1 / 59

Conservation Laws and Femtoscopy of Small Systems

Conservation Laws and Femtoscopy of Small Systems. [nucl-th/0612080]. Zbigniew Chaj ę cki and Michael A. Lisa The Ohio State University. Outline. Introduction / Motivation intriguing pp versus AA [reminder] data features not under control: Energy-momentum conservation?

akira
Download Presentation

Conservation Laws and Femtoscopy of Small Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Conservation Laws and Femtoscopy of Small Systems [nucl-th/0612080] Zbigniew Chajęcki and Michael A. LisaThe Ohio State University 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  2. Outline • 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 Energy and Momentum Conservation Induced Correlations • Experimentalists’ recipe: Fitting correlation functions [in progress] • Conclusion 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  3. Id. pion femtoscopy in p+p @ STAR STAR preliminary mT (GeV) mT (GeV) Z. Ch. (for STAR) QM05, NP A774:599-602,2006 • For the first time: femtoscopy in p+p and A+A measured in same experiment, same analysis definitions, …. • great opportunity to compare physics • what causes mT-dependence in p+p? • same cause as in A+A? 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  4. Ratio of femtoscopic radii Ratio of (AuAu, CuCu, dAu) HBT radii by pp • All pT(mT) dependences of HBT radii observed bySTAR scale with pp although it’s expected that different origins drivethese dependences • Femtoscopic radii scale with pp • Scary coincidence or something deeper? Z. Ch. (for STAR) QM05, NP A774:599-602,2006 pp, dAu, CuCu - STAR preliminary 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  5. Clear interpretation clouded by data features Non-femtoscopic q-anisotropic behaviour at large |q| does this structure affect femtoscopic region as well? d+Au: peripheral collisions STAR preliminary Qx<0.12 GeV/c 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  6. Spherical Harmonic Decomposition of the Correlation Function 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  7. Spherical Harmonic Decomposition of CF This new method of analysis represents, in my opinion, a real breakthrough. […] it has a good chance to become a standard tool in all experiments. A. Bialas, ISMD 2005 QLONG Q  QOUT  QSIDE • Cartesian-space (out-side-long) naturally encodes physics, but is poor/inefficient representation • Recognize symmetries of Q-space -- decompose by spherical harmonics! • Direct connection to source shapes [Danielewicz,Pratt: nucl-th/0501003] – decomposition of CF on cartesian harmonics • ~immune to acceptance • full information content at a glance[thanks to symmetries]  : [0,2p]  : [0,p] Z.Ch., Gutierrez, Lisa, Lopez-Noriega, nucl-ex/0505009 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  8. Decomposition of CF onto Spherical Harmonics Au+Au: central collisions C(Qout) C(Qside) C(Qlong) Z.Ch., Gutierrez, Lisa, Lopez-Noriega, [nucl-ex/0505009] Pratt, Danielewicz [nucl-th/0501003] Qx<0.03 GeV/c 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  9. Decomposition of CF onto Spherical Harmonics d+Au: peripheral collisions Z.Ch., Gutierrez, Lisa, Lopez-Noriega, [nucl-ex/0505009] Pratt, Danielewicz [nucl-th/0501003] STAR preliminary 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  10. Multiplicity dependence of the baseline Baseline problem is increasing with decreasing multiplicity STAR preliminary 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  11. GenBod Phase-Space Event Generator 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  12. GenBod: Phase-space sampling with energy/momentum conservation Energy-momentum conservation in n-body system Events generated randomly, but each has an Event Weight P conservation Induces “trivial” correlations (i.e. even for M=1) WT ~ probability of event to occur • 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 ! 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  13. Sampling MC Events Low probability (PS weight) 30 particles High probability (PS weight) To treat MC events identical to measured events we have to sample them according to WT (PS weight) Then we can construct CF 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  14. CF from GenBod Varying frame and kinematic cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  15. N=18, <K>=0.9 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  16. N=18, <K>=0.9 GeV, LabCMS Frame - ||<0.5 • The shape of the CF is sensitive to • kinematic cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  17. N=18, <K>=0.9 GeV, LCMS Frame - no cuts • The shape of the CF is sensitive to • kinematic cuts • frame 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  18. N=18, <K>=0.9 GeV, LCMS Frame - ||<0.5 • The shape of the CF is sensitive to • kinematic cuts • frame 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  19. GenBod Varying multiplicity and total energy 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  20. N=6, <K>=0.5 GeV, LCMS Frame - no cuts • The shape of the CF is sensitive to • kinematic cuts • frame 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  21. N=9, <K>=0.5 GeV, LCMS Frame - no cuts • The shape of the CF is sensitive to • kinematic cuts • frame • particle multiplicity 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  22. N=15, <K>=0.5 GeV, LCMS Frame - no cuts • The shape of the CF is sensitive to • kinematic cuts • frame • particle multiplicity 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  23. N=18, <K>=0.5 GeV, LCMS Frame - no cuts • The shape of the CF is sensitive to • kinematic cuts • frame • particle multiplicity 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  24. 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 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  25. 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 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  26. Findings • Energy and Momentum Conservation Induced Correlations (EMCICs) “resemble” our data so, EMCICs... on the right track... • But what to do with that? • Sensitivity to s, multiplicity 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!! • Danielewicz et al, PRC38 120 (1988) • Borghini, Dinh, & Ollitraut PRC62 034902 (2000) we generalize their 2D pT considerations to 4-vectors 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  27. k-particle distributions w/ phase-space constraints k-particle distribution (k<N) with P.S. restriction single-particle distribution w/o P.S. restriction 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  28. Central Limit Theorem Can we assume that E and p are not correlated ? For simplicity we will assume that all particles are identical (e.g. pions) -> they have the same average energy and RMS’s of energy/momentum Then, we can apply CLT (the distribution of averages from any distribution approaches Gaussian with increase of N) k-particle distribution in N-particle system 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  29. E - p correlations? 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  30. EMCICs in single-particle distribution ? What if all events had the same “parent” distribution f, and all centrality dependence of spectra was due just to loosening of P.S. restrictions as N increased? in this case, the index i is only keeping track of particle type 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  31. k-particle correlation function 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  32. 2-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) 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  33. 2-particle CF (1st term in 1/N expansion) “The pT term” “The E term” “The pZ term” Names used in the following plots 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  34. 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 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  35. N=6, <K>=0.5 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  36. N=9, <K>=0.5 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  37. N=15, <K>=0.5 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  38. N=18, <K>=0.5 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  39. N=18, <K>=0.7 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  40. N=18, <K>=0.9 GeV, LabCMS Frame - no cuts 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  41. Findings • first-order and full calculations agree well for N>9 • will be important for “experimentalist’s recipe” • Non-trivial competition/cooperation between pT, pz, E terms • all three important • pT1•pT2 term does affect “out-versus-side” (A22) • pz term has finite contribution to A22 (“out-versus-side”) • calculations come close to reproducing simulation for reasonable (N-2) and energy 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  42. The Experimentalist’s Recipe - average of X over # of pairs for each Q-bin Fitting formula: 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  43. EMCIC’s FIT: N=18, <K>=0.9GeV, LCMS 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  44. Fit contours 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  45. The Complete Experimentalist’s Recipe or image this … 9 fit parameters - 4 femtoscopic - normalization - 4 EMCICs or any other parameterization of CF Fit this …. 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  46. 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 to energy-momentum conservation • sampled by GenBod event generator • generates EMCICs quantified by Alm’s • stronger effects for small mult and/or s • Analytic calculation of EMCICs • 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 pT, pz, E conservation effects • Physically correct “recipe” to fit/remove EMCICs • 4 new parameters, determined @ large |Q| • parameters are “physical” - values may be guessed 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  47. Thanks to: • Alexy Stavinsky & Konstantin Mikhaylov (Moscow) [suggestion to use Genbod] • Jean-Yves Ollitrault (Saclay) & Nicolas Borghini (Bielefeld)[original correlation formula] • Adam Kisiel (Warsaw)[don’t forget energy conservation] • Ulrich Heinz (Columbus)[validating energy constraint in CLT] 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  48. Some properties of Alm coefficients • Alm = 0 for l or m odd – identical particle correlations (for non-id particles, odd l encodes shift information) • A00(Q) ≈ one-dimensional “CF(Qinv)” (bump ~ 1/R) • Alm(Q) = l,0 where correlations vanish • Al≠0,m(Q) ≠ 0  anisotropy in Q space • Im[Alm] = 0 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  49. Long-range correlations : JETS ? • Jets as a origin of the baseline problem ?? • The idea was to try to eliminate pions coming from jet fragmentation from data sample. It can be done by applying an event cut which accepts only events that have no high-pt tracks (jets). HBT analyses where done for three classes of events • all- all events accepted – as a reference • soft – only events without high-pT tracks ( highest-pT < 1.2 GeV/c was chosen) • hard- only events with least one track with pT > 2 GeV/c 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

  50. RL < RT ~acceptance free RL > RT RO < RS Simple, Gaussian source calculations RO > RS 23rd WWND, Big Sky, MT - Feb. 12-17, 2007

More Related