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 transcript:

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

ma lisa - ALICE week Feb Muenster Outline LHC predictions –H.I. see SPHIC06 talk (nucl-th/ ) –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

ma lisa - ALICE week Feb Muenster Introduction & Motivation

ma lisa - ALICE week Feb Muenster MicroexplosionsFemtoexplosions  J/m 3 5 GeV/fm 3 = J/m 3 ss0.1  J 1  J T10 6 K200 MeV = 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

ma lisa - ALICE week Feb Muenster MicroexplosionsFemtoexplosions ss0.1  J 1  J  J/m 3 5 GeV/fm 3 = J/m 3 T10 6 K200 MeV = 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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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/

ma lisa - ALICE week Feb 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/

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

ma lisa - ALICE week Feb Muenster p+p: A clear reference system?

ma lisa - ALICE week Feb Muenster STAR preliminary m T (GeV) Z. Chajecki QM05 nucl-ex/ femtoscopy in 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?)

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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?

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

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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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...)

ma lisa - ALICE week Feb Muenster Genbod

ma lisa - ALICE week Feb 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)

ma lisa - ALICE week Feb Muenster Genbod:phasespace sampling w/ P- conservation F. James, Monte Carlo Phase Space CERN REPORT (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

ma lisa - ALICE week Feb 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

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

ma lisa - ALICE week Feb Muenster CF from GenBod Varying frame and kinematic cuts

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

ma lisa - ALICE week Feb 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

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

ma lisa - ALICE week Feb 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

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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb Muenster GenBod Varying multiplicity and total energy

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

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

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

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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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, PRC (1988) Borghini, Dinh, & Ollitraut PRC (2000) –D spatial dimensions and M-cumulants Borghini, Euro. Phys. C (2003) –3+1 (  p+E) conservation and femtoscopy Chajecki & MAL, nucl-th/ [WPCF06] –  p T conservation and 3-particle correlations Borghini,nucl-th/

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

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

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

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

ma lisa - ALICE week Feb Muenster CLT & ∑E - ∑p correlations

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

ma lisa - ALICE week Feb 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)

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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

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

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

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

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

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

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

ma lisa - ALICE week Feb 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]...

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb Muenster 18 pions, =0.9 GeV

ma lisa - ALICE week Feb Muenster

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

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

ma lisa - ALICE week Feb 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, large |Q| –parameters are “physical” - values may be guessed

ma lisa - ALICE week Feb 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

ma lisa - ALICE week Feb 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]

ma lisa - ALICE week Feb Muenster Extra Slides

ma lisa - ALICE week Feb 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

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

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

ma lisa - ALICE week Feb Muenster d+Au

ma lisa - ALICE week Feb Muenster Schematic: How Genbod works 1/3

ma lisa - ALICE week Feb Muenster flow chart, in text F. James, CERN REPORT (1968)

ma lisa - ALICE week Feb Muenster F. James, CERN REPORT (1968)

ma lisa - ALICE week Feb Muenster Schematic: How Genbod works 2/3

ma lisa - ALICE week Feb Muenster Schematic: How Genbod works 3/3

ma lisa - ALICE week Feb 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 (1968)