Femtoscopy in heavy ion collisions Mike Lisa The

Femtoscopy in heavy ion collisions Mike Lisa The Ohio State University ! “School” lecture May 2005 ! The Berkeley School Femtoscopy - malisa 1

2 Outline 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: k. T, m. T – new substructure: m 1≠m 2 • Interpretations (& puzzles) – Messages from data itself – Model comparisons – Prelim. comparison: pp, d. A • Summary * in time and in s. NN May 2005 The Berkeley School - Femtoscopy - malisa

First, a word from our sponsor… Workshop on femtoscopy at RHIC 21 June 2005 @ BNL RHIC/AGS Users’ Meeting http: //www. star. bnl. gov/~panitkin/Users. Meeting_05/ Femtoscopy in Relativistic Heavy Ion Collisions MAL, S. Pratt, R. Soltz, U. Wiedemann Ann. Rev. Nucl. Part. Sci. 2006; nucl-ex/0505014 May 2005 The Berkeley School Femtoscopy - malisa 3

4 “RHIC Month One” May 2005 The Berkeley School - Femtoscopy - malisa

Motivation Formalism Experiment Trends Models Spacetime - an annoying bump on the road (to Stockholm? ) STAR, PRC 66 (2002) 034904 STAR, PRL 93 (2004) 252301 Ann. Rev. Nucl. Part. Sci. 46 (1996) 71 • 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 (? ) May 2005 The Berkeley School - Femtoscopy - malisa 5

Motivation Formalism Experiment Trends Models Disintegration timescale - expectation 6 3 D 1 -fluid Hydrodynamics Rischke & Gyulassy, NPA 608, 479 (1996) d. N/dt with transition time “ ” Long-standing favorite signature of QGP: • increase in , ROUT/RSIDE due to deconfinement transition • hoped-for “turn on” as QGP threshold is reached May 2005 The Berkeley School - Femtoscopy - malisa “ ”

Motivation Formalism Experiment Trends 7 Models “Short” and “long” – in seconds 10 -24 10 -18 10 -12 10 -6 100 106 1012 as many yoctoseconds (10 -24 s ~ 3 fm/c) in a second as seconds in 10 thousand trillion years Today’s lecture May 2005 The Berkeley School - Femtoscopy - malisa 1018 1024

Motivation Formalism Experiment Trends Models Correlation function b/t particles a, b prime: pair frame pa Separation distribution pa pb xa xb May 2005 xa xb The Berkeley School - Femtoscopy - malisa pb 8

Motivation Formalism Experiment Trends Models Reminder • Two-particle interferometry: p-space separation space-time separation ng R lo x 1 p 1 qside p 2 Rside x 2 qout qlong Rout source sp(x) = homogeneity region [Sinyukov(95)] connections with “whole source” always model-dependent Rside Pratt-Bertsch (“out-side-long”) decomposition designed to help disentangle space & time Rout May 2005 The Berkeley School - Femtoscopy - malisa 9

Motivation Formalism Experiment Trends Models Measurable substructure Size, shape, and orientation of homogeneity regions Gaussian parameterization May 2005 The Berkeley School - Femtoscopy - malisa 10

Motivation Formalism Experiment Trends Models Measurable substructure Average separation between homogeneity regions Gaussian parameterization May 2005 The Berkeley School - Femtoscopy - malisa also rside , rlong 11

Motivation Formalism Experiment Trends Models Experimental definition of CF how to access this rich substructure. . . A() = “signal” s. p. p. s. p. acceptance correlations B() = “reference” s. p. p. s. p. acceptance () = corrections May 2005 The Berkeley School - Femtoscopy - malisa 12

Motivation Formalism Experiment Trends 13 Models The Pairwise distributions Collection of selected particles within selected events: event 1 event 2 event 3 event n … a b a b “Real” pairs form A( ab) signal or numerator May 2005 ab The Berkeley School - Femtoscopy - malisa a b

Motivation Formalism Experiment Trends The Pairwise distributions 14 Models Collection of selected particles within selected events: event 1 event 2 event 3 event n … a a “Real” pairs form A( ab) signal or numerator May 2005 ab b b a b “Mixed” pairs form B( ab) background or denominator ab The Berkeley School - Femtoscopy - malisa

Motivation Formalism Experiment Trends The Pairwise distributions Models 15 Collection of selected particles within selected events: event 1 event 2 event 3 event n … “Real” pairs form A( ab) signal or numerator May 2005 ab C( ab) “Mixed” pairs form ratio C=A/B B( ab) background or “only” correlations denominator ab The Berkeley School - Femtoscopy - malisa ab

Motivation Formalism Experiment Trends 16 Models Caution: mix “similar” events event 2 event 1 … • 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 b a a A( y) high y unlikely B( y) y May 2005 The Berkeley School - Femtoscopy - malisa a b b high y likely y

Motivation Formalism Experiment Trends 17 Models Caution: mix “similar” events event 2 event 1 … • 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 A( ) b a a high unlikely B( ) May 2005 The Berkeley School - Femtoscopy - malisa a b b high likely

Motivation Formalism Experiment Trends Models 18 Caution: mix “similar” events event 1 event 2 … • 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 Alternatives to event-mixing * • singles (Lisa 1991) Properly-constructed background • unlike-sign (Abreu 1992) cancellation of noncorrelated (single-particle) effects in A(), B() due to s. p. phasespace and • pbacceptance -pb (Stavinskiy 2004) physical* and detector-induced correlations • Monteremain Carlo (Duque 2003) • detector configuration (run/time) * femtoscopic and nonfemtoscopic May 2005 * (Kopylov 1974) The Berkeley School - Femtoscopy - malisa

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 May 2005 The Berkeley School - Femtoscopy - malisa 19

Motivation Formalism Experiment Trends 20 Models Identifying likely splits Example: quantity based on pairwise relative topology “better” than Nhits cut or Q-cut Used by STAR May 2005 SEVERE HIGH ELEVATED GUARDED LOW LOW The Berkeley School - Femtoscopy - malisa

Motivation Formalism Experiment Trends Models Pairwise cut removes splitting effect “all” gone SL = “splitting likelihood” May 2005 The Berkeley School - Femtoscopy - malisa 21

Motivation Formalism Experiment Trends Models Track merging due to hit merging STARNote 238 track-crossing points “hits” too close in 2 D space cannot be resolved track merging likelihood quantified by relative hit positions May 2005 The Berkeley School - Femtoscopy - malisa 22

Motivation Formalism Experiment Trends 23 Models Pairwise cut removes merging effect track-crossing points “hits” too close in 2 D space cannot be resolved track merging likelihood quantified by relative hit positions anti-merging cut Wait-- how do you cut pairs you don’t see? May 2005 The Berkeley School - Femtoscopy - malisa “all” gone

Motivation Formalism Experiment Trends 24 Models Pairwise cut removes merging effect A( ) B( ) track-crossing points “hits” too close in 2 D space cannot be resolved track merging likelihood quantified by relative hit positions Before: A() shows merging anti-merging cut After: B() loses bathwater and some baby A() loses some baby Cancellation in ratio Wait-- how do you cut pairs you don’t see? Similarly, splitting cut in B() cut works mostly on background distribution - which tracks would merge? May 2005 The Berkeley School - Femtoscopy - malisa

Motivation Formalism Experiment Trends Models 25 1 a) Momentum Resolution iterative correction of C(q) via convolution of single-particle dp (~1%) with assumed correlation p. T/p. T Corrections 1: Finite Resolution Effects 0. 01 1 b) Event Plane Resolution for azimuthally-sensitive analyses: correct 1000’s of Fourier coefficients a la Poskanzer&Voloshin (rad) ≤ 5% effect on sizes STAR. PRL 86 (2001) 402 0. 01 (rad) ~ 10% effect on shape 0. 01 1 May 2005 The Berkeley School - Femtoscopy - malisa p (Ge. V/c)

Motivation Formalism Experiment Trends Models Corrections 2 a: Uncorrelated “contamination” correlation strength diluted (~x 3) by “white” noise from • random false tracks • mis-PID • weak decay daughters* may be corrected or included in fit Ctrue Cmeas Assuming identical junk and real s. p. p. s. * not strictly uncorrelated noise May 2005 = “good” pair fraction The Berkeley School - Femtoscopy - malisa 26

Motivation Formalism Experiment Trends Models Corrections 2 b: 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 May 2005 The Berkeley School - Femtoscopy - malisa 27

Motivation Formalism Experiment Trends Models Extraction of length scales maximum-likelihood fit to usually used (even for non-id) Gaussian parameterization of a-b separation for identical pions • F(Qinv) = integrated squared Coulomb wavefunction • “contamination” included via • NB: Gaussian source: not Gaussian CF May 2005 The Berkeley School - Femtoscopy - malisa 28

Motivation Formalism Experiment Trends Models Cross-check Coulomb with non-id a = - ; b = + STAR PRC 71 044906 (2005) F(Qinv) “contaminated” F(Qinv) May 2005 The Berkeley School - Femtoscopy - malisa 29

Motivation Formalism Experiment Trends Models 1 D projections: a limited view STAR PRC 71 044906 (2005) • Usually, quality of data and fit shown in 1 D projections • Narrow integration best out “Gaussian fit” (remember: not Gaussian CF) • limited view of data – see talks of Adam, Scott, Sandra – tomorrow: a better way side May 2005 The Berkeley School - Femtoscopy - malisa long 30

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. . . ) May 2005 The Berkeley School - Femtoscopy - malisa 31

Motivation Formalism Experiment Trends 32 Models The perennial non-Gaussianness CF is “mostly” Gaussian STAR tried “Edgeworth” functional expansion (Csorgo 2000) STAR PRC 71 044906 (2005) Rl (fm) RO/RS • 20% effect in Rlong! systematic error. . . ? • appears fit captures dominant length. School scale- Femtoscopy - malisa May 2005 The Berkeley RS (fm) RO (fm) among few quantitative estimates of non-Gaussian shape

Motivation Formalism Experiment Trends Models Trends, soft sector, and RHI history Finally, we understand it! Just one event! Gyulassy 1995 May 2005 6 decades of E/A (2 decades of s. NN) The Berkeley School - Femtoscopy - malisa Art’s talk. Compiled by A. Wetzler (2005) 33

Motivation Formalism Experiment Trends Models Systematic decades (years and energy) 15 10 Heinz/Jacak Wiedemann/Heinz Csorgo Tomasik/Wiedemann Boal/Jennings/Gelbke 20 Lisa/Pratt/Soltz/Wiedemann AGS/SPS/RHIC HBT papers (expt) A. D. Chacon et al, Phys. Rev. C 43 2670 (1991) G. Alexander, Rep. Prog. Phys. 66 481 (2003) R = 1. 2 (fm) • A 1/3 “R = 5 fm” 5 ‘ 85 ‘ 90 ‘ 95 ‘ 00 ‘ 05 • Pion HBT @ Bevalac: “largely confirming nuclear dimensions” • Since 90’s: increasingly detailed understanding and study w/ high stats May 2005 The Berkeley School - Femtoscopy - malisa 34

Motivation Formalism Experiment Trends Models Systematic decades (years and energy) 15 10 Heinz/Jacak Wiedemann/Heinz Csorgo Tomasik/Wiedemann Boal/Jennings/Gelbke 20 Lisa/Pratt/Soltz/Wiedemann AGS/SPS/RHIC HBT papers (expt) y |b| 5 p. T ‘ 85 ‘ 90 ‘ 95 ‘ 00 ‘ 05 • Pion HBT @ Bevalac: “largely confirming nuclear dimensions” • Since 90’s: increasingly detailed understanding and study w/ high stats May 2005 The Berkeley School - Femtoscopy - malisa 35

Motivation Formalism Experiment Trends 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 [E 877(‘ 99)] • SPS [NA 44(‘ 99)] May 2005 The Berkeley School - Femtoscopy - malisa Models 36

Motivation Formalism Experiment Trends Models NA 44 ZPC (2000) SPS: NA 44/NA 49 S+S / S+Pb / Pb+Pb • b 0 increase size; neither is scaling variable • A, B May 2005 The Berkeley School - Femtoscopy - malisa 37

Motivation Formalism Experiment Trends Models 38 • Heavy and light data from AGS, SPS, RHIC • Generalize A 1/3 Npart 1/3 • 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 May 2005 • (breaks The Berkeley School - Femtoscopy - malisa down s < 5 Ge. V)

Motivation Formalism Experiment Strongly-interacting 6 Li released from an asymmetric trap O’Hara, et al, Science 298 2179 (2002) Trends 39 Models What can we learn? ? in-planeextended transverse FO shape + collective velocity evolution time estimate check independent of RL(p. T) out-of-plane-extended May 2005 Teaney, & School Shuryak- Femtoscopy nucl-th/0110037 The. Lauret, Berkeley - malisa

Motivation Formalism Experiment Trends Models small RS • observe the source from all angles with respect to RP • expect oscillations in HBT radii big RS May 2005 The Berkeley School - Femtoscopy - malisa 40

Motivation Formalism Experiment • observe the source from all angles with respect to RP • expect oscillations in HBT radii (including “new” cross-terms) de si Trends side out R 2 out-side<0 when pair=135º May 2005 t ou The Berkeley School - Femtoscopy - malisa Models 41

Motivation Formalism Experiment Trends Models STAR, PRL 93 012301 (2004) Measured final source* shape R 2 out-side<0 when pair=135º ever see that symmetry at ycm ? * model-dependent. Discussed next time May 2005 42 The Berkeley School - Femtoscopy - malisa

Motivation Formalism Experiment Trends Models STAR, PRL 93 012301 (2004) Measured final source* shape central collisions mid-central collisions peripheral collisions no message here so far. Passes sanity check * model-dependent. Discussed next time May 2005 43 The Berkeley School - Femtoscopy - malisa

44 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 d. N/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 as. HBT and y≠ 0 and a≠b May 2005 The Berkeley School - Femtoscopy - malisa

45 Outline 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: k. T, m. T – new substructure: m 1≠m 2 • Interpretations (& puzzles) – Messages from data itself – Model comparisons – Prelim. comparison: pp, d. A • Summary * in time and in s. NN May 2005 The Berkeley School - Femtoscopy - malisa