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Conservation laws & femtoscopy of small systems

This presentation explores femtoscopy in small systems and EMCICs, highlighting the conservation laws and dynamics of small collision systems. Includes discussions on global conservation effects, restricted phase space calculations, and experimental fitting of correlation functions. Topics such as phase structure of bulk systems and generating a deconfined state are also covered. Theoretical and experimental perspectives on collision dynamics are examined, providing insights into nuclear and particle interactions.

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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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