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Conservation laws & femtoscopy of small systems

Conservation laws & femtoscopy of small systems. Zbigniew Chajeçki & Mike Lisa Ohio State University. nucl-th/0612080. Outline. Introduction RHI, femtoscopy, & collectivity in bulk matter including: new representation of correlation functions the p+p “reference”

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Conservation laws & femtoscopy of small systems

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  1. Conservation laws & femtoscopy of small systems Zbigniew Chajeçki & Mike Lisa Ohio State University nucl-th/0612080 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  2. Outline • Introduction • RHI, femtoscopy, & collectivity in bulk matter • including: new representation of correlation functions • the p+p “reference” • intriguing features pp versus AA • non-femtoscopic effects • Global conservation effects (EMCICs) • Restricted phasespace calculations: GenBod (FOWL) • Analytic EMCIC calculations • Experimentalists’ recipe: • Fitting correlation functions [in progress] • Summary ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  3. PHOBOS BRAHMS RHIC PHENIX STAR Nuclear Particle AGS TANDEMS ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  4. Nuclear Particle STAR ~500 Collaborators Why heavy ion collisions? ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  5. 2 types (?) of collisions... looks like fun... looks like a mess... ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  6. A dynamical but crude view of the collision c/o UrQMD Collaboration, Frankfurt In this model, insufficient re-interactions ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  7. A dynamical but crude view of the collision In this model, insufficient re-interactions ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  8. R.H.I.C. defined... • collision of nuclei sufficiently large that nuclear details unimportant • distinct from nuclear or particle physics • “Geranium on Linoleum” • sufficiently large for meaningful bulk & thermodynamic quantities • non-trivial spatial scales & geometry drive bulk dynamics (e.g. flow) • how big is “sufficient” ? • important reference issue ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  9. phase structure of bulk system: • driving symmetries • long-range collective behaviour • “new” physics [superfluidity in l-He] • relevance of meaningful EoS ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  10. Generating a deconfined state • Present understanding of Quantum Chromodynamics (QCD) • heating • compression •  deconfined color matter ! Hadronic Matter (confined) Nuclear Matter (confined) Quark Gluon Plasma deconfined ! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  11. Expectations from Lattice QCD /T4 ~ # degrees of freedom deconfined: many d.o.f. confined: few d.o.f. TC ≈ 173 MeV ≈ 21012 K ≈ 130,000T[Sun’s core] ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  12. The four elements from 400 BC to 2000AD 400 BC : all creation Water Air ? Earth Fire ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  13. RHIC energies: the first quantitative success of hydro • direct access to EoS (phase transitions, lattice, etc.) EoS: P versus  versus n (Heinz et al) ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  14. energy quickly deposited • enter plasma phase • expand hydrodynamically • cool back to original phase • do geometric “postmortem” & infer momentum ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  15. energy quickly deposited • enter plasma phase • expand hydrodynamically • cool back to original phase • do geometric “postmortem” & infer momentum ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  16. b = 0  “central collision” many particles produced “peripheral collision” fewer particles produced Impact parameter & Reaction plane ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  17. b = 0  “central collision” many particles produced “peripheral collision” fewer particles produced Impact parameter & Reaction plane ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  18. How do semi-central collisions evolve? 1) Superposition of independent p+p: momenta pointed at random relative to reaction plane ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  19. How do semi-central collisions evolve? 1) Superposition of independent p+p: high density / pressure at center momenta pointed at random relative to reaction plane 2) Evolution as a bulksystem Pressure gradients (larger in-plane) push bulk “out”  “flow” “zero” pressure in surrounding vacuum more, faster particles seen in-plane ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  20. N N   0 0 /4 /4 /2 /2 3/4 3/4 -RP (rad) -RP (rad) How do semi-central collisions evolve? 1) Superposition of independent p+p: momenta pointed at random relative to reaction plane 2) Evolution as a bulksystem Pressure gradients (larger in-plane) push bulk “out”  “flow” more, faster particles seen in-plane ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  21. Azimuthal distributions at RHIC STAR, PRL90 032301 (2003) b ≈ 6.5 fm b ≈ 4 fm “central” collisions midcentral collisions ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  22. RHIC serves the perfect liquid Azimuthal distributions at RHIC STAR, PRL90 032301 (2003) b ≈ 10 fm b ≈ 6.5 fm b ≈ 4 fm peripheral collisions ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  23. 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, presently under study 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 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  24. Beyond press releases:Access to the dynamically-generated geometric substructure? The feature of collectivity: space is globally correlated with momentum ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  25. The Bottom line… if a pion is emitted, it is more likely to emit another pionwith very similar momentumif the source is small Creation probability r(x,p) = U*U F.T. of pion source Measurable! probingsource geometry through interferometry p1 r1 x1 p source r(x) 1 m x2 r2 p2 experimentally measuring this enhanced probability: quite challenging 5 fm ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  26. Au+Au: central collisions C(Qout) C(Qside) Au+Au R ~ 6 fm p+p R ~ 1 fm C(Qlong) d+Au R ~ 2 fm 3 “radii” by using 3-D vector q Correlation functions for different colliding systems STAR preliminary C2(Qinv) Qinv (GeV/c) Different colliding systems studied at RHIC Interferometry probes the smallest scales ever measured ! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  27. Au+Au: central collisions C(Qout) C(Qside) pa pa C(Qlong) pb pb xa xa xb xb 3 “radii” by using 3-D vector q Femtoscopic information • femtoscopic correlation at low |q| • must vanish at high |q|. [indep “direction”] ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  28. Au+Au: central collisions C(Qout) C(Qside) QLONG Q C(Qlong)  QOUT  QSIDE 3 “radii” by using 3-D vector q Femtoscopic information - Spherical harmonic representation nucl-ex/0505009 This new method of analysis represents a real breakthrough. ...(should) become a standard tool in all experiments. - A. Bialas, ISMD 2005 • femtoscopic correlation at low |q| • must vanish at high |q|. [indep “direction”] ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  29. Au+Au: central collisions C(Qout) C(Qside) C(Qlong) 3 “radii” by using 3-D vector q Femtoscopic information - Spherical harmonic representation nucl-ex/0505009 L=0 L=2 M=0 L=2 M=2 • femtoscopic correlation at low |q| • must vanish at high |q|. [indep “direction”] • ALM(Q) = L,0 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  30. Why do the radii fallwith increasing momentum ?? ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  31. Why do the radii fallwith increasing momentum ?? It’s collective flow !! Directgeometrical/dynamicalevidence for bulk behaviour!!! Amount of flow consistent with p-space nucl-th/0312024 Huge, diverse systematics consistent with this substructure nucl-ex/0505014 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  32. p+p: A clear reference system? ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  33. STAR preliminary mT (GeV) mT (GeV) femtoscopy in p+p @ STAR Z. Chajecki QM05 nucl-ex/0510014 • 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... • pT-dependence in p+p? • (same cause as in A+A?) ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  34. Ratio of (AuAu, CuCu, dAu) HBT radii by pp pp, dAu, CuCu - STAR preliminary Surprising („puzzling”) scaling A. Bialasz (ISMD05): I personally feel that its solution may provide new insight into the hadronization process of QCD HBT radii scale with pp Scary coincidence or something deeper? On the face: same geometric substructure ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  35. STAR preliminary d+Au peripheral collisions Gaussian fit BUT... Clear interpretation clouded by data features Non-femtoscopic q-anisotropic behaviour at large |q| does this structure affect femtoscopic region as well? ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  36. STAR preliminary d+Au peripheral collisions Gaussian fit Decomposition of CF onto Spherical Harmonics non-femtoscopic structure (not just “non-Gaussian”) Z.Ch., Gutierrez, MAL, Lopez-Noriega, nucl-ex/0505009 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  37. 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 effectsat low q ? • A possibility: energy-momentum conservation? • must be there somewhere! • but how to calculate / model ?(Upon consideration, non-trivial...) ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  38. statistics: “density of states” larger particle momentum more available states P conservation Induces “trivial” correlations (i.e. even for M=1) energy-momentum conservation in n-body states spectrum of kinematic quantity  (angle, momentum) given by n-body Phasespace factor Rn ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  39. 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) ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  40. ALL EVENTS ARE EQUAL, BUT SOME EVENTS ARE MORE EQUAL THAN OTHERS 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 ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  41. 6 particles ALL EVENTS ARE EQUAL, BUT SOME EVENTS ARE MORE EQUAL THAN OTHERS larger particle momentum more available states “Rounder” events: higher WT ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  42. ALL EVENTS ARE EQUAL, BUT SOME EVENTS ARE MORE EQUAL THAN OTHERS 30 particles larger particle momentum more available states “Rounder” events: higher WT ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  43. Genbod:phasespace sampling w/ P-conservation • Treat identical to measured events • use WT directly • MC sample WT • Form CF and SHD ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  44. Effect of varying frame & kinematic cuts Watch the green squares --  ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  45. N=18 <K>=0.9 GeV; LabCMS Frame - no cuts Watch the green squares ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  46. N=18 <K>=0.9 GeV; LabCMS Frame - ||<0.5 Watch the green squares kinematic cuts have strong effect! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  47. N=18 <K>=0.9 GeV, LCMS - no cuts Watch the green squares kinematic cuts have strong effect! as does choice of frame! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  48. N=18 <K>=0.9 GeV; LCMS - ||<0.5 Watch the green squares kinematic cuts have strong effect! as does choice of frame! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  49. N=18 <K>=0.9 GeV; PRF - no cuts Watch the green squares kinematic cuts have strong effect! as does choice of frame! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

  50. N=18 <K>=0.9 GeV; PRF - ||<0.5 Watch the green squares kinematic cuts have strong effect! as does choice of frame! ma lisa - Femtoscopy in small systems & EMCICs - Kent State University - January 2007

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