Heavy ion collisions Correlations in particle production Sergei

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

Correlations: vast world, future of RHIC measurements General trend – toward many particle correlation: inclusive semiinclusive 2 -particle many particle correlations. - Anisotropic flow > two – particle correlations > three particle correlation (mixed harmonics) > 4 - and more particle correlation. - Fluctuations in conserved charges > electric charge, Outline: strangeness, baryon number - Transverse momentum correlations (/fluctuations) - Correlations due -to. Correlation the systemfunctions, evolutionfluctuations. dynamics/expansion - particle correlations in results the intermediate and high pt region. - Main from 2 particle transverse momentum correlations > Many particle correlations and the structure of the away–side measurements jet (width in >phi and eta, and multiplicity particles participating centrality incidentof energy dependence out-of-plane in the recoil). > widening of the correlations in rapidity. > Spatial distribution of due partons in the transverse plane - Correlations to transverse radial flow > High pt particle correlation relative to the reaction plane > pt correlations in-plane - Global Polarization > Elongation of rapidity correlations with centrality; narrowing - Parity (and/or CP) violation. of the Charge Balance Function. Both are based >on the analysis of correlations Azimuthal correlations & Balance function in particle production to correlations: the orientation of ‘jet tomography’) > High relative pt – low pt ( and the system orbital momentum - Physics of hadronization -Summary > Constituent quark coalescence and correlations page 2 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

2 -particle correlation functions “Inclusive” Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) “Probability” to find a “correlated” pair ISR data. Filled circles – sqrt(s) = 63 Ge. V RHIC: PHOBOS? Production via Nc clusters [e. g. independent NN collisions] Relation to fluctuations =const C (y 1 -y 2) ! “Fluctuations” are determined by the “average“ value of the correlation function over momentum region under study. page 3 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - 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 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” , |y 1 -y 2|>1 correlations as mostly “free” from jet contribution). page 4 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

: experimental observations. All data on <dpt dpt> are STAR preliminary, taken from talks of G. Westwall (STAR) at QM 2004 and Nuclear Dynamics WSs ‘ 04 and ‘ 05 Smooth dependence both on collision energy and centrality page 5 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Short and long range correlations R( ) ~ 1 - | | <R> (Y) ~ 1 - 4/3 Y, where Y= ( )max/2 “Inclusive” Blue dotted lines assume the same . Note difference in slopes (red vs blue) – broadening of R( ) with centrality ISR data. Filled circles – sqrt(s) = 63 Ge. V A way to do it better study directly as function of y 1 and y 2 page 6 S. A. Voloshin 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - max

: centrality dependence Data: G. Westfall (STAR), QM 2004 Rcc(0) 0. 66 Production via Nc clusters (Nc~Npart/2) [e. g. independent NN collisions] page 7 In a superposition of two independent collisions, the. At ratio of the probability that into a randomly midrapidity, the probability find a chosen pairisboth particles are from same particle about 60% larger if onethe particle collision to the probability that two particles has been already detected. are from different collisions is about 1. 66 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

: centrality dependence Data: G. Westfall (STAR), QM 2004 Can it be due to transverse radial flow? K. Braune et al, PLB 123 (1983) 467 Production via Nc clusters (Nc~Npart/2) [e. g. independent NN collisions] page 8 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

“Elementary” NN-collision. Correlation functions. y y it apid r Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) x Correlations are due to local charge(s) conservation, resonances, due to fluctuations in number of produced strings, e. g. number of qqcollisions. Rcc(0) 0. 66 page 9 “Probability” to find a “correlated” pair ISR 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Radial flow mean pt correlations y pp collision ity d i p a r x AA collision 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 transverse expansion “brings” totally new mechanism for momentum correlations, not present in NN-collisions 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 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) 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. page 10 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Transverse radial expansion STAR Collaboration, PRL 92, 112301 (2004) AA collision y ity id rap n=1 x 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 page 11 t r n Note: uniform source density at r < R has been assumed 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Sensitivity to the velocity profile Results for n=0. 5 and n=2 are shown Mean pt is almost insensitive to the actual velocity profile. The correlations are. In general, mean pt is sensitive to the first moment of the respective transverse rapidity distribution while the two particle correlation are measuring the second moment. page 12 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Brief comparison to data n=1 n=0. 5 Possible reasons for discrepancy: - diffusion, thermalization time - spatial source profile (not uniform density in transverse plane, e. g. cylinder shell) page 13 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

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

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 <mt> increases due to the transverse radial 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. page 15 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - 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 2 d correlations (rapidity X azimuth) Shown below – hand drawn sketch. Central Peripheral page 16 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

x correlations, II Talk by André Mischke (STAR) In central Au-Au: - jet-like correlation (short range) sits on top of a wide, nearly flat correlation in eta. d+Au, 40 -100% STAR preliminary Au+Au, 0 -5% 3 < p. T(trig. ) < 6 Ge. V/c 2 < p. T(asso. ) < p. T(trig. ) ICPAQGP 2005 17 24 November 2020 Armesto, Wiedemann et al. , PRL 93, 242301 (2004) 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) S. A. Voloshin

Azimuthal correlations Figures are shown for particles from the same NN collision. Dilution factor to be applied! n=1, T=110 Me. V 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 No momentum conservation effects has been included. Those would be important for the charge independent first harmonic correlations. page 18 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

AA collision. “Single jet tomography”. AA collision 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 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. page 19 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

summary 2 -particle transverse momentum correlation: -similar from SPS to full RHIC collision energies - smooth centrality dependence, qualitatively consistent as due to transverse radial expansion page 20 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 pt 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. 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

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

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) page 22 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Comparison to Fpt 200 Ge. V Au+Au STAR Cuts | | < 1. 0 = 360 0. 1 < pt < 2 Ge. V 200 Ge. V Au+Au STAR with PHENIX Cuts | | < 0. 35 = 2 x 90 0. 2 < pt < 2 Ge. V page 23 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

Parity violation study via 3 -particle correlations hep-ph/0406311 Looking for the effect of D. Kharzeev, hep-ph/0406125 projections onto reaction plane 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 d. N/dy~100, |a|~1%. Projections on the direction of angular momentum All effects non sensitive to the RP cancel out! Possible systematics: clusters that flow And using only one particle instead of the event flow vector note that for a rapidity region symmetric with respect to the midrapidity v 1=0 page 24 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

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

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

Short range correlations and PSD Long range ~1/N HBT ~ (dpt)(dpt)~1/(Rs*Ro*Rl) HBT/Long range ~N/(Rs*Ro*Rl) ~ PSD page 27 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin

near-side correlations (cont’d) correlation width STAR preliminary correlated yield 3 < p. T(trig. ) < 4 Ge. V/c 2 < p. T(asso. ) < p. T(trig. ) | | < 1. 0 • Significant broadening at low p. T(trig. ), disappears with increasing p. T(trig. ) • Nch(asso. ) invariant with collision system • Understanding: - Recombination effects ? - Interplay of medium-induced gluon radiation and collective longitudinal flow ? ICPAQGP 2005 28 24 November 2020 Armesto et al. , PRL 93, 242301 (2004) S. A. Voloshin, nucl-th/0312065 S. A. Voloshin

Relation to the mean pt 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) page 29 5 th International Conference on Physics and Astrophysics of GQP, Kolkata , August 8 - S. A. Voloshin