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Ma lisa - ALICE week 12-16 Feb 2007 - Muenster EMCICs and the femtoscopy of small systems Mike Lisa & Zbigniew Chajecki Ohio State University.

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Presentation on theme: "Ma lisa - ALICE week 12-16 Feb 2007 - Muenster EMCICs and the femtoscopy of small systems Mike Lisa & Zbigniew Chajecki Ohio State University."— Presentation transcript:

1 ma lisa - ALICE week 12-16 Feb 2007 - Muenster EMCICs and the femtoscopy of small systems Mike Lisa & Zbigniew Chajecki Ohio State University

2 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Outline LHC predictions –H.I. see SPHIC06 talk (nucl-th/0701058) –p+p: see talk of T. Humanic Introduction / Motivation –intriguing pp versus AA [reminder] –data features not under control: Energy-momentum conservation? SHD as a diagnostic tool [reminder] Phase-space event generation: GenBod Analytic calculation of EMCIC Experimentalists’ recipe: Fitting correlation functions [in progress] Conclusion

3 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Introduction & Motivation

4 ma lisa - ALICE week 12-16 Feb 2007 - Muenster MicroexplosionsFemtoexplosions  10 17 J/m 3 5 GeV/fm 3 = 10 36 J/m 3 ss0.1  J 1  J T10 6 K200 MeV = 10 12 K rate10 18 K/sec10 35 K/s energy quickly deposited enter plasma phase expand hydrodynamically cool back to original phase do geometric “postmortem” & infer momentum

5 ma lisa - ALICE week 12-16 Feb 2007 - Muenster MicroexplosionsFemtoexplosions ss0.1  J 1  J  10 17 J/m 3 5 GeV/fm 3 = 10 36 J/m 3 T10 6 K200 MeV = 10 12 K rate10 18 K/sec10 35 K/s energy quickly deposited enter plasma phase expand hydrodynamically cool back to original phase do geometric “postmortem” & infer momentum

6 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Beyond press releases The detailed work now underway is what can probe & constrain sQGP properties It is probably not press-release material......but, hey, you’ve already got your coffee mug Nature of EoS under investigation ; agreement with data may be accidental ; viscous hydro under development ; assumption of thermalization in question sensitive to modeling of initial state, under study

7 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Femtoscopic information xaxa xbxb papa pbpb xaxa xbxb papa pbpb femtoscopic correlation at low |q| must vanish at high |q|. [indep “direction”] Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) 3 “radii” by using 3-D vector q

8 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Femtoscopic information - Spherical harmonic representation femtoscopic correlation at low |q| must vanish at high |q|. [indep “direction”] Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) 3 “radii” by using 3-D vector q Q OUT   Q SIDE Q LONG Q nucl-ex/0505009

9 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Femtoscopic information - Spherical harmonic representation femtoscopic correlation at low |q| must vanish at high |q|. [indep “direction”] A LM (Q) =  L,0 Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) 3 “radii” by using 3-D vector q L=0 L=2 M=0 L=2 M=2 nucl-ex/0505009

10 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Kinematic dependence of femtoscopy: Geometrical/dynamical evidence of bulk behaviour Amount of flow consistent with p-space nucl-th/0312024 Huge, diverse systematics consistent with this substructure nucl-ex/0505014

11 ma lisa - ALICE week 12-16 Feb 2007 - Muenster p+p: A clear reference system?

12 ma lisa - ALICE week 12-16 Feb 2007 - Muenster STAR preliminary m T (GeV) Z. Chajecki QM05 nucl-ex/0510014 femtoscopy in p+p @ STAR Decades of femtoscopy in p+p and in A+A, but... for the first time: femtoscopy in p+p and A+A in same experiment, same analysis definitions... unique opportunity to compare physics ~ 1 fm makes sense, but... p T -dependence in p+p? (same cause as in A+A?)

13 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Surprising („puzzling”) scaling HBT radii scale with pp Scary coincidence or something deeper? On the face: same geometric substructure pp, dAu, CuCu - STAR preliminary Ratio of (AuAu, CuCu, dAu) HBT radii by pp A. Bialasz (ISMD05): I personally feel that its solution may provide new insight into the hadronization process of QCD

14 ma lisa - ALICE week 12-16 Feb 2007 - Muenster BUT... Clear interpretation clouded by data features STAR preliminary d+Au peripheral collisions Gaussian fit Non-femtoscopic q-anisotropic behaviour at large |q| does this structure affect femtoscopic region as well?

15 ma lisa - ALICE week 12-16 Feb 2007 - Muenster STAR preliminary d+Au peripheral collisions Gaussian fit Decomposition of CF onto Spherical Harmonics Z.Ch., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009 non-femtoscopic structure (not just “non-Gaussian”)

16 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Baseline problems with small systems: previous treatments STAR preliminary d+Au peripheral collisions Gaussian fit ad hoc, but try it...

17 ma lisa - ALICE week 12-16 Feb 2007 - Muenster STAR preliminary d+Au peripheral collisions NA22 fit Try NA22 empirical form NA22 fit data Spherical harmonics L =1 M=0 L =2 M=0 L =1 M=1 L =2 M=2

18 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Just push on....?... no! –Irresponsible to ad-hoc fit (often the practice) or ignore (!!) & interpret without understanding data –no particular reason to expect non-femtoscopic effect to be limited to non-femtoscopic (large-q) region not-understood or -controlled contaminating correlated effects at low q ? A possibility: energy-momentum conservation? –must be there somewhere! –but how to calculate / model ? (Upon consideration, non-trivial...)

19 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Genbod

20 ma lisa - ALICE week 12-16 Feb 2007 - Muenster energy-momentum conservation in n-body states spectrum of kinematic quantity  (angle, momentum) given by n-body Phasespace factor R n statistics: “density of states” larger particle momentum  more available states P  conservation Induces “trivial” correlations (i.e. even for M=1)

21 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Genbod:phasespace sampling w/ P- conservation F. James, Monte Carlo Phase Space CERN REPORT 68-15 (1 May 1968) Sampling a parent phasespace, conserves energy & momentum explicitly –no other correlations between particles Events generated randomly, but each has an Event Weight WT ~ probability of event to occur ALL EVENTS ARE EQUAL, BUT SOME EVENTS ARE MORE EQUAL THAN OTHERS

22 ma lisa - ALICE week 12-16 Feb 2007 - Muenster “Rounder” events: higher WT ALL EVENTS ARE EQUAL, BUT SOME EVENTS ARE MORE EQUAL THAN OTHERS larger particle momentum  more available states 30 particles

23 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Genbod:phasespace sampling w/ P- conservation Treat identical to measured events use WT directly MC sample WT Form CF and SHD

24 ma lisa - ALICE week 12-16 Feb 2007 - Muenster CF from GenBod Varying frame and kinematic cuts

25 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LabCMS Frame - no cuts

26 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LabCMS Frame - |  | =0.9 GeV, LabCMS Frame - |  |<0.5 The shape of the CF is sensitive to kinematic cuts

27 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame

28 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LCMS Frame - |  | =0.9 GeV, LCMS Frame - |  |<0.5 The shape of the CF is sensitive to kinematic cuts frame

29 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, PR Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame

30 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, PR Frame - |  | =0.9 GeV, PR Frame - |  |<0.5 The shape of the CF is sensitive to kinematic cuts frame

31 ma lisa - ALICE week 12-16 Feb 2007 - Muenster GenBod Varying multiplicity and total energy

32 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=6, =0.5 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame

33 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=9, =0.5 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame particle multiplicity

34 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=15, =0.5 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame particle multiplicity

35 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.5 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame particle multiplicity

36 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.7 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame particle multiplicity total energy : √s

37 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LCMS Frame - no cuts The shape of the CF is sensitive to kinematic cuts frame particle multiplicity total energy : √s The shape of the CF is sensitive to kinematic cuts frame particle multiplicity total energy : √s

38 ma lisa - ALICE week 12-16 Feb 2007 - Muenster So... Energy & Momentum Conservation Induced Correlations (EMCICs) “resemble” our data –... on the right track... But what to do with that? –Sensitivity to  s, Mult of particles of interest and other particles –will depend on p 1 and p 2 of particles forming pairs in |Q| bins  risky to “correct” data with Genbod... Solution: calculate EMCICs using data!! –  p T conservation and v 2 Danielewicz et al, PRC38 120 (1988) Borghini, Dinh, & Ollitraut PRC62 034902 (2000) –D spatial dimensions and M-cumulants Borghini, Euro. Phys. C30 381 (2003) –3+1 (  p+E) conservation and femtoscopy Chajecki & MAL, nucl-th/0612080 - [WPCF06] –  p T conservation and 3-particle correlations Borghini,nucl-th/0612093

39 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Distributions w/ phasespace constraints single-particle distribution w/o P.S. restriction

40 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Distributions w/ phasespace constraints single-particle distribution w/o P.S. restriction k-particle distribution (k<N) with P.S. restriction

41 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Distributions w/ phasespace constraints single-particle distribution w/o P.S. restriction k-particle distribution (k<N) with P.S. restriction

42 ma lisa - ALICE week 12-16 Feb 2007 - Muenster But... Energy conservation coupled to on-shell constraint  huge correlations between E tot, P X,tot, P Y,tot, P Z,tot ???

43 ma lisa - ALICE week 12-16 Feb 2007 - Muenster CLT & ∑E - ∑p correlations

44 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Using central limit theorem (“large N-k”) k-particle distribution in N-particle system N.B. relevant later

45 ma lisa - ALICE week 12-16 Feb 2007 - Muenster k-particle correlation function Dependence on “parent” distrib f vanishes, except for energy/momentum means and RMS 2-particle correlation function (1 st term in 1/N expansion)

46 ma lisa - ALICE week 12-16 Feb 2007 - Muenster 2-particle correlation function (1 st term in 1/N expansion) “The p T term” “The p Z term” “The E term” Names used in the following plots

47 ma lisa - ALICE week 12-16 Feb 2007 - Muenster EMCICs Effect of varying multiplicity & total energy Same plots as before, but now we look at: p T ( ), p z (  ) and E (  ) first-order terms full (  ) versus first-order (  ) calculation simulation ( ) versus first-order (  ) calculation

48 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=6, =0.5 GeV, LabCMS Frame - no cuts

49 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=9, =0.5 GeV, LabCMS Frame - no cuts

50 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=15, =0.5 GeV, LabCMS Frame - no cuts

51 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.5 GeV, LabCMS Frame - no cuts

52 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.7 GeV, LabCMS Frame - no cuts

53 ma lisa - ALICE week 12-16 Feb 2007 - Muenster N=18, =0.9 GeV, LabCMS Frame - no cuts

54 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Findings first-order and full calculations agree well for N>9 –will be important for “experimentalist’s recipe” Non-trivial competition/cooperation between p T, p z, E terms –all three important p T1 p T2 term does affect “out-versus-side” (A 22 ) p z term has finite contribution to A 22 (“out-versus-side”) calculations come close to reproducing simulation for reasonable (N-2) and energy, but don’t nail it. Why? –neither (N-k) nor  s is infinite –however, probably more important... [next slide]...

55 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Remember... relevant quantities are average over the (unmeasured) “parent” distribution, not the physical distribution of course, the experimentalist never measures all particles (including neutrinos) or anyway, so maybe not a big loss

56 ma lisa - ALICE week 12-16 Feb 2007 - Muenster The experimentalist’s recipe Treat the not-precisely-known factors as fit parameters (4 of them) values determined mostly by large-|Q|; should not cause “fitting hell” look, you will either ignore it or fit it ad-hoc anyway (both wrong) this recipe provides physically meaningful, justified form

57 ma lisa - ALICE week 12-16 Feb 2007 - Muenster 18 pions, =0.9 GeV

58 ma lisa - ALICE week 12-16 Feb 2007 - Muenster

59 The COMPLETE experimentalist’s recipe femtoscopic function of choice fit this......or image this...

60 ma lisa - ALICE week 12-16 Feb 2007 - Muenster “Full” fit to min-bias d+Au - work in progress data EMCIC Femto (gauss) full

61 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Summary understanding the femtoscopy of small systems –important physics-wise –should not be attempted until data fully under control SHD: “efficient” tool to study 3D structure Restricted P.S. due EMCIC –sampled by GenBod event generator –stronger effects for small mult and/or  s Analytic calculation of EMCIC –k-th order CF given by ratio of correction factors –“parent” only relevant in momentum variances –first-order expansion works well for N>9 –non-trivial interaction b/t p T, p z, E conservation effects Physically correct “recipe” to fit/remove MCIC –4 parameters, determined @ large |Q| –parameters are “physical” - values may be guessed

62 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Famous picture from famous article by famous guy Energy loss of energetic partons in quark-gluon plasma: Possible extinction of high p T jets in hadron-hadron collisions J.D. Bjorken, 1982 b

63 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Thanks to... Alexy Stavinsky & Konstantin Mikhaylov (Moscow) [original suggestion to use Genbod] Nicolas Borghini (Bielefeld) & Jean-Yves Ollitrault (Saclay) [helpful guidance and explanation of previous work] Adam Kisiel (Warsaw) [emphasize energy conservation; resonance effects in  + -  - ] Ulrich Heinz (Columbus) [suggestions on validating CLT in 3+1 case]

64 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Extra Slides

65 ma lisa - ALICE week 12-16 Feb 2007 - Muenster CLT? distribution of N uncorrelated numbers (and then scaled by N, for convenience) Note we are not starting with a very Gaussian distribution!! “pretty Gaussian” for N=4 (but  2 /dof~2.5) “Gaussian” by N=10

66 ma lisa - ALICE week 12-16 Feb 2007 - Muenster What is an A lm ? Q OUT   Q SIDE Q LONG Q nucl-ex/0505009 C(|Q|=0.39,cos ,  )

67 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Multiplicity dependence of the baseline Baseline problem is increasing with decreasing multiplicity STAR preliminary

68 ma lisa - ALICE week 12-16 Feb 2007 - Muenster d+Au

69 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Schematic: How Genbod works 1/3

70 ma lisa - ALICE week 12-16 Feb 2007 - Muenster flow chart, in text F. James, CERN REPORT 68-15 (1968)

71 ma lisa - ALICE week 12-16 Feb 2007 - Muenster F. James, CERN REPORT 68-15 (1968)

72 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Schematic: How Genbod works 2/3

73 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Schematic: How Genbod works 3/3

74 ma lisa - ALICE week 12-16 Feb 2007 - Muenster Example of use of total phase space integral In absence of “physics” in M : (i.e. phase-space dominated) single-particle spectrum of  : “spectrum of events”: F. James, CERN REPORT 68-15 (1968)

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