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