1

RapidityRapidity, , AzimuthalAzimuthal and and MultiplicityMultiplicity DependencesDependences of of Mean Transverse Mean Transverse

MomentumMomentum and and Transverse Momentum Transverse Momentum CorrelationsCorrelations

in in ++p and Kp and K++pp collisions collisions at GeVat GeV

The NA22 CollaborationThe NA22 Collaboration

Presented by Huang YanpingInstitute of Particle Physics/WuhanAug. 10, 2005

22s

Huang Yanping ISMD05,Aug.10 2

OutlineOutline IntroductionIntroduction

Motivation Measures of pt fluctuation Advantages of the data

Results and DiscussionResults and Discussion Rapidity dependence Azimuthal dependence Multiplicity dependence

SummarySummary

Huang Yanping ISMD05,Aug.10 3

Since transverse momenta of the final state particles Since transverse momenta of the final state particles are are produced after the collisionproduced after the collision and carry the and carry the information of information of system expansionsystem expansion, their fluctuations , their fluctuations are considered to be a good probe for are considered to be a good probe for QGPQGP and a trace and a trace of of local thermal equilibriumlocal thermal equilibrium..

Why e-by-e fluctuation of Why e-by-e fluctuation of transverse momentum?transverse momentum?

Provide additional valuable insight into the particle Provide additional valuable insight into the particle production mechanismproduction mechanism and and dynamical evolutiondynamical evolution, , which cannot be extracted from the conventional which cannot be extracted from the conventional single-particle inclusive distribution.single-particle inclusive distribution.

Huang Yanping ISMD05,Aug.10 4

Heavy ion collisionsHeavy ion collisionsevolution(expansion)

Collisions between twoLorentz-contracted “plates”

Cool down andfreeze out as hadrons

How does the fluctuation behave, where no QGP is How does the fluctuation behave, where no QGP is expected ?expected ?

1) What is the formed hot matter? QGP ?2) How does the system expand?

How does the transverse expansion relate to the longitudinal How does the transverse expansion relate to the longitudinal

expansion?expansion?

Huang Yanping ISMD05,Aug.10 5

MotivationMotivationevolution(expansion)

Collisions between twoLorentz-contracted “plates”

Cool down andfreeze out as hadrons

How does the fluctuation behave, where no QGP is How does the fluctuation behave, where no QGP is expected ?expected ?

1) What is the formed hot matter? QGP ?2) How does the system expand?

Mean transverse momentumMean transverse momentum Expansion velocityExpansion velocity

Transverse momentum Transverse momentum

correlationcorrelation

Transverse expansion Transverse expansion

velocityvelocity[S.A.Voloshin, Nucl.Phys.A 727,287(2003)]

How does the transverse expansion relate to the longitudinal How does the transverse expansion relate to the longitudinal

expansion?expansion?

Huang Yanping ISMD05,Aug.10 6

Current experimental Current experimental resultsresults

The non-monotonic dependence may be due to the effects of equilibration, jet quenching and radial flow saturation.

Huang Yanping ISMD05,Aug.10 7

Summary of Event-by-event <pSummary of Event-by-event <ptt> > Fluctuation MeasuresFluctuation Measures

.,inclp

pp

T

T

TF

N

pTpdynp

T

T

22

,

2 2

.,2

.,, inclpinclppnp TTTT

22., TTinclp pp

T

N

F

pTT

T

p

T

pp

2

T

dynp

dynpp pT

TT

||sgn

2,2

,

, ,Tp t i t jp p

pT,dynpT,dyn FFpTpT

pTpTpT,npT,n

<<ppt,it,ippt,jt,j>> pTpT

Huang Yanping ISMD05,Aug.10 8

Summary of Event-by-event <pSummary of Event-by-event <ptt> > Fluctuation MeasuresFluctuation Measures

pT,dynpT,dyn FFpTpT

pTpTpT,npT,n

<<ppt,it,ippt,jt,j>> pTpT

1 1,ti tj

i j i j

p p

Huang Yanping ISMD05,Aug.10 9

Measures of pMeasures of ptt correlationcorrelation

Event mean two-particle pEvent mean two-particle ptt correlation correlation

1 1,

, 21

1

ch chn n

ti tji j i j

ti tjch ch tn n

p

pp

p

R p

1 1,

, 21

1

ch chn n

ti tji j i j

ch ct

h ti tj

p p

R p pn n p

Which one is Which one is better ?better ?

Inclusive mean two-particle pInclusive mean two-particle ptt correlation correlation

Huang Yanping ISMD05,Aug.10 10

A total of 44 524 NSD eventsA total of 44 524 NSD events

0.0010.001GeV/GeV/cc < p< ptt < 10 < 10 GeV/ GeV/c c

over full over full 4π4π acceptance acceptance

Advantages of the Advantages of the datadata

Huang Yanping ISMD05,Aug.10 11

Results and Discussion

Rapidity DependenceRapidity Dependence

Azimuthal DependenceAzimuthal Dependence

Multiplicity DependenceMultiplicity Dependence

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Rapidity Dependence of <pt>

<p<ptt>, or the expansion velocity of the >, or the expansion velocity of the system is longitudinal momentum relatedsystem is longitudinal momentum related

▲▲ NA22 data NA22 data ∆∆ PYTHIAPYTHIA

Au+Au at 200GeV from star

Similar to the sea-full effect. Pythia can’t describe the effect.

The sea-gull effect is smeared in the nulceus collisions. Remnant effect exist.

Huang Yanping ISMD05,Aug.10 13

Rapidity Dependence of pt correlation

R is independent of the size and R is independent of the size and position of the position of the rapidity window.rapidity window.

is strongly dependent on is strongly dependent on rapidity.rapidity.R

The transverse The transverse correlation is longitudinal correlation is longitudinal momentum momentum independent/boost independent/boost invariant.invariant.R is well normalized and R is well normalized and more robust than more robust than R'R' . .

Huang Yanping ISMD05,Aug.10 14

Azimuthal DependenceNA22 NA4

9

Acceptance

cut

1.1<1.1<y<2.6y<2.6

0.005<pt<1.5Ge0.005<pt<1.5Gevv

collisionnucleus

+++p +p

KK+++p+pp+pp+p

pt10.91±1.54

2.2± 0.3

▲▲ NA22 dataNA22 data

∆∆ PYTHIAPYTHIA

» » <<pptt> is independent of the azimuthal size> is independent of the azimuthal size

» The dependence of R the constraint of energy and momentum conservation

Huang Yanping ISMD05,Aug.10 15

Multiplicity Dependence

Both <pt> and R decrease with increasing multiplicity.Both <pt> and R decrease with increasing multiplicity.

The smaller the event-multiplicity is, the stronger The smaller the event-multiplicity is, the stronger the event mean two-particle pthe event mean two-particle ptt correlation is. correlation is.

Huang Yanping ISMD05,Aug.10 16

Summary

Both <pBoth <ptt> and R decrease with the increasing > and R decrease with the increasing multiplicity, the smaller event-multiplicity is , multiplicity, the smaller event-multiplicity is , the stronger the correlation is.the stronger the correlation is.

The mean transverse momentum is longitudinal The mean transverse momentum is longitudinal momentum related, and the correlation is momentum related, and the correlation is longitudinal momentum independent. PYTHIA longitudinal momentum independent. PYTHIA can roughly describe the rapidity dependence of can roughly describe the rapidity dependence of R but not for <pR but not for <ptt> .> .

cut

<p<ptt> is uniformly distributed in plane, but due > is uniformly distributed in plane, but due to energy-momentum conservation, R strongly to energy-momentum conservation, R strongly depends on .depends on .

Huang Yanping ISMD05,Aug.10 17