1. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page1 Heavy ion collisions: Correlations in particle production Sergei A. Voloshin Wayne State University, Detroit, Michigan

2. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page2 - 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 p t 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 p t 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 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 > p t 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

3. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page3 2-particle correlation functions Production via N c clusters [e.g. independent NN collisions]  =const  C  (y 1 -y 2 ) ! Relation to fluctuations “Fluctuations” are determined by the “average“ value of the correlation function over momentum region under study. “Inclusive” ISR data. Filled circles – sqrt(s) = 63 GeV RHIC: PHOBOS? Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) “Probability” to find a “correlated” pair

4. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page4 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 Possibilities: - test scaling with N ch, N part, N bin, 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”, |y 1 -y 2 |>1 correlations as mostly “free” from jet contribution).

5. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page5 : experimental observations. All data on are STAR preliminary, taken from talks of G. Westwall (STAR) at QM2004 and Nuclear Dynamics WSs ‘04 and ‘05 Smooth dependence both on collision energy and centrality

6. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page6 Short and long range correlations ISR data. Filled circles – sqrt(s) = 63 GeV “Inclusive” R (  ) ~ 1 -  |  |  (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 y 1 and y 2

7. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page7 R cc (0)  0.66 : centrality dependence Production via N c clusters (N c ~N part /2) [e.g. independent NN collisions] Data: G. Westfall (STAR), QM2004 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

8. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page8 : centrality dependence Production via N c clusters (N c ~N part /2) [e.g. independent NN collisions] Data: G. Westfall (STAR), QM2004 K. Braune et al, PLB 123 (1983) 467  Can it be due to transverse radial flow?

9. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page9 “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 R cc (0)  0.66 Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) “Probability” to find a “correlated” pair ISR

10. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page10 Radial flow  mean p t 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 p t )  Position-momentum correlations caused by transverse expansion “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 m t  decrease in 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)

11. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page11 Transverse radial expansion Blast wave parameterization (Schnedermann, Sollfrank, Heinz, PRC 48, 2462 (1993), d 3 n/d 3 p ~ e -E/T ) of the source at freeze-out: Parameters: T-temperature, velocity profile  t  r n STAR Collaboration, PRL 92, 112301 (2004) AA collision Note: uniform source density at r < R has been assumed y rapidity x n=1

12. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page12 Sensitivity to the velocity profile Results for n=0.5 and n=2 are shown Mean p t is almost insensitive to the actual velocity profile. The correlations are. In general, mean p t is sensitive to the first moment of the respective transverse rapidity distribution while the two particle correlation are measuring the second moment.

13. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page13 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

14. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page14 Initial and freeze-out configurations Final initial Uncertainty: particles are at the same position at the moment of production, but the blast wave 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?

15. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page15 Rapidity correlations How to disentangle “initial” correlations at the parton production stage and obtained due to the transverse expansion? - Charge dependent and charge independent correlations. - Correlation of conserved charges (Balance Functions). In this case the correlations existed 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 As increases due to the transverse radial flow, the balance function gets narrower. For the BW parameters used above, indeed increases for about 15-20%, but the centrality dependence is somewhat different from what is observed in the narrowing of the Balance Function.

16. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page16  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.   PeripheralCentral

17. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page17 In central Au-Au: - 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 < p T (trig.) < 6 GeV/c 2 < p T (asso.) < p T (trig.) Talk by André Mischke (STAR) Armesto, Wiedemann et al., PRL93, 242301 (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” scenario everything would widen, in “transverse” flow widening is charge independent, but charge balance function would shrink (similar to lower pt’s)

18. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page18 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 transverse flow, > 0.25, would contradict “non-flow” estimates in elliptic flow measurements n=1, T=110 MeV

19. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page19 AA collision. “Single jet tomography”. The plot on the right shows particle azimuthal distribution (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 relative to 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

20. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page20 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) particle rapidity, transverse momentum, and azimuthal correlations. 2.This phenomenon provides a natural (at present, qualitative) explanation of the centrality dependence of mean p t pseudorapidity/azimuthal angle correlations. It can be further used to study the details of the system equilibration/thermalization and evolution (e.g. thermalization time, velocity profile, etc.) 3.Transverse radial flow “push” of particles created in the same NN collision where hard scattering occurred + jet quenching leads to azimuthal correlations of high pt “trigger” particle with “soft” particles at rather different rapidity. The mean transverse momentum of the associated particles would be a measure of how deep in the system the hard collision occurred. 2-particle transverse momentum correlation : -similar from SPS to full RHIC collision energies - smooth centrality dependence, qualitatively consistent as due to transverse radial expansion

21. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page21 EXTRA SLIDES

22. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page22 Ebye and inclusive approaches Most of the present measurements are done this way Would be better, easier to analyze theoretically. (! Numerically both are very close)

23. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page23 Comparison to F pt 200 GeV Au+Au STAR with PHENIX Cuts |  | < 0.35  = 2x90  0.2 < p t < 2 GeV 200 GeV Au+Au STAR Cuts |  | < 1.0  = 360  0.1 < p t < 2 GeV

24. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page24 Parity violation study via 3-particle correlations a > 0  preferential emission along the angular momentum The 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 note that for a rapidity region symmetric with respect to the midrapidity v 1 =0 hep-ph/0406311 All effects non sensitive to the RP cancel out! Possible systematics: clusters that flow Looking for the effect of D. Kharzeev, hep-ph/0406125

25. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page25 Same charge /all in AuAu@200 G. Westfall

26. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page26 Short and long range correlations II ISR data. Filled circles – sqrt(s) = 63 GeV “Inclusive” 2-particle correlation functions: Would it be OK to approximate R(  ) ~ const + a  (  ) ??? “Global temperature fluctuations” “short range correlations” max

27. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page27 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

28. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page28  near-side correlations (cont’d) Significant broadening at low p T (trig.), Significant broadening at low p T (trig.), disappears with increasing p T (trig.) disappears with increasing p T (trig.) N ch (asso.) invariant with collision system N ch (asso.) invariant with collision system Understanding: - Recombination effects ? Understanding: - Recombination effects ? - Interplay of medium-induced - Interplay of medium-induced gluon radiation and collective gluon radiation and collective longitudinal flow ? longitudinal flow ? correlation width Armesto et al., PRL93, 242301 (2004) S.A. Voloshin, nucl-th/0312065 STAR preliminary correlated yield 3 < p T (trig.) < 4 GeV/c 2 < p T (asso.) < p T (trig.) |  | < 1.0

29. S.A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata, August 8-12, 2005page29 Relation to the mean p t fluctuations 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 charged particles and only positive or only negative, even if there is no difference between charges in terms of correlations)