q Workshop of European Group on Ultrarelativistic Heavy Ion Physics from STAR to ALICE Close velocity Correlations Jan Pluta, Warsaw University of Technology JINR, Dubna

The starting point

Podgorecki, Kopylov, Smorodinski Dubna, 1974 Weekly meeting of propane bubble chamber group Lednicky and Lyuboshitz solved the problem of final state interaction Kopylov and Podgoretsky settled the basics of correlation femtoscopy: correlation function, mixing technique, role of space-time charakterist Grishin, propane bubble chamber group and others in Dubna - measured the two- particle correlations

q out q side q long R side R long R out x1x1 x2x2 p1p1 p2p2 Two-particle interferometry: p-space separation  space-time separation HBT: Quantum interference between identical particles q (GeV/c) C (q) 1 2 –Final-state effects (Coulomb, strong) also can cause correlations, need to be accounted for Gaussian model (3-d): The basic notions

HBT at RHIC...

HBT Excitation Function

“RHIC HBT puzzle” unexpected (small) sizes R out /R side = (approx.) 1 P t dependence do not agree with models The same P t dependence for pp, dAu and AuAu STAR 130 GeV PHENIX 130 GeV

RHIC/AGS/SPS Systematics ≈ 400 MeV (RHIC) ≈ 390 MeV (SPS) Lisa, Pratt, Soltz, Wiedemann, nucl-ex/ STAR DATA STAR DATA - prelim.) Pion HBT radii from different systems and at different energies scale with (dN ch /dη) 1/3 Z.Chajęcki, QM’2005

System expansion: Initial vs Final Size Proton initial size = 0.89 fm from e-scattering Smooth expansion of the system from p+p to Au+Au AuAu: system expands pp (dAu): no or less expansion Collisions at 200GeV only

Transverse mass dependence in Au+Au In Au+Au p T (m T ) dependence attributed to collective expansion of the source STAR, PRC 71 (2005) Calc. with Blast-Wave - Retiere, Lisa, PRC 70 (2004)

Consistency check on flow – kaons

Hania Gos, Kromeriz’05

More confirmation STAR preliminary

Surprising („puzzling”) scaling  All p T (m T ) dependences of HBT radii observed by STAR scale with pp although it’s expected that different origins drive these dependences HBT radii scale with pp Scary coincidence or something deeper? pp, dAu, CuCu - STAR preliminary Ratio of (AuAu, CuCu, dAu) HBT radii by pp

Hania Gos, Kromeriz’05

Nonidentical particle correlations – the asymmetry analysis k* 1 Catching up Effective interaction time larger Stronger correlation Moving away Effective Interaction time smaller Weaker correlation “Double” ratio Sensitive to the space-time asymmetry in the emission process R.Lednicky, V. L.Lyuboshitz, B.Erazmus, D.Nouais, Phys.Lett. B373 (1996) 30. C-C- C+C+ C+C+ C-C- Kinematics selection along some direction e.g. k Out, k Side, cos(v,k) Heavier particle faster Lighter particle faster Adam Kisiel, Fabrice Retiere

Pion-Kaon at 200 AGeV Good agreement for same-charge combinations Clear emission asymmetry signal Out double ratio Side double ratio Sigma: 17.3 ± 0.8 fm Mean: -7.0 ± 1.2 fm STAR preliminary syst syst syst syst. kaon fasterpion faster

STAR preliminary Λ peaks Mean: -7.4 ± 0.9 fm Sigma: 15.1 ± 0.4 fm Pion-Proton 130 AGeV Good agreement for identical and opposite charge combinations We observe Lambda peaks at k*~decay momentum of Λ Out double ratio Side double ratio syst syst syst syst. Fit assumes source is a gaussian in r* out proton fasterpion faster

Hania Gos, Kromeriz’05

Origins of asymmetry Measures asymmetry in pair rest frame is a combination of time and space shifts in source frame In heavy-ion collisions one expects difference in emission time from resonance decays pion average = 16.1 kaon average = 14.8 time shift = 1.3 pionemissiontimes kaonemissiontimes primordial all all primordial THERMINATOR calculation Adam Kisiel, Kromeriz’05

Space asymmetry from flow Transverse momentum of particles is composed of the thermal (randomly distributed) and flow (directed “outwards”) components With no flow average emission point is at center of the source and the length of homogeneity is the whole source Flow makes the source smaller (“size”-p correlation) AND shifted in outwards direction (x-p correlation) For particles with large mass thermal motion matters less – they are shifted more in “out” direction. The difference is measured as emission asymmetry. pionemissionpoints kaonemissionpoints protonemissionpoints out side THERMINATOR calculation

Fourier coefficients of HBT(  ) oscillations RxRx RyRy  initial =  final STAR Collaboration, nucl-ex/ Out-of-plane sources at freeze-out –Pressure and/or expansion time was not sufficient to quench initial shape From v 2 we know... –Strong in-plane flow → significant pressure build-up in system  Short expansion time plays dominant role in out-of-plane freeze-out source shapes eccentricity Time

Dmitri Peresounko Direct photon interferometry PHENIX; d+Au collisions at √s NN =200 GeV

ImagingTechnique Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997). PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation ==  Source Function Emitting source 1D Koonin Pratt Eqn. Paul Chung, Stony Brook

Nature hides her secrets in data (D) Question 0: Do the models (E,F,G,H) describe the data? Answer 0: These models fail, but this is not a puzzle. Q. 1: Are any other models that descibe the data? A. 1: Yes, there are three models (A,B,C) that cannot be excluded (Conf. Lev. > 0.1 %) Q. 2: Do these models have anything in common? A. 2: Yes, and this where the data (D) are. This common part is what Nature is trying to tell us. D Model B Model A Model H Model G Model E Model F Model C T.Csorgo, Kromeriz’05 Rewiew of Bose-Einstein/HBT Correlations in high energy heavy ion physics

Acceptable Comparison of results of models

Acceptable

Comparison of results of models

~Acceptable

Comparison of results of models ~Acceptable

Comparison of results of models

The HBT test Less unpromising models: don’t fail fitting Au+Au HBT RHIC –nucl-th/ Multiphase Transport model (AMPT) Z. Lin, C. M. Ko, S. Pal –nucl-th/ Hadron rescattering model ``T. Humanic –nucl-th/ Buda-Lund hydro (hep-ph/ , ) T. Csorgo, B. Lörstad, A. Ster et al. (nucl-th/ , / , / ) –hep-ph/ Cracow model (single freeze-out, thermal) W. Broniowski, A. Baran, W. Florkowski –nucl-ex/ Blast wave model (Schnedermann, Heinz) M. A. Lisa, F. Retiere, PRC70, (2004) –hep-ph/ Time dependent Duke hydro model T. Renk –nucl-th/ Seattle model (quantum opacity) J. G. Cramer, G. A. Miller, J.M.S. Wu, J.-H. Yoon –nucl-th/ Kiev-Nantes model Borysova, Sinyukov, Akkelin, Erazmus, Karpenko -> More restrictive tests are needed: spectra, v2, HBT, dn/dy T.Csorgo, Kromeriz’05

Successfull models at RHIC (1): Blastwave F. Retiere, nucl-ex/ ; F. Retiere and M. A. Lisa, nucl-th/ Spectra v2v2 HBT T=106 ± 1 MeV = ± c = ± c R InPlane = 11.1 ± 0.2 fm R OutOfPlane = 12.1 ± 0.2 fm Life time (  ) = 8.4 ± 0.2 fm/c Emission duration = 1.9 ± 0.2 fm/c  2 /dof = 120 / 86 (Errors are statistical only, CL = 0.91 %) Neglect of resonances

Successfull model (2): Cracow model nucl-th/ Model features: Thermal model included (abundances driven by T chem and  B ) Assumes full Hubble flow Sudden freeze-out (at a constant proper-time) Single freeze-out, T chem = T kin Boost-invariance All resonances included, they decay but do not rescatter.

Future plans at LHC

RHIC/AGS/SPS Systematics ≈ 400 MeV (RHIC) ≈ 390 MeV (SPS)...and expectations for LHC Assuming the same tendency: /3 = /3 =20 R expected < 10fm

Pion freezeout times are about twice as long at LHC compared to RHIC Tom Humanic, Kromeriz’05 Pion freezeout time and z-position for LHC form rescattering calculations

Projected 3D two-pion C 2 for LHC Pb+Pb from rescattering for b=8 fm centrality and p T bin MeV/c Two-pion correlation function for LHC form rescattering calculations

Transverse radius parameters for LHC vs. RHIC Transverse radius parameters are somewhat larger and show a stronger p T dependence for LHC compared with RHIC

R Long and parameters for LHC vs. RHIC R Long for LHC is almost twice as large as for RHIC reflecting longer freezeout times; behaves about the same at LHC and RHIC

Current status of momentum correlation analysis 1.„HBT-analyser” – a dedicated sofrware for momentum coorelation analysis at ALICE - ready and integrated in Ali-root environment 2.Experimental factors specific for correlation analysis: track splitting, merging, two-particle resolution and PD - evaluated for different two-particle systems 3.Universal fitting procedure for identical and nonidentical particles „Corfit” – ready, but not integrated yet in Ali-root environment 4.Influence of hard processes (jets) on particle correlatins – under investigations 5.Single event pion interferometry will be possible at ALICE Results of PPR preparation; Chapter 6.3 Momentum Correlations

Current status of momentum correlation analysis For details see: ALICE-INT , One and two-particle resolution and PID ALICE-INT , Two-tracks effects at ALICE ALICE-INT , Some specific features of momentum correlations to be seen at ALICE (draft-0) Formalism of two-particle correlations Particle correlations for expanding sources Role of Coulomb and strong final state interactions Nonidentical particle correlations and space-time asymmetries Azimuthally sensitive HBT Formation of light (anti)nuclei Multi-particle Coulomb effects Correlation measurements of two-particle scattering Influence of resonance decays on two-particle correlations

Some examples

Simulation chain for particle correlations

Two Particle Resolutions Resolution (r.m.s) [MeV] Q inv Q out Q side Q long PDC04TP PDC0 4TPPDC04TPPDC04TP +  pp -- xx pp xx pp xx Almost the same results after ten years of work – very well ( ! ) : reasonable first estimation, and very good complete reconstruction. Compare the results presented in „Technical Proposal” (TP, in 1995) and obtained from PDC04 (in 2005) Piotr Skowroński

Track Merging Anti-Merging cut as implemented by STAR –Cutting on average distance between two tracks in TPC –Space coordinates of tracks are calculated assuming helix shape using track parameters as reconstructed in the inner part of TPC

Single event pion-pion interferometry (with FSI)... by Zbyszek Chajęcki, (r o =8fm)

Single event pion-pion interferometry by Hania GOS

We are looking forward, working, and waiting for the first event of ALICE

Two-particle kinematics LCMS: (P 1 +P 2 ) z =0

Getting quantitative - What can be probed through fitting? Source of particle 1 Source of particle 2 Boost to pair rest frame When fitting “double-ratios” two independent variables are accessible: - Mean shift ( ) or μ - Sigma (  r* )  r* =  pair  r  –  pair  t   r* separation in pair rest frame Function of  pair (  pair ) Separation between source 1 and 2 in pair rest frame rr r [fm] r* [fm]

Two important events; sources of information and discussion forum: Quark Matter Conference and satellite topical meeting.