Jinghua FuInstitute of Particle Physics, CCNU, Wuhan TUHEP, Tsinghua University, Beijing

On the Measurement of Event Mean Pt Fluctuations

Motivation Analytical Considerations Monte Carlo Simulations Summary

2/14

Transverse Momentum and Temperature Fluctuations

Single event transverse momentum distribution from thermal model

Transverse momentum fluctuations sensitive to temperature fluctuations

T

pmppP tttT

22

exp~)(

)(~

~)(

22 Tp

TdppPpp

Tt

ttTtTt

Aug09-15 ISMD2005, kromeriz 3/14

Experimental Event-by-Event Pt Fluctuation Measurements

Event average pt fluctuations

Observables

stat22

dyn2

1

)()()(

1

ttt

it

ppp

n

i tp

MMM

pn

M

2,

2dynam ,,,, npppp tTtt

F

stat2 )(

tpMdyn

2 )(tp

M )(2

tpM= -

2,

22,

2,

2

,

2

)(:

:

)(:

)(:49

,

,,

inclptpparnp

M

MM

p

par

inclp

par

tppar

p

inclp

par

tppar

p

ttt

mixeventtp

mixeventtpdatatp

t

tt

t

t

t

t

pMnSTAR

FPHENIX

nn

pMnCERES

n

pMnNA

Observables

Measurement

sqrt(sN

N)T/<T>,

Most central

T/<T>,

At the peak

PHENIX 200 1.8% 3.7%

STAR 130 1.7% 3.8%

CERES 17 1.3% 2.2%

NA49 17 0.6% 1.7%

J.T.Mitchell QM2004

Results from different experiments

Aug09-15 ISMD2005, kromeriz 6/14

Ttp pM

t

2dyn

2 )( ?

n

iitp p

nM

t1

,

1)( tTttTt

pPppdp

Are they the same?

Aug09-15 ISMD2005, kromeriz 7/14

Analytical Considerations

Variance of theoretical event mean pt

Factorial moments

M

m mtTmttTttTtpPppPpdpp

1

222 )()()(

M

mpmmmp

mT

M

m

pm

pmT

n

pnnnppp

11

)1()1()()(

M

m

mmmpmT

M

m

pm

pmT pnnn

pnnnppp

11 )1()1(

)1()1()()(

(Fixed multiplicity)

(Non-Fixed Multiplicity)

Aug09-15 ISMD2005, kromeriz 8/14

(1) Fixed Multiplicity

tjttit

p

n

i it

n

i itTt

pppp

Mn

n

pnn

pnn

p

t

,,

dyn

2

stat1 ,2

1 ,22

1

)1(

1

)1(

1

jtitpTtppM

n

np

t ,,dyn

22

1

Aug09-15 ISMD2005, kromeriz 9/14

(2) Non-Fixed Multiplicity

n

i itp1 ,

dyn1 ,2

dyn

2

dyn1 ,22

npM

npp

n

i itp

n

i itTt

t

measure fluctuations of measure fluctuations of

dyn1 ,

2 npn

i it

dyn1 ,

2 npn

i it

n

i it np1 ,

Aug09-15 ISMD2005, kromeriz 10/14

HIJING Monte Carlo Simulations

2,000,000 min-bias Au-Au collision events

pseudo-rapidity

transverse momentum

GeV200NNS

1||

cpt GeV/22.0

11/14

Fixed Multiplicity

Multiplicity fixed at n=5,10,20,50,100, 200,500 Theoretical event mean

transverse momentum fluctuations has a similar results as dynamical fluctuations of event average transverse momentum.

In measuring event average transverse

momentum fluctuations, the statistical contribution is dominant even for high multiplicity sample

12/14

Non-FixedMultiplicity

Number of participants fixed from peripheral to central collisions at 10,50,100,150,200,250,300

Hijing simulations show that is large than for fixed number of participant event samples, their dependence on average multiplicity are similar

dyn1 ,

2 npn

i it

dyn1 ,

2 npn

i it

dyn1 ,2 np

n

i it

Aug09-15 ISMD2005, kromeriz 13/14

First and Second Order Moments

dyn1 ,2

dyn2

dyn1 ,22

)( npM

npp

n

i itp

n

i itTt

t

npM

npnppp

n

i itp

n

i it

n

i ittTt

t

1 ,

1 ,1 ,incl

First Order:

Second Order:

Summary

For fixed multiplicity

For non-Fixed multiplicity

and other similar observables can’t be directly related to

Measure both of them in Ebye analysis

dyn2 )(

tpM

dyn2

,,2 )(

tpjtitTtMppp

dyn2

dyn1 ,22 )(

tp

n

i itTtMnpp

)(2 T

Thanks ! References: PRC68,064904(2003)

PRC72,017901(2005)

Aug09-15 ISMD2005, kromeriz 15/14

Summary

221111

22121111212,1221

dyn1 ,22

)()(

)()()(

)()(

tttt

tttttttttttt

n

i itTt

dppdpp

dpppdpppdpdppppp

npp

221111

221111212,12

12)()(

)()()(

tttt

tttttttt

dppdpp

dppdppdpdpppR

Robust Variance: