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## Femtoscopy in heavy ion collisions

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**!**! “School” lecture Femtoscopy in heavy ion collisions Mike Lisa The Ohio State University The Berkeley School - Femtoscopy - malisa**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**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**“RHIC Month One”**The Berkeley School - Femtoscopy - malisa**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**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**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**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**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**Motivation**Formalism Experiment Trends Models Gaussian parameterization Measurable substructure Size, shape, and orientation of homogeneity regions The Berkeley School - Femtoscopy - malisa**Motivation**Formalism Experiment Trends Models Gaussian parameterization Measurable substructure Average separation between homogeneity regions alsorside , rlong The Berkeley School - Femtoscopy - malisa**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**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**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**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**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**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**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**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**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**Motivation**Formalism Experiment Trends Models SL = “splitting likelihood” Pairwise cut removes splitting effect “all” gone The Berkeley School - Femtoscopy - malisa**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**Motivation**Formalism Experiment Trends Models • Most basic sanity check: • Forget homogeneity regions or fancy stuff. • Do femtoscopic length scales increase as • b0 • A,B ? • Nucleon scales clearly larger for more central collisions • AGS [E877(‘99)] • SPS [NA44(‘99)] The Berkeley School - Femtoscopy - malisa**NA44 ZPC (2000)**Motivation Formalism Experiment Trends Models SPS: NA44/NA49 S+S / S+Pb / Pb+Pb • b0 • A,B increase size; neither is scaling variable The Berkeley School - Femtoscopy - malisa**Motivation**Formalism Experiment Trends Models • Heavy and light data from AGS, SPS, RHIC • Generalize A1/3Npart1/3 • 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**?**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**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**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**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**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**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**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**End Lecture I**The Berkeley School - Femtoscopy - malisa**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**Motivation**Formalism Experiment Trends Models The Berkeley School - Femtoscopy - malisa**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