Two-pion interferometry for the granular sources in t

he heavy ion collisions at RHIC and LHC energies

Wei-Ning Zhang

1) Dalian University of Technology, Dalian, China

2) Harbin Institute of Technology, Harbin, China

Outline

Introduction

Granular source model of QGP droplets

Granular source HBT results for RHIC and LHC heavy ion collisions

Summary and discussions

In high energy heavy ion collisions, HBT interferometry is a useful tool to probe the space-time of the particle-emitting source.

To explain RHIC HBT data we proposed the granular source model of QGP droplets (PRC74,024908,2006;PRC80,044908,2009).In this work we will investigate the HBT interferometry in the granular source model in ultrarelativistic heavy ion collisions. We will explain the LHC and RHIC HBT results consistently with the granular source model.

I. Introduction

The HBT measurements at RHIC high energies indicate it is hard to describe the source space-time by a simple evolution model. HBT data give strong constraints for the source model.

Recently, the HBT measurement for the =2.76 TeV Pb-Pb most central collisions at LHC has been performed. A consistent explanation to the HBT data of the RHIC and LHC experiments is required naturally for the source models.

NNs

II. Granular source model of QGP droplets

NeXusIn ultrarelativistic heavy ion collisions the system reaches local equilibrium at . Then, there’s a rapid expansion in beam direction.

0

Because of the initial fluctuation, the local equilibrium system isn’t spatially uniform.

0t

z

(a)

(PRL93,182301,2004) It may form many tubes during the fast longitudinal expansion, and finally fragment into many droplets due to the “sausage” instability and surface tension.

0=t t

(c)

(a) Local equilibrium

(b) Fast expansion

(c) Breakup to droplets

(PRC74,024908,2006) 0 0 < <t t

(b)

Assume: System fragments and forms granular source of QGP droplets at 0 0( )t

The source evolution after t0 is superposition of all the evolution of the droplets, each droplets evolves hydrodynamically.

Droplet initial distribution

Initial velocity of the droplet

2 20 0( ) exp( 2 ),P r r

Gaussian distribution for the Initial radius of the droplet

Bjorken longitudinal scaling invariant hypothesis

fm)( 2.5

We use two kinds of EOS in the hydrodynamic calculations:

EOS-I

3

c

c c

11 tanh ,

1 T

T Ts T

s T

c c170 MeV, 0.05 ,T T T

3.6,Q Hd d

c c

3

( 1) 2( 1)

250 MeVfm

B T s

EOS-II

S95p-PCE

(C. Shen, U. Heinz, P. Huovinen, H. Song, PRC 82, 054904, 2010)

Droplet evolution

0 0 fm/ct

1 02 fm/ct r

2 03 fm/ct r

3 04 fm/ct r

The droplet evolutions for the two EOSs are different, because of the much difference of the sound velocities of the two EOSs.

decdir( ) ( )dir dir ( 80 MeV)( ) (1 ) , f f

fc cT T T T T T

f cT TP T f e f e

Pion freeze-out temperature distribution

direct production

resonance decay

Assume system fragments when local density decreases at a certain value.

model parameters ：

0dir 0.85 (0.75), 1.40, 8 fm, Tf b R

30 0200 MeV ( =2.2 GeV/fm );T

dec 90 MeV,T dir MeV,10T

For RHIC 200 GeV Au-Au :NNs

6.5 (6.8) fm , 3.5 fm ;R R

0 4.3 fm c,t 0.65 (0.55),Ta

7.8 (8.0) fm , 5.4 fmR R

0 8.0 fm c,tFor LHC 2.76 TeV Pb-Pb :NNs

0.65,Ta

Pion transverse momentum spectra of the granular sources and the data of 2.76TeV Pb-Pb and 200GeV Au-Au

III. Granular source HBT results for RHIC & LHC HIC

Space-time distributions of pion source points Assume system fragments when the local density decreases at a certain value.

RHIC, 200 GeV Au-Au:NNs

6.5 (5.5) fm R0 3.5 fm4.3 fm c, Rt

7.8 (8.0) fm R0 5.4 fm8.0 fm c, Rt

LHC, 2.76 TeV Pb-Pb:NNs

0=t t

The HBT radii of granular sources agree well with the experimental data of RHIC 200GeV Au-Au and LHC 2.76TeV Pb-Pb.

HBT results

The wider distributions of the transverse and longitudinal source points for the LHC granular source lead to the larger transverse and longitudinal HBT radii than those for the RHIC granular source.

Although the larger breakup time t0 for the LHC source leads to a larger source radii and lifetime, the limited value of for the gran-ular sources and the large droplet transverse velocity lead to the result of Ro/Rs≈1 ! ( ) 2

__2 2 2out side tTR R v

__

1 2t | t t |

IV. Summary and discussions

We investigate the two-pion interferometry in ultrarelativistic heavy ion collisions in the granular source model of QGPd. The pion transverse momentum spectra and HBT radii of the granular sources agree well with the RHIC \sqrt{s_{NN}}=200 GeV Au-Au and LHC \sqrt{s_{NN}}=2.76 TeV Pb-Pb collisions.

In our model the granular sources for the LHC and RHIC collisions have the same droplet initial temperature (energy density) and the same forms of droplet distribution and velocity, but different initial system breakup time.

The larger breakup time leads to the larger longitudinal and transverse distributions of the source points, and hence leads to larger HBT radii Ro, Rs, and Rl.

However, the limited average relative emitting time of granular source and the larger droplet transverse expansion velocity lead to the ratio of the transverse HBT radii, Ro/Rs≈1.

In our granular source model, there are strong correlations between the droplet space-time and velocity. The particle transverse momentum and HBT data at the RHIC and LHC experiments give strong constraints for the granular source model.

The consistent explaination of the granular source model to these experimental dada will be helpful to understand the formation and evolution of the particle-emitting source in the ultrarelativistic heavy ion collisions.

Thanks for your attention!

Backup

2 2 2 2o sR R V

(a)

(b)

(W.N. Zhang, M.J. Efaaf, C.Y. Wong, PRC70, 2004,024903)

The freeze-out time scales with the source size (initial radius rd).

Always Ro>Rs for the hydrodynamic source

Small radius rd small source lifetime τ .

QGP initially

ρ( Xd ) ,)2/exp( 22Gd RX G dR r

Ro/Rs ≈1 for the granular source

drO Xd 2

A granular source with QGP droplets initially

out

small τ

large initial fluctuation + rapid expansion + surface tension

(PRC74,024908,2006)the rapidly increased bulk viscosity

near the QCD transition

(Torrieri,Tomasik,Mishustin,PRC77,034903,2008)

NeXus

b. Other effects may lead to the granular structure

For a set of variables of relative momentum,

Once obtaining the temperature and velocity as functions of space-time by hydrodynamics, we construct the correlation function as:

1. Generate droplet (\rho_0, z_0), (v_d⊥, v_dz), and r’_0 by MC, according to their distributions.

2. Obtain T_f according to the probability P(T_f), and get the space-time coordinates of source-point in the droplet frame based on T(r’, t’), then, obtain source-point velocities based on v’(r’, t’).

(1)

(2)

(3)

(4)

(5)

(6)

3. Generate a pion momentum (p’_x, p’_y, p’_z) based on BE distribution in the droplet frame, and obtain the momentum and space-tine coordinates of the source-point in the source frame by Lorentz transformations.

4. Repeat step 1-3 for a pion pair, calculate (q_o, q_s, q_l), and add the weights w11=(A1)^2(A2)^2= (E’1/E1)(E’2/E2) and w12=\Phi^2 in the (q_o, q_s, q_l) bins for the Cor and Uncor, respectively.

5. Repeat step 1-4 to generate the distributions Cor(q_o, q_s, q_l) and Uncor(q_o, q_s, q_l), and get the two-pion correlation function C(q_o, q_s, q_l)=Cor(q_o, q_s, q_l).

(PRC70, 024903, 2004; PRC71, 064908,2005)

decdir( ) ( )dir dir ( 80 MeV)( ) (1 ) , f f

fc cT T T T T T

f cT TP T f e f e

Pion freeze-out temperature distribution

direct production

resonance decay

Assume system fragments when local density decreases at a certain value.

Pion transverse momentum spectra of the granular sources and the data of 2.76TeV Pb-Pb and 200GeV Au-Au

model parameters ：

0dir 0.85 (0.75), 1.40, 8 fm, Tf b R

30 0200 MeV ( =2.2 GeV/fm );T

dec 90 MeV,T dir MeV,10T

For RHIC 200 GeV Au-Au :NNs

6.5 (6.8) fm , 3.5 fm ;R R

0 4.3 fm c,t 0.65 (0.55),Ta

(G.Baym,B.Friman,J.Blozot,M.Soyeur,W.Czyz,NPA407,541,1983)

7.8 (8.0) fm , 5.4 fmR R

0 8.0 fm c,tFor LHC 2.76 TeV Pb-Pb :NNs

0.65,Ta

(W. N. Zhang et al.Phys.Rev.,1995,C51:922)

)](exp[)1()exp(1),( 20

22122

1122122

11212 RaqaqppC nn

2 2 2 23 12 23 31where | |, .ij i jq p p q q q q

Event average

Comparing with exp. data

Model Calculation

Physics Results

Fragmentation and formation of granular droplets

Model CalculationAveraging

Results

The important property ─ short lifetimes ─ of granular source can survive from the final event average and lead to an observable space-time effect the HBT puzzle !

c. Model calculations

? ──

9/23

fragmentation mechanism

fragmentation signals

Because there are so many unstable factors in the earlier stages, a fragmentation may be a possible case. So, it is possible a granular source! To study the fragmentation mechanism and to look for the fragmentation signals!