2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 1 S.A. Voloshin
Anisotropic Flow and Phase transitions,
…and a little bit on fluctuations/correlations
Sergei Voloshin Wayne State University, Detroit
Outline:
- Anisotropic flow: where to look for a phase transition- v1(y) - directed flow “wiggle”- v2(pt) – constituent quark number scaling- v2(pt) – “mass splitting” and QGP- v2(energy,centrality) – approaching “hydro limit”
- v2/ vs dN/dy/S, any “wiggle/step”?
- Correlation functions and fluctuations.- Centrality dependence of <dpt dpt> and radial flow.
- Conclusions
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 2 S.A. Voloshin
...)φ)(v)(φv(dydp
Nd
dφdydp
Nd
tt
2cos2cos212
121
23
Directed flow Elliptic flow
Term “flow” does not mean necessarily “hydro” flow – used only to emphasize the collectivebehavior multiparticle azimuthal correlation.
Anisotropic flow
Fourier decomposition of single particle inclusive spectra:
X
Z b
XZ – the reaction plane
Picture: © UrQMDAnisotropic flow correlationswith respect to the reaction plane
Note large orbital angular momen-tum in the system. - Parity violation - Orbital momentum particle spin.
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 3 S.A. Voloshin
Hydro: “antiflow”, “third flow component”
Net baryon density
Csernai, Rohrich, PLB 458 (1999) 454. Magas, Csernai, Strottman, hep-ph/0010307
Brachmann, Soff, Dumitru, Stocker, Maruhn, GreinerBravina, Rischke , PRC 61 (2000) 024909
- Strongest at the softest point?- The same for pions and protons ?
rapidity
v1
flowantiflo
w
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 4 S.A. Voloshin
Third flow component as the QGP signal
L.P. Csernai, D. RohrichPRL 458 (1999) 454
“Wiggle is present only for the QGP EoS.
tx pvp 1
This calculations have been done at 11 AGeV. Would the results change for RHIC?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 5 S.A. Voloshin
Wiggle from anti-flow: development in time.
J. Brachmann Soff, Dumitru, Stocker, Maruhn, GreinerBravina, Rischke,PRC 61, 024909 (2000)
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 6 S.A. Voloshin
Wiggle from uRQMD
Marcus Bleicher, Horst StockerPLB 526, (2002) 309-314
“Rich” dependence on the particle type: baryons, antibaryons, mesons
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 7 S.A. Voloshin
Anti-flow from shadowing
Anti-flow is developingin more peripheral collisions
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 8 S.A. Voloshin
Directed flow “wiggle” in cascade models
z
x
Radial flow <x px> > 0
rapidity
px, v1
R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803
x
rapidity
px
x
Baryon stopping
“wiggle”
R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003
The wiggle is pronounced only at high energiesDoes the picture contradict FOPI resultson different isotope collisions?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 9 S.A. Voloshin
QM2002
Warning: Large systematic errors!
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 10 S.A. Voloshin
Laszlo’s slide from BNL Flow workshop ‘03
The slope of v1(eta) at eta=0is indeed as in antiflowscenario, … but also the sameas always for pions at lowerenergies
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 11 S.A. Voloshin
PHOBOS, v1(eta)
Qualitatively the samepicture from SPS energiesto highest RHIC energy.
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 12 S.A. Voloshin
STAR: ZDC-SMD
SMD is an 8 channel by 7 channel hodoscope that sits directly on the face of the 2nd ZDC module
What about ALICE, CMS, do they have something like that?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 13 S.A. Voloshin
v1(eta), v1(pt), AuAu@62 GeV,different centralities
STAR preliminary
Qualitatively the picture is very similar at different centralities
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 14 S.A. Voloshin
Comparison with models. Centrality dependence
STAR preliminarySTAR preliminary
- In order to prove the “wiggle” one needs identified particle measurementsand look for the change of sign of the slope with energy/centrality. At 62 GeV the errorbars are too large, we hope to have it such results for 200 GeV data.
Neither model describes v1(eta) close to midrapidty
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 15 S.A. Voloshin
Elliptic Flow.
XZ-plane - the reaction plane
Transverse Plane
22
22
xyxy
ε
X
Y
)cos( φ222
22
2yx
yx
pp
ppv
v2 > 0, E877, PRL 73 (1994) 2532
Sensitive to “early” times.(Free streaming kills )
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 16 S.A. Voloshin
Elliptic flow as function of …
- Integrated values of v2 noticeably increase with energy- The slope of v2(pt) increase slowly Most of the increase in integrated v2 comes from the increase in mean pt.
In mid and more central collisions elliptic flow is rather well described by hydro model
PHOBOS
It is measured vs:- collision energy- transverse momentum- centrality- rapidity- particle ID
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 17 S.A. Voloshin
Integrated vIntegrated v2 2 at different energiesat different energies
(0-40% central)(0-40% central)
We still have to analyze carefully the centrality dependence
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 18 S.A. Voloshin
Constituent quark model + coalescence
Side-notes:a) more particles produced via coalescence rather than
parton fragmentation larger mean pt…)b higher baryon/meson ratio)c lower multiplicity per “participant”
coalescence fragmentationLow pt quarks High pt quarks
Taking into account that in coalescence
and in fragmentation ,
there could be a region in quark pt where only few quarks coalesce, but give hadronsin the hadron pt region where most hadrons are produced via coalescence.
, , / 2t quark t mesonp p
, , /t quark t mesonp p z
In the low pt region density is large and most quarks coalesce: N hadron ~ N quark
2 2 / 4 2( )t tBp Bpe e In the high pt region fragmentation eventually wins:
2(( / 2) )n nt tp p
Only in the intermediate region (rare processes) coalescence can be
described by:
2
3
3
3
3
2/
Mq
q
q
M
M pppd
nd
pd
nd)2/(2)( ,2,2 tqtM pvpv
)3/(3)( ,2,2 tqtB pvpv
S.V., QM2002D. Molnar, S.V., PRL 2003
-> D. Molnar, QM2004, in progress-> Bass, Fries, Mueller. Nonaka; Levai, Ko; …-> Eremin, S.V.
R. Fries
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 19 S.A. Voloshin
Constiuent quark scaling: v2 and RCP
- Constituent quark scaling holds well. Deviations are where expected.- Elliptic flow saturates at pt~ 1 GeV, just at constituent quark scale. An accident?
Gas of constituent quarks – deconfinement !?
AuAu@62 GeVSTAR Preliminary
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 20 S.A. Voloshin
AuAu@62 GeVSTAR Preliminary
PHENIX: const. quark scaling, v2 saturates at RHIC energy
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 21 S.A. Voloshin
Are they thermalized?
S. Pratt, S. Pal , nucl-th/0409038
Two pictures correspond to the same v2 of quarks, buta) v2(B) = 3/2 v2(M) (no thermalization ?) b) v2(B) = v2(M) (freeze-out at constant phase space density)
My conclusion: constituent quark scaling - Deconfinement!- No thermalization (at least in this region of pt) (Freeze-out at constant density in the configuration space)
The same mechanism at sqrt(s_NN) 200 and 62 GeV. If thermalized, disappear at LHC??
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 22 S.A. Voloshin
v2(pt) at 200 GeV. “Mass splitting”.
Mass dependence is rather well reproduced by hydrodynamical model calculations.Note dependence on the EoS.
But qualitatively such a mass dependence will be present in any model, for example, in the constituent quark coalescence picture(heavier particle larger difference in constituent quark momenta)
Data: PHENIX, Nucl. Phys. A715, 599, 2003Hydro: P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen, S.V., Phys. Lett. B503, 58, 2001;
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 23 S.A. Voloshin
v2(pt) @ 200 and 62 GeV
0 ~ 80 % star p
reliminary
pion
Y. Bai (STAR), DNP ‘04
Pt
min. bias 0 ~ 80%
star preliminary
STAR expects good identified particle v2 measurements up to relatively high pt.Need detailed/tuned hydro calculations for different centralities and identified particles.
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 24 S.A. Voloshin
Centrality dependence. Hydro and Low Density limits
Hydro: P.F. Kolb, et al
v 2 /
5 10 b (fm)
SV & A. Poskanzer, PLB 474 (2000) 27
hydro
LDL
(pts are RQMD v2.4)
Hydro: v2~
Ollitrault, PRD 46 (1992) 229
Low Density Limit: v2~ dN/dy / A
Heiselberg & Levy, PRC C59 (1999) 2716
RHIC 160 GeV/A
SPS
SPS 40 GeV/A
b (fm)Suppressed scale!
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 25 S.A. Voloshin
v2/ and phase transitions
Centrality dependence: Sorge, PRL 82 2048 (’99), Heiselberg & Levy, PRC 59 2716 (’99)
Dependence on the particle density in the transverse plane: S.V. & A. Poskanzer, PLB 474 (2000) 27
“Cold” deconfinement?
Uncertainties:Hydro limits: slightly dependon initial conditionsData: no systematic errors,shaded area –uncertainty incentrality determinations.Curves: “hand made”
E877 NA49
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 26 S.A. Voloshin
Heinz, Kolb, Sollfrank
30000400402 /*..dydN
v
Hydro limits
RHIC 160 GeV/A
SPS
SPS 40 GeV/A
b (fm)Suppressed scale!
Hydro: P.F. Kolb, et al
v 2 /
Hydro: v2~ Ollitrault, PRD 46 (1992) 229
Low Density Limit: v2~ dN/dy / SHeiselberg & Levy, PRC C59 (1999) 2716
Questions to address: - is it saturating?- what happens at SPS energies? Any ‘wiggle’?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 27 S.A. Voloshin
“Cold” deconfinement, color percolation?
Percolation point by H. Satz, QM2002
CERN SPS energies b ~ 4 fmRHIC: b ~ 7 fm
There is a need for the “next generation”of this plot: better estimates of epsilon,adding more data (in particular 62 GeV)
It is a real pity that NA49 measurements have so large systematic uncertainty. Need detector with better azimuthal acceptance (could be just a simple extra detector used to determine the RP) .
FT RHIC?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 28 S.A. Voloshin
But is it surprising?:
pppp
mmp
pv
5~;2~
;5~;~2
v2 stays the same?
STAR SQM04
Charm flow (via electron measurements)
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 29 S.A. Voloshin
Correlations/fluctuations
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 30 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
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
)(1 yCconst
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 31 S.A. Voloshin
<pt> fluctuations: 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 32 S.A. Voloshin
Multiplicity fluctuations
1)()(
),(~,
~2
~~2)1()1(
11
2
22,
Y bbY aa
Y baba
abdyndd
ddRRRR
nn
nn
n
nn
n
nn
“Charge” fluctuations
42
14
nnRRRD )
~~~(
2
21
21
212
2
22
21
21
212
212
2
112
2
)r(nnD
nn
δnδn
n
)n(
n
)n(
r
)r(
n
nr
!
- Free from “volume” fluctuations - Fails at small < n2 >
- < n++ n-> - “used” multiplicity, subject to cuts and acceptance
Rnn
σω n
n
~1
2
Particle ratios:
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 33 S.A. Voloshin
Comparison to PHENIX, Fpt (slide from G. Westfall (STAR), QM’04)
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
mixedT
mixedTrealT
mixedT
mixedTrealTpt
T
TT F
,
,,
,
,,
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 34 S.A. Voloshin
STAR Preliminary
Elliptic flow contribution to <dpt dpt>
Shengli Huang (STAR)USTC RHIC Workshop,Hefei, China , Oct. 2004
y
xIn-plane
Out-of-plane
Could be better to plot <dpt dpt> /<pt>^2
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 35 S.A. Voloshin
correlations: elongation in
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
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
A way to do it better study directly as function of y1 and y2
2,1, tt pp
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 36 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 37 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
ISR2
6.1)1( nnn
At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected.
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 38 S.A. Voloshin
Radial flow 2- particle 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-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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 39 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 40 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 41 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 42 S.A. Voloshin
Extracting Near-Side Jet Yields
d+Au, 40-100%
Au+Au, 0-5%
STAR preliminary
3 < pT(trig) < 6 GeV2 < pT(assoc) < pT(trig)
In Au+Au, jet-like correlation sits on top of an additional, approximately flat correlation in
D. Magestro (STAR) –Hard Probes 2004
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 43 S.A. Voloshin
Brief comparison to data: centrality dependence
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
2,1, tt pp
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 44 S.A. Voloshin
correlation 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.)
1. Avoid using ratios (n+/n-, K+/K0,…), use to get rid of “volume” fluctuations and be free from problems related to low multiplicities.2. If use normalized variance – correct for the efficiency.
abbbaa RRR~
2~~
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 45 S.A. Voloshin
EXTRA SLIDES
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 46 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 (narrowed) 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.
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 47 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?
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 48 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 49 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 50 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
2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005
page 51 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