S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page1 Heavy ion collisions: Correlations in particle

5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005

page 1 S.A. Voloshin

Heavy ion collisions:Correlations in particle

production

Sergei A. Voloshin

Wayne State University, Detroit, Michigan



- Anisotropic flow > two – particle correlations > three particle correlation (mixed harmonics) > 4- and more particle correlation.- Fluctuations in conserved charges > electric charge, strangeness, baryon number- Transverse momentum correlations (/fluctuations)- Correlations due to the system evolution dynamics/expansion- particle correlations in the intermediate and high pt region. > Many particle correlations and the structure of the away–side jet (width in phi and eta, multiplicity of particles participating in the recoil). > Spatial distribution of partons in the transverse plane > High pt particle correlation relative to the reaction plane - Global Polarization - Parity (and/or CP) violation. Both are based on the analysis of correlations in particle production relative to the orientation of the system orbital momentum- Physics of hadronization > Constituent quark coalescence and correlations

- Anisotropic flow > two – particle correlations > three particle correlation (mixed harmonics) > 4- and more particle correlation.- Fluctuations in conserved charges > electric charge, strangeness, baryon number- Transverse momentum correlations (/fluctuations)- Correlations due to the system evolution dynamics/expansion- particle correlations in the intermediate and high pt region. > Many particle correlations and the structure of the away–side jet (width in phi and eta, multiplicity of particles participating

in the recoil). > Spatial distribution of partons in the transverse plane > High pt particle correlation relative to the reaction plane - Global Polarization - Parity (and/or CP) violation. Both are based on the analysis of correlations in particle production relative to the orientation of the system orbital momentum- Physics of hadronization > Constituent quark coalescence and correlations

Correlations: vast world, future of RHIC measurements

General trend – toward many particle correlation: inclusive semiinclusive 2-particle many particle correlations.

in-plane

out-of-plane

L

Outline:

- Correlation functions, fluctuations.- Main results from 2 particle transverse momentum correlations measurements > centrality and incident energy dependence > widening of the correlations in rapidity.- Correlations due to transverse radial flow > pt correlations > Elongation of rapidity correlations with centrality; narrowing of the Charge Balance Function. > Azimuthal correlations & Balance function in > High pt – low pt correlations: ( and ‘jet tomography’)

-Summary



2-particle correlation functions

cc

ccccNc

cccNc

cNc

N

R

yyN

yyNyyNNyyNR

yyNNyyNyyyNy}1{

2}1{

11}1{

12

2}1{

11}1{

12

2}1{

11}1{

121}1{

2}{

2}1{

11}1{

121}1{

221}{

2}1{

1}{

1

)()(

)()()()()1(),(

)()()1(),(),();()(

Production via Nc clusters [e.g. independent NN collisions]

Rnn

n)n(nn

n

nn)n(n

n

nn

n

σω n

n

~

11

1

1

2

2

2222

)()(

),(~

211121

2121

yydydy

yyCdydyR

=const C(y1-y2) !

Relation to fluctuations

“Fluctuations” are determined by the “average“ valueof the correlationfunction over momentumregion under study.

“Inclusive”

ISR data. Filled circles – sqrt(s) = 63 GeVRHIC: PHOBOS?

)1(),(;)( 212211 nnyydydynydy

)()(),(),( 211121221 yyyyyyC

)(

),(),(

11

2121 y

yyCyyB

)()(

),(),(

2111

2121 yy

yyCyyR

Distribution of “correlated” pairs:

Distribution of “associated” particles (2) per “trigger” particle (1)

“Probability” to find a “correlated” pair



Observables and observables.

What are the main requirements for a good observable?-- be sensitive to the physics under study -- be defined at the “theoretical level”, be detector/experiment independent -- have clear physical meaning-- not to be limited in scope, provide new venues for further study

;tt,it,i ppδp Possibilities:- test scaling with Nch, Npart, Nbin, etc.-Particles “1” and “2” could be of different type (e.g. same/opposite charge), - taken from different rapidity/azimuthal angle regions (e.g. “same-side” , |y1-y2|>1 correlations as mostly “free” from jet contribution).

,2,1, tt pp



: experimental observations.

All data on <dpt dpt> are STAR preliminary, taken from talksof G. Westwall (STAR) at QM2004and Nuclear Dynamics WSs ‘04 and ‘05

2,1, tt pp

Smooth dependence both on collisionenergy and centrality



Short and long range correlations

ISR data. Filled circles – sqrt(s) = 63 GeV

“Inclusive” R() ~ 1 - ||<R> (Y) ~ 1 - 4/3 Y,where Y= ()max/2

max

Blue dotted lines assume the same .Note difference in slopes (red vs blue) –broadening of R() with centrality

A way to do it better study directly as function of y1 and y2

2,1, tt pp



Rcc(0)0.66

: centrality dependence

Production via Nc clusters (Nc~Npart/2) [e.g. independent NN collisions]

Data: G. Westfall (STAR), QM2004

NNNNcoll

NNN

nnnN

nnD

coll )1()1(

)1(2

NNttNAAtt ppDppcoll 2,1,2,1,

1)1(~

2

n

nnR

2,1, tt pp

At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected.

In a superposition of two independent collisions,the ratio of the probability that in a randomly chosen pair both particles are from the same collision to the probability that two particles are from different collisions is about 1.66



: centrality dependence

Production via Nc clusters (Nc~Npart/2) [e.g. independent NN collisions]

Data: G. Westfall (STAR), QM2004

NNNNcoll

NNN

nnnN

nnD

coll )1()1(

)1(2

NNttNAAtt ppDppcoll 2,1,2,1,

1)1(~

2

n

nnR

2,1, tt pp

K. Braune et al, PLB 123 (1983) 467

,1 ,2t t

t

p pR

p

014.0/2

2,1, ttt ppp

Can it be due to transverse radial flow?



“Elementary” NN-collision. Correlation functions.

Correlations are due to local charge(s) conservation, resonances, due to fluctuations in number of produced strings, e.g. number of qq-collisions.

x

y

rapidity

Rcc(0)0.66

)1(),(

)(

21221

1

nnyydydy

nydy

)()(),(),( 211121221 yyyyyyC

)(

),(),(

11

2121 y

yyCyyB

)()(

),(),(

2111

2121 yy

yyCyyR

Distribution of “correlated” pairs:

Distribution of “associated” particles (2) per “trigger” particle (1)

“Probability” to find a “correlated” pair

ISR

26.1)1( nnn



Radial flow mean pt correlations

All particles produced in the same NN-collision (qq-string) experience the transverse radial “push” that is(a) in the same direction (leads to correlations in phi)(b) the same in magnitude ( correlations in pt) Position-momentum correlations caused by transverseexpansion “brings” totally new mechanism for momentum correlations, not present in NN-collisions

x

y

rapidity

pp collision

AA collision

In what follows, radial expansion is treated as given. Not necessarily as due to pressure in thermalized matter, could be considered a la “parton wind”; but numerical calculations are done in the blast wave model.

Just a few “details”:-Long range rapidity correlations (“bump”- narrow in phi and wide in rapidity, charge independent)-Stronger 2-particle pt correlation in narrow phi bins-Narrowing of the charge balance function( -- increase in mt decreasein rapidity separation) [same as in S. Pratt et al, in “late hadronization scenario”]- Charge correlations in phi. Azimuthal Balance function

Everything evolving with centrality (radial flow)

)sinh( ymp tz



Transverse radial expansion

])cos()sinh()cosh()cosh(

exp[)cosh(0

3

3

T

pyymyymddyrdr

pd

nEd stttstR

stss

Blast wave parameterization (Schnedermann, Sollfrank, Heinz, PRC 48, 2462 (1993), d3n/d3p ~ e-E/T)of the source at freeze-out:

Parameters: T-temperature, velocity profile t r n

STAR Collaboration, PRL 92, 112301 (2004)

)sinh();cosh(;)()(0

012

3

tt

ttt

t

R

tttt T

p

T

mIKmrdr

pddy

nd

AA collision

Note: uniform source densityat r < R has been assumed

y

rapidity

xn=1



Sensitivity to the velocity profilen

t r

Results for n=0.5 and n=2 are shown

Mean pt is almost insensitive to the actualvelocity profile.The correlations are.

In general, mean pt is sensitive to the first momentof the respective transverse rapidity distribution while the two particle correlation are measuring the second moment.

)44/()2( 222 nntt



Brief comparison to data

Possible reasons for discrepancy:- diffusion, thermalization time - spatial source profile (not uniform density in transverse plane, e.g. cylinder shell)

n=1

n=0.5



Initial and freeze-out configurations

Finalinitial

Uncertainty: particles are at the same positionat the moment of production, but the blastwave parameterization is done at freeze-out

Smearing would depend on the - thermalization time (which is supposedly small)- diffusion during the system evolution before freeze-out- non-zero “expansion velocity” in pp

Should we take it as a possibility to study all the above effects?



Rapidity correlations

How to disentangle “initial” correlations at the parton production stage and obtaineddue to the transverse expansion? - Charge dependent and charge independent correlations.

- Correlation of conserved charges (Balance Functions). In this case the correlationsexisted already at the production moment would be modified by radial flow.

- Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction.

Charge Balance function

ymymp ttz )sinh(

As <mt> increases due to the transverseradial flow, the balance function gets narrower.

For the BW parameters used above,<mt> indeed increases for about 15-20%,but the centrality dependence is somewhat different from what is observed in the narrowing of the Balance Function.



x correlations

- Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction. For those, one needs 2d correlations (rapidity X azimuth) Shown below – hand drawn sketch.

Peripheral Central



In central Au-Au: In central Au-Au:

- jet-like correlation (short range) - jet-like correlation (short range)

sits on top of a wide, nearly flat sits on top of a wide, nearly flat

correlation in eta.correlation in eta.

d+Au, 40-100%

Au+Au, 0-5%

STAR preliminary

3 < pT(trig.) < 6 GeV/c2 < pT(asso.) < pT(trig.)

Talk by AndrTalk by Andréé Mischke (STAR) Mischke (STAR)

Armesto, Wiedemann Armesto, Wiedemann et al., et al., PRL93, 242301 PRL93, 242301 (2004) (2004)

x correlations, II

Q: How one could distinguish between two scenarios?A: Correlations. Check for charge dependent and charge independent correlations. In “longitudinal flow” scenarioeverything would widen, in “transverse” flow widening is charge independent, but charge balance function would shrink (similarto lower pt’s)



Azimuthal correlations

Figures are shown for particles from the same NN collision. Dilution factor to be applied!

No momentum conservation effects has been included. Those would be important for the charge independent first harmonic correlations.

First and second harmonics of the distribution on the left

! - the large values of transverseflow, > 0.25, would contradict “non-flow” estimates in elliptic flow measurements

n=1, T=110 MeV



AA collision. “Single jet tomography”.

The plot on the right shows particle azimuthaldistribution (integrated over all pt’s) with respect to the boost direction.In order to compare with data it should be also convoluted with jet azimuthal distribution relativeto radial direction.

In this picture, the transverse momentum of the (same side, large ) associated particles would be a measure of the space position the hard scattering occurred

AA collision



summary

1. Transverse radial flow leads to strong space-momentum correlation. In combination with space correlations between particles created in the same NN collision, it leads to characteristic two (and many) particlerapidity, transverse momentum, and azimuthal correlations.

2. This phenomenon provides a natural (at present, qualitative) explanation of the centrality dependence of mean pt pseudorapidity/azimuthal anglecorrelations. It can be further used to study the details of the systemequilibration/thermalization and evolution (e.g. thermalization time, velocityprofile, etc.)

3. Transverse radial flow “push” of particles created in the same NN collisionwhere hard scattering occurred + jet quenching leads to azimuthal correlations of high pt “trigger” particle with “soft” particles at ratherdifferent rapidity. The mean transverse momentum of the associated particles would be a measure of how deep in the system the hard collisionoccurred.

2-particle transverse momentum correlation:-similar from SPS to full RHIC collision energies- smooth centrality dependence, qualitatively consistent as due totransverse radial expansion



EXTRA SLIDES



Ebye and inclusive approaches

i

itt pM

p ,

1k

kt

evt p

Np 1

.ppδp tt,it,i ;δpδp jijt,it,

kk

k iit

ttt,it,i M

ppppδp

,

;

),,,(

)],(),(),,,([

),,,(

),,,(

22,11,22,21,1

22,111,122,11,22,1,2,21,1

22,11,22,21,1

22,11,22,1,2,21,1

2,1,

21

21

21

21

tttt

tttttttt

tttt

tttttt

tt

ppdpddpd

ppppppdpddpd

ppdpddpd

ppppdpddpd

pp

Most of the present measurementsare done this way

Would be better, easier to analyze theoretically.

(! Numerically both are very close)

)2,1(C



Comparison to Fpt

TTT

FptT,realT,mixed

T,mixedT,realT,mixed

T,mixed

200 GeV Au+AuSTAR withPHENIX Cuts

|| < 0.35 = 2x900.2 < pt < 2 GeV

200 GeV Au+AuSTAR Cuts

|| < 1.0 = 3600.1 < pt < 2 GeV



Parity violation study via 3-particle correlations

sin21 ad

dN

a > 0 preferential emission along the angular momentumThe sign can vary event by event, a~Q/N, where Q is the topological charge, |Q|=1,2,…at dN/dy~100, |a|~1%.

And using only one particle instead of the event flow vector

projections onto reaction plane Projections on the direction of angular momentum

)22cos()()2cos(

)sin()sin()cos()cos(

2,1,12

2222

RPbababa

baba

aavv

note that for a rapidity region symmetric with respect to the midrapidity v1=0

hep-ph/0406311

All effects non sensitive to the RPcancel out!

Possible systematics:clusters that flow

cbabacba

cbcacbca

vaavv ,2,1,1 )()2cos(

)sin()sin()cos()cos(

L

Looking for the effect ofD. Kharzeev, hep-ph/0406125



Same charge /all in AuAu@200

G. Westfall



Short and long range correlations II

ISR data. Filled circles – sqrt(s) = 63 GeV

“Inclusive”

2-particle correlation functions:

)1(),(

)(

1)()(

),(),(

21221

1

2111

21221

nnyydydy

nydy

yy

yyyyR

Would it be OK to approximate

R() ~ const + a() ???

“Global temperaturefluctuations” “short range

correlations”

max



Short range correlations and PSD

Long range ~1/N

HBT ~ (dpt)(dpt)(dpt)~1/(Rs*Ro*Rl)

HBT/Long range ~N/(Rs*Ro*Rl) ~ PSD



near-side correlations (cont’d)near-side correlations (cont’d)

• Significant broadening at low pSignificant broadening at low pTT(trig.), (trig.), disappears with increasing pdisappears with increasing pTT(trig.)(trig.)• NNchch(asso.) invariant with collision system (asso.) invariant with collision system • Understanding: - Recombination effects ?Understanding: - Recombination effects ?

- Interplay of - Interplay of medium-induced medium-induced gluon radiation gluon radiation and collective and collective longitudinal flow ?longitudinal flow ?

correlation width

Armesto et al., Armesto et al., PRL93, 242301 PRL93, 242301 (2004) (2004) S.A. Voloshin, nucl-th/0312065S.A. Voloshin, nucl-th/0312065

STAR preliminarySTAR preliminary correlated yield

3 < pT(trig.) < 4 GeV/c2 < pT(asso.) < pT(trig.)

|| < 1.0



2,

2,,,

22

2,,

2,2

222

11

1

1

dynamicalplstatisticapjijtitt

tji

jtiti

itttp

tt

t

M

MppMMpM

M

ppppM

pp

Relation to the mean pt fluctuations

i

itt pM

p ,

1k

kt

evt p

Np 1

MM

pp inclusivepttlstatisticap

t

t

2,

222

,

jijt,t,i2

dynamical,p δpδpσt

Statistical fluctuations = those in the case of independent particle production with the same single-particle inclusive distributions.

-The relation is approximate

-M – the number of particles used, subject to acceptance/track quality cuts (e.g. differs about factor of two for all chargedparticles and only positive or only negative, even if there is no difference between charges in terms of correlations)

inclp

tt

inclpppp

t

tttt

Mpp

M

,

2,1,

,

2

Documents

S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page1 Heavy ion collisions: Correlations in particle