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Transcript of S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August...
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 2 S.A. Voloshin
- 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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 3 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 4 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 5 S.A. Voloshin
: 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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 6 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 7 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 8 S.A. Voloshin
: 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?
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 9 S.A. Voloshin
“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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 10 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 11 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 12 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 13 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 14 S.A. Voloshin
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?
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 15 S.A. Voloshin
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.
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 16 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 17 S.A. Voloshin
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)
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 18 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 19 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 20 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 21 S.A. Voloshin
EXTRA SLIDES
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 22 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 23 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 24 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 25 S.A. Voloshin
Same charge /all in AuAu@200
G. Westfall
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 26 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 27 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 28 S.A. Voloshin
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
5th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8-12, 2005
page 29 S.A. Voloshin
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