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EMCICs and the femtoscopy of small systems

EMCICs and the femtoscopy of small systems. Mike Lisa & Zbigniew Chajecki Ohio State University. 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]

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EMCICs and the femtoscopy of small systems

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

  2. 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 ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  3. energy quickly deposited • enter plasma phase • expand hydrodynamically • cool back to original phase • do geometric “postmortem” & infer momentum ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  4. energy quickly deposited • enter plasma phase • expand hydrodynamically • cool back to original phase • do geometric “postmortem” & infer momentum ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  5. RHIC serves the perfect liquid Beyond press releases 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 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 - ALICE week 12-16 Feb 2007 - Muenster

  6. 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 - ALICE week 12-16 Feb 2007 - Muenster

  7. 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 • femtoscopic correlation at low |q| • must vanish at high |q|. [indep “direction”] ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  8. 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 - ALICE week 12-16 Feb 2007 - Muenster

  9. 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 ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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

  11. 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 - ALICE week 12-16 Feb 2007 - Muenster

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

  13. 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 - ALICE week 12-16 Feb 2007 - Muenster

  14. 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 - ALICE week 12-16 Feb 2007 - Muenster

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

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

  17. 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 - ALICE week 12-16 Feb 2007 - Muenster

  18. 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 - ALICE week 12-16 Feb 2007 - Muenster

  19. 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 - ALICE week 12-16 Feb 2007 - Muenster

  20. 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 - ALICE week 12-16 Feb 2007 - Muenster

  21. 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 12-16 Feb 2007 - Muenster

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

  23. N=18, <K>=0.9 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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

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

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

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

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

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

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

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

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

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

  34. N=18, <K>=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 12-16 Feb 2007 - Muenster

  35. N=18, <K>=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 12-16 Feb 2007 - Muenster

  36. 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 p1 and p2 of particles forming pairs in |Q| bins • risky to “correct” data with Genbod... • Solution: calculate EMCICs using data!! • pT conservation and v2 • 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] • pT conservation and 3-particle correlations • Borghini ,nucl-th/0612093 ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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

  38. 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 12-16 Feb 2007 - Muenster

  39. 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 12-16 Feb 2007 - Muenster

  40. But... Energy conservation coupled to on-shell constraint  huge correlations between Etot, PX,tot, PY,tot, PZ,tot ??? ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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

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

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

  44. 2-particle correlation function (1st term in 1/N expansion) “The pT term” “The E term” “The pZ term” Names used in the following plots ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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

  46. N=6, <K>=0.5 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  47. N=9, <K>=0.5 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  48. N=15, <K>=0.5 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  49. N=18, <K>=0.5 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

  50. N=18, <K>=0.7 GeV, LabCMS Frame - no cuts ma lisa - ALICE week 12-16 Feb 2007 - Muenster

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