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Femtoscopy in heavy ion collisions

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  1. ! ! “School” lecture Femtoscopy in heavy ion collisions Mike Lisa The Ohio State University The Berkeley School - Femtoscopy - malisa

  2. Lecture I - basics and sanity check Motivation (brief) Formalism (brief reminder) accessible geometric substructure Some experimental details 2 decades* of data systematics system size: AB, |b|, Npart... system shape: (P,b) Lecture II - dynamics (insanity check?) data systematics [cnt’d] boost-invariance?: Y transverse dynamics: kT, mT new substructure: m1≠m2 Interpretations (& puzzles) Messages from data itself Model comparisons Prelim. comparison: pp, dA Summary Outline * in time and in sNN The Berkeley School - Femtoscopy - malisa

  3. Workshop on femtoscopy at RHIC 21 June 2005 @ BNL RHIC/AGS Users’ Meeting http://www.star.bnl.gov/~panitkin/UsersMeeting_05/ Femtoscopy in Relativistic Heavy Ion Collisions MAL, S. Pratt, R. Soltz, U. Wiedemann Ann. Rev. Nucl. Part. Sci. 2006; nucl-ex/0505014 First, a word from our sponsor… The Berkeley School - Femtoscopy - malisa

  4. “RHIC Month One” The Berkeley School - Femtoscopy - malisa

  5. Motivation Formalism Experiment Trends Models Ann.Rev.Nucl.Part.Sci. 46 (1996) 71 STAR, PRC66 (2002) 034904 STAR, PRL93 (2004) 252301 Spacetime - an annoying bump on the road (to Stockholm?) • Non-trivial space-time - the hallmark of R.H.I.C. • Initial state: dominates further dynamics • Intermediate state: impt element in exciting signals • Final state: • Geometric structural scale is THE defining feature of QGP • Temporal scale sensitive to deconfinement transition (?) The Berkeley School - Femtoscopy - malisa

  6. Motivation Formalism Experiment Trends Models dN/dt time Disintegration timescale - expectation 3D 1-fluid Hydrodynamics Rischke & Gyulassy, NPA 608, 479 (1996) with transition “” “” • Long-standing favorite signature of QGP: • increase in , ROUT/RSIDE due to deconfinement  confinement transition • hoped-for “turn on” as QGP threshold is reached The Berkeley School - Femtoscopy - malisa

  7. Motivation Formalism Experiment Trends Models 10-24 10-18 10-12 10-6 100 106 1012 1018 1024 Today’s lecture “Short” and “long” – in seconds as many yoctoseconds (10-24 s ~ 3 fm/c) in a second as seconds in 10 thousand trillion years The Berkeley School - Femtoscopy - malisa

  8. Motivation Formalism Experiment Trends Models prime: pair frame pa pa pb pb xa xa xb xb Correlation function b/t particles a,b Separation distribution The Berkeley School - Femtoscopy - malisa

  9. Rlong p1 qside x1 Motivation Formalism Experiment Trends Models p2 qout Rside qlong x2 Rout Rside Rout Reminder • Two-particle interferometry: p-space separation  space-time separation source sp(x) = homogeneity region [Sinyukov(95)]  connections with “whole source” always model-dependent Pratt-Bertsch (“out-side-long”) decomposition designed to help disentangle space & time The Berkeley School - Femtoscopy - malisa

  10. Motivation Formalism Experiment Trends Models Gaussian parameterization Measurable substructure Size, shape, and orientation of homogeneity regions The Berkeley School - Femtoscopy - malisa

  11. Motivation Formalism Experiment Trends Models Gaussian parameterization Measurable substructure Average separation between homogeneity regions alsorside , rlong The Berkeley School - Femtoscopy - malisa

  12. Motivation Formalism Experiment Trends Models Experimental definition of CF how to access this rich substructure... A() = “signal” s.p. p.s.  s.p. acceptance  correlations B() = “reference” s.p. p.s.  s.p. acceptance () = corrections The Berkeley School - Femtoscopy - malisa

  13. Collection of selected particles within selected events: event 1 event 2 event 3 event n … Motivation Formalism Experiment Trends Models a a a b b b a b A(ab) ab The Pairwise distributions “Real” pairs form signal or numerator The Berkeley School - Femtoscopy - malisa

  14. Collection of selected particles within selected events: event 1 event 2 event 3 event n … Motivation Formalism Experiment Trends Models a a b b a b B(ab) A(ab) ab ab The Pairwise distributions “Real” pairs form signal or numerator “Mixed” pairs form background or denominator The Berkeley School - Femtoscopy - malisa

  15. Collection of selected particles within selected events: event 1 event 2 event 3 event n … Motivation Formalism Experiment Trends Models B(ab) A(ab) ab ab The Pairwise distributions C(ab) “Real” pairs form signal or numerator “Mixed” pairs form background or denominator ratio C=A/B “only” correlations ab The Berkeley School - Femtoscopy - malisa

  16. event 2 … event 1 Motivation Formalism Experiment Trends Models a a a b b b B(y) A(y) y y Caution: mix “similar” events • Allow range of event-wise characteristics into analysis • Particles in “Real” pairs (obviously) come from similar events • must be similar for “mixed” pairs • in vertex position high y likely high y unlikely The Berkeley School - Femtoscopy - malisa

  17. event 2 … event 1 Motivation Formalism Experiment Trends Models a a a b b b B() A()   Caution: mix “similar” events • Allow range of event-wise characteristics into analysis • Particles in “Real” pairs (obviously) come from similar events • must be similar for “mixed” pairs • in vertex position • in reaction plane orientation high  likely high  unlikely The Berkeley School - Femtoscopy - malisa

  18. event 2 … event 1 Motivation Formalism Experiment Trends Models • Alternatives to event-mixing * • singles (Lisa 1991) • unlike-sign (Abreu 1992) • pb -pb(Stavinskiy 2004) • Monte Carlo (Duque 2003) * (Kopylov 1974) • Properly-constructed background • cancellation of noncorrelated (single-particle) effectsin A(), B() due to s.p. phasespace and acceptance • physical* and detector-induced correlations remain * femtoscopic and nonfemtoscopic Caution: mix “similar” events • Allow range of event-wise characteristics into analysis • Particles in “Real” pairs (obviously) come from similar events • must be similar for “mixed” pairs • in vertex position • in reaction plane orientation • detector configuration (run/time) The Berkeley School - Femtoscopy - malisa

  19. Motivation Formalism Experiment Trends Models Common correlated* detector effects Splitting: confused tracker finds 2 tracks due to one particle Merging: two particles overlap & become indistinguishable Both usually small enough (<%) to be ignored in all except femtoscopic analyses * increased/decreased likelihood of finding a track, due to the presence of another track The Berkeley School - Femtoscopy - malisa

  20. Motivation Formalism Experiment Trends Models SEVERE SEVERE SEVERE SEVERE HIGH HIGH HIGH HIGH ELEVATED ELEVATED ELEVATED ELEVATED GUARDED GUARDED GUARDED GUARDED LOW LOW LOW LOW Identifying likely splits Example: quantity based on pairwise relative topology “better” than Nhits cut or Q-cut Used by STAR The Berkeley School - Femtoscopy - malisa

  21. Motivation Formalism Experiment Trends Models SL = “splitting likelihood” Pairwise cut removes splitting effect  “all” gone The Berkeley School - Femtoscopy - malisa

  22. STARNote 238 Motivation Formalism Experiment Trends Models Track merging due to hit merging track-crossing points “hits” too close in 2D space cannot be resolved track merging likelihood quantified by relative hit positions The Berkeley School - Femtoscopy - malisa

  23. Motivation Formalism Experiment Trends Models Wait-- how do you cut pairs you don’t see? Pairwise cut removes merging effect track-crossing points “hits” too close in 2D space cannot be resolved track merging likelihood quantified by relative hit positions  “all” gone anti-merging cut The Berkeley School - Femtoscopy - malisa

  24. Motivation Formalism Experiment Trends Models Before: A() shows merging After: B() loses bathwater and some babyA() loses some baby Cancellation in ratio B() A() Wait-- how do you cut pairs you don’t see?   Pairwise cut removes merging effect track-crossing points “hits” too close in 2D space cannot be resolved track merging likelihood quantified by relative hit positions anti-merging cut Similarly, splitting cut in B() cut works mostly on background distribution - which tracks would merge? The Berkeley School - Femtoscopy - malisa

  25. pT/pT STAR. PRL 86 (2001) 402 0.01 Motivation Formalism Experiment Trends Models  (rad) 0.01  (rad) 0.01 p (GeV/c) 1 Corrections 1: Finite Resolution Effects 1a) Momentum Resolution iterative correction of C(q) via convolution of single-particle dp (~1%) with assumed correlation ≤ 5% effect on sizes 1b) Event Plane Resolution for azimuthally-sensitive analyses: correct 1000’s of Fourier coefficients a la Poskanzer&Voloshin ~ 10% effect on shape The Berkeley School - Femtoscopy - malisa

  26. Motivation Formalism Experiment Trends Models Assuming identical junk and real s.p. p.s.  = “good” pair fraction Corrections 2a:Uncorrelated “contamination” • correlation strength diluted (~x3) by “white” noise from • random false tracks • mis-PID • weak decay daughters* may be corrected or included in fit Ctrue Cmeas * not strictly uncorrelated noise The Berkeley School - Femtoscopy - malisa

  27. Motivation Formalism Experiment Trends Models Corrections 2b:Correlated “contamination” • e.g. correlated -p feeddown into p-p correlations • non-trivial : requires model & Monte Carlo • not commonly done (but will become more common) • not discussed further here The Berkeley School - Femtoscopy - malisa

  28. Gaussian parameterization of a-b separation usually used (even for non-id) Motivation Formalism Experiment Trends Models for identical pions • F(Qinv) = integrated squared Coulomb wavefunction • “contamination” included via  • NB: Gaussian source: not Gaussian CF Extraction of length scales maximum-likelihood fit to The Berkeley School - Femtoscopy - malisa

  29. only Coulomb-suppress the fraction of pairs () which are direct pions “Diluted Correction” a pair either participates in both BE and Coulomb, or neither Bowler-Sinyukov method (not a “correction”) Various Coulomb “Corrections” account for Coulomb suppression in all background pairs “Standard Correction” This slide was not in the talk, but I found it in my Heavy Ion Forum (Oct2002) and thought it might be nice here. Anyway, this is where I’ll come to look for it. The Berkeley School - Femtoscopy - malisa

  30. Motivation Formalism Experiment Trends Models Cross-check Coulomb with non-id a = - ; b = + STAR PRC71 044906 (2005) F(Qinv) “contaminated” F(Qinv) The Berkeley School - Femtoscopy - malisa

  31. Motivation Formalism Experiment Trends Models 1D projections: a limited view STAR PRC71 044906 (2005) • Usually, quality of data and fit shown in 1D projections • Narrow integration best • limited view of data • see talks of Adam, Scott, Sandra • tomorrow: a better way out “Gaussian fit” (remember: not Gaussian CF) side long The Berkeley School - Femtoscopy - malisa

  32. Motivation Formalism Experiment Trends Models The perennial non-Gaussianness • Source has never been fully Gaussian. c.f. J. Sullivan @ SPS • periodically re-discovered, with little change; information condensation needed to observe systematic data trends • non-Gaussianness @ RHIC reported in first and subsequent HBT measurements • imaging is probably best solution (but even then...) The Berkeley School - Femtoscopy - malisa

  33. Motivation Formalism Experiment Trends Models RS (fm) RO (fm) RO/RS Rl (fm) The perennial non-Gaussianness • CF is “mostly” Gaussian • STAR tried “Edgeworth” functional expansion (Csorgo 2000) among few quantitative estimates of non-Gaussian shape STAR PRC71 044906 (2005) • 20% effect in Rlong! systematic error...? • appears fit captures dominant length scale The Berkeley School - Femtoscopy - malisa

  34. Finally, we understand it! Gyulassy 1995 Motivation Formalism Experiment Trends Models Just one event! Trends, soft sector, and RHI history 6 decades of E/A (2 decades of sNN) Art’s talk. Compiled by A. Wetzler (2005) The Berkeley School - Femtoscopy - malisa

  35. A.D. Chacon et al, Phys. Rev. C43 2670 (1991) G. Alexander, Rep. Prog. Phys. 66 481 (2003) AGS/SPS/RHIC HBT papers (expt) Heinz/Jacak Wiedemann/Heinz Csorgo 20 Lisa/Pratt/Soltz/Wiedemann R = 1.2 (fm)•A1/3 Tomasik/Wiedemann Boal/Jennings/Gelbke 15 Motivation Formalism Experiment Trends Models 10 5 ‘85 ‘90 ‘95 ‘00 ‘05 Systematic decades (years and energy) “R = 5 fm” • Pion HBT @ Bevalac: “largely confirming nuclear dimensions” • Since 90’s: increasingly detailed understanding and study w/ high stats The Berkeley School - Femtoscopy - malisa

  36. AGS/SPS/RHIC HBT papers (expt) Heinz/Jacak Wiedemann/Heinz Csorgo 20 Lisa/Pratt/Soltz/Wiedemann Tomasik/Wiedemann Boal/Jennings/Gelbke 15 y Motivation Formalism Experiment Trends Models 10 5 |b| ‘85 ‘90 ‘95 ‘00 ‘05 pT Systematic decades (years and energy) • Pion HBT @ Bevalac: “largely confirming nuclear dimensions” • Since 90’s: increasingly detailed understanding and study w/ high stats The Berkeley School - Femtoscopy - malisa

  37. Motivation Formalism Experiment Trends Models • Most basic sanity check: • Forget homogeneity regions or fancy stuff. • Do femtoscopic length scales increase as • b0 • A,B ? • Nucleon scales clearly larger for more central collisions • AGS [E877(‘99)] • SPS [NA44(‘99)] The Berkeley School - Femtoscopy - malisa

  38. NA44 ZPC (2000) Motivation Formalism Experiment Trends Models SPS: NA44/NA49 S+S / S+Pb / Pb+Pb • b0 • A,B increase size; neither is scaling variable The Berkeley School - Femtoscopy - malisa

  39. Motivation Formalism Experiment Trends Models • Heavy and light data from AGS, SPS, RHIC • Generalize A1/3Npart1/3 • not bad ! • connection w/ init. size? • ~s-ordering in “geometrical” Rlong, Rside • Mult = K(s)*Npart • source of residual s dep? • ...Yes! common scaling • common density (?) drives radii, not init. geometry • (breaks down s < 5 GeV) The Berkeley School - Femtoscopy - malisa

  40. ? in-plane-extended Motivation Formalism Experiment Trends Models out-of-plane-extended Strongly-interacting 6Li released from an asymmetric trap O’Hara, et al, Science 298 2179 (2002) What can we learn? transverse FO shape + collective velocity  evolution time estimate check independent of RL(pT) Teaney, Lauret, & Shuryak nucl-th/0110037 The Berkeley School - Femtoscopy - malisa

  41. small RS Motivation Formalism Experiment Trends Models big RS • observe the source from all angles with respect to RP • expect oscillations in HBT radii The Berkeley School - Femtoscopy - malisa

  42. side side Motivation Formalism Experiment Trends Models out out • observe the source from all angles with respect to RP • expect oscillations in HBT radii (including “new” cross-terms) R2out-side<0 when pair=135º The Berkeley School - Femtoscopy - malisa

  43. Motivation Formalism Experiment Trends Models Measured final source* shape STAR, PRL93 012301 (2004) R2out-side<0 when pair=135º ever see that symmetry at ycm ? * model-dependent. Discussed next time The Berkeley School - Femtoscopy - malisa

  44. central collisions mid-central collisions Motivation Formalism Experiment Trends Models peripheral collisions Measured final source* shape STAR, PRL93 012301 (2004) no message here so far. Passes sanity check * model-dependent. Discussed next time The Berkeley School - Femtoscopy - malisa

  45. Summary of Lecture I • Non-trivial space-time evolution/structure: Defining feature of our field. p-space = 1/2 the story (and not the best half) • Rich substructure accessible via femtoscopy • size, shape, orientation, displacement • “only” homogeneity regions probed  connections to “whole source” model-dependent • source size sanity check pans out • reveals scaling with dN/dy; “explains” larger source at RHIC • refutes periodic suggestion that HBT radii dominated by nonfemtoscopic scales • broken symmetry (b≠0)--> more detailed information • source shape sanity check pans out • next time: more asHBT and y≠0 and a≠b The Berkeley School - Femtoscopy - malisa

  46. Lecture I - basics and sanity check Motivation (brief) Formalism (brief reminder) accessible geometric substructure Some experimental details 2 decades* of data systematics system size: AB, |b|, Npart... system shape: (P,b) Lecture II - dynamics (insanity check?) data systematics [cnt’d] boost-invariance?: Y transverse dynamics: kT, mT new substructure: m1≠m2 Interpretations (& puzzles) Messages from data itself Model comparisons Prelim. comparison: pp, dA Summary Outline * in time and in sNN The Berkeley School - Femtoscopy - malisa

  47. End Lecture I The Berkeley School - Femtoscopy - malisa

  48. start lecture 2 with • connect overall SIZE and SHAPE of source at F.O. with dynamics/evolution (x2 expansion, rounder source; also include whether these facts are consistent with 9 fm/c -- could be...) • then go into more direct femtoscopic signatures of dynamics (pT, mT dep, YKP, etc...) The Berkeley School - Femtoscopy - malisa

  49. Motivation Formalism Experiment Trends Models The Berkeley School - Femtoscopy - malisa

  50. central collisions mid-central collisions Motivation Formalism Experiment Trends Models peripheral collisions Measured final source shape STAR, PRL93 012301 (2004) Expected evolution: ? The Berkeley School - Femtoscopy - malisa