, 2011. 11. 7-11 12
Summary A multiplicity correlation is proposed to measure non-hydro contribution.
The forward-backward multiplicity correlation <ηFηB> is small in the transport model.
The jet contribution is significant in intermediate pT.
The elliptic anisotropy correlation is proposed to measure the non-collective contribution from elliptic flow.
Thank You!
Multiplicity Correlation Simulation
Na Li, CPOD, 2011. 11. 7-11 13
The effect of <ηFηB> is small when g is relative large.
2 24 (1 )M F BFBC g g
Inputs:• Mflow and Mjet are constrained by g• (Mflow +Mjet ) fluctuates ±20% • φflow randomly generated between [0, 2π]• φjet randomly generated between [0, 2π] , and associated particles are generated within ±π/16 according to jet direction
CFB is consistent with the theoretical value. The method is not very sensitive with the pure multiplicity fluctuation.
No correlation in the simulation Real case?
2
2 22 22 2 2 2
2 2
2 2 2 2
(1 ) 2 (1 ) 4 (1 )
(1 ) (1 )
f f j F B fVFB
f j f j
g v g g v v g vC
g v g v g v g v
Non-hydro Contribution in v2
2 2 2(1 ) f jv g v g v
jet contribution correlation of flow multiplicity fluctuation
Na Li, CPOD, 2011. 11. 7-11 14
22 2
2 2
F BVFB F B
V VC
V V
0F B
L. X. Han, Phys.Rev.C 83, 047901 (2011)22
22
2
jg v
v
22 2
2 2
1F B
VFB F B
V VC
V V
If: the multiplicity of flow particle in each side fluctuate correlated
Inputs:• Nflow and Njet are constrained by g• (Nflow +Njet ) fluctuates ±20%
Add in v2 signal
• Associated particles are generated within ±π/8 •according to jet direction
Na Li, CPOD, 2011. 11. 7-11 15
A. M. Poskanzer, Phys.Rev.C 58, 1671(1998)
02 sin ( )n
n
v nn
2
2
0.12
0.07
flow
jet
v
v
grey markers: jet corn = π/4
Elliptic Correlation Simulation
The pure jet elliptic anisotropy v2 could be extracted from when g≥0.3