1. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 1 How interesting is momentum conservation? (How important is it?) Mike Lisa & Zbigniew Chajecki O Oxygen 15.9994 8 2626 S Sulfur 32.066 16 286286 U Uranium 238.02891 92 2 8 18 32 21 9 2

2. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 2 Outline Touchstones in R.H.I.C. at RHIC Crucial: apples::apples reference to p+p collisions (little/no collectivity?) femtoscopy (similarity to AA “coincidental”?) –importance of conservation laws (EMCICs *) soft-sector spectra (differences: “trivial” or physics?) –importance of conservation laws (EMCICs *) hard-sector spectra (R AA ) clear signal of physical quenching AA versus pp R AA versus R pp –importance of conservation laws (EMCICs *) “Conclusions” EMCICs: Energy and Momentum Conservation Induced Correlations

3. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 3 Introduction: Heavy ions & bulk matter

4. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 4 Perfect Press Releases Perfect or not, creation of a bulk system at RHIC is established - flow This system is very color dense and largely opaque to partons traversing it - R AA ?Are these statements unique to A+A collisions? blah blahthe quick brown/..fox...jumped..ove... th lazydog /// whatever one wants to say here s.....is just fine with mw. It’s not mattering at all. This is just a bunch of squiglly, unreadable text on this sllide I hope nobody can read itanyways since it is all nonsense. Not like that distinguishes it very much from much of my other writing, of course. But what the hell... OKlet’s just finish this lnbe and we’re done ature of EoS unde estigation ; agreement wi data might be accidental ; viscous hydrodynamics under development ; assumption of thermalization in question sensitivity to modeling of initial state, under intense study

5. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 5 Spectra v2v2 HBT Flow-dominated “Blast-wave” toy models capture main characteristics e.g. PRC70 044907 (2004)  K R (fm) m T (GeV/c) STAR PRL 91 262301 (2003) space-momentum substructure mapped in detail

6. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 6 AA versus pp: pion femtoscopy

7. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 7 p+p: A clear reference system?

8. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 8 STAR, nucl-ex/0305015 high pT suppression pQCD + Shadowing + Cronin pQCD + Shadowing + Cronin + Energy Loss Importance of a p+p reference : “jet quenching” in hard sector Deduced initial gluon density at   = 0.2 fm/c dN glue /dy ≈ 800-1200   ≈ 15 GeV/fm 3 (e.g. X.N. Wang nucl-th/0307036) R AA : the 2nd “crucial result” @ RHIC what about soft sector comparisons?

9. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 9 Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) Obtaining 3D radii from 3D correlation functions Au+Au: “Gaussian” radii capture bulk scales (but c.f. talk of R. Lacey) R(p T ) consistent with explosive flow typical “Gaussian” fitting function

10. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 10 The essence of CMB at a glance - decomposing WMAP survey (average over m  no “special” direction)

11. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 11 also: Danielewicz,Pratt: nucl-th/0501003 The essence of the 3D correlation function at a glance: SH decomposition Q OU T   Q SIDE Q LONG Q Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) 3 “radii” by using 3-D vector q extract 3D information from 3D CF but typically view projections (“set of zero measure”) identical treatment as CMB decomposition, except now direction matters (keep m) nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]

12. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 12 also: Danielewicz,Pratt: nucl-th/0501003 The essence of the 3D correlation function at a glance: SH decomposition Q OU T   Q SIDE Q LONG Q A l,m coefficients encode strength and order of angular oscillations simulated events nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]

13. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 13 also: Danielewicz,Pratt: nucl-th/0501003 The essence of the 3D correlation function at a glance: SH decomposition A l,m coefficients encode strength and order of angular oscillations... for each |Q| ! simulated events EMCICs only nucl-ex/0505009 & arXiv:0803.0022 [nucl-th]

14. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 14 also: Danielewicz,Pratt: nucl-th/0501003 The essence of the 3D correlation function at a glance: SH decomposition A l,m coefficients encode strength and order of angular oscillations... for each |Q| ! “full” 3D structure at a glance We have many values of Q, but only a few (l,m) combos CMB: have only one “Q-bin” but ~1000 relevant l values! --> similar data volume simulated events EMCICs only [Genbod; F. James 1968] nucl-ex/0505009 & arXiv:0803.0022 [nucl-th] simulated events EMCICs only

15. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 15 Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) Obtaining 3D radii from 3D correlation functions Au+Au: “Gaussian” radii capture bulk scales (but c.f. talk of R. Lacey) R(p T ) consistent with explosive flow typical “Gaussian” fitting function

16. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 16 Au+Au: central collisions C(Q out ) C(Q side ) C(Q long ) Obtaining 3D radii from 3D correlation functions

17. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 17 Obtaining 3D radii from 3D correlation functions Au+Au: “Gaussian” radii capture bulk scales (but c.f. talk of R. Lacey) R(p T ) consistent with explosive flow p+p (d+A): strong non-femtoscopic correlations not a “normalization” problem not a “non-Gaussian effect” typical “Gaussian” fitting function STAR preliminary d+Au peripheral collisions Gaussian fit

18. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 18 Obtaining 3D radii from 3D correlation functions STAR preliminary d+Au peripheral collisions Gaussian fit

19. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 19 We are not alone...

20. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 20 We are not alone... Non-femto correlations in B-E analysis through the years: CLEO PRD32 (1985) 2294NA22, Z. Phys. C71 (1996) 405 Q x <0.04 GeV/c OPAL, CERN-PH-EP/2007-025 (submitted to Eur. Phys. J. C.) Q x <0.2 GeV/c

21. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 21 non-femto “large-Q” behaviour - various approaches ignore it various ad-hoc parameterizations divide by  +  - (only semi-successful, and only semi-justified) divide by MonteCarlo PYTHIA, tuning until tail is matched (similar to ad-hoc) Can we understand it in terms of simplest-possible effect- correlations induced by conservation laws? Z. Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC

22. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 22 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)

23. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 23 Example of use of total phase space integral In absence of “physics” in M : (i.e. phase-space dominated) single-particle spectrum (e.g. p T ): “spectrum of events”: F. James, CERN REPORT 68-15 (1968) Hagedorn

24. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 24 Correlations arising from conservation laws (PS constraints) single-particle distribution w/o P.S. restriction k-particle distribution (k<N) with P.S. restriction no other correlations what we measure

25. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 25 Using central limit theorem (“large N-k”) k-particle distribution in N-particle system N.B. relevant later –Danielewicz et al, PRC38 120 (1988) –Borghini, Dinh, & Ollitraut PRC62 034902 (2000) –Borghini Eur. Phys. J. C30:381 ﾐ 385, (2003) –Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC

26. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 26 Using central limit theorem (“large N-k”) k-particle distribution in N-particle system N.B. relevant later –Danielewicz et al, PRC38 120 (1988) –Borghini, Dinh, & Ollitraut PRC62 034902 (2000) –Borghini Eur. Phys. J. C30:381 ﾐ 385, (2003) –Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC exact expression: calculable numerically (iteratively) correpondence with CLT discussed in detail in arXiv:0803.0022 [nucl-th] (for “femtoscopic” correlations -others need individual study)

27. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 27 Effects on single-particle distribution in this case, the index i is only keeping track of particle type, really

28. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 28 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)

29. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 29 Various fits to the pion correlation function (p+p) fit methodR out [fm]R side [fm]R long [fm] standard0.65 +/- 0.010.85 +/- 0.011.42 +/- 0.02 "NA22"1.18 +/- 0.021.05 +/- 0.021.75 +/- 0.03 "zeta-beta"1.01 +/- 0.030.79 +/- 0.031.52 +/- 0.05 EMCICs (constr.)1.05 +/- 0.021.06 +/- 0.021.66 +/- 0.03 EMCICs(free)1.06 +/- 0.021.08 +/- 0.021.69 +/- 0.03 plotting artifact

30. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 30 p+p minbias

31. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 31 Improved fit with non-femto correlations included minbias p+p collisions fem + non-fem fit methodR out [fm]R side [fm]R long [fm] standard0.65 +/- 0.010.85 +/- 0.011.42 +/- 0.02 "NA22"1.18 +/- 0.021.05 +/- 0.021.75 +/- 0.03 "zeta-beta"1.01 +/- 0.030.79 +/- 0.031.52 +/- 0.05 EMCICs (constr.)1.05 +/- 0.021.06 +/- 0.021.66 +/- 0.03 EMCICs(free)1.06 +/- 0.021.08 +/- 0.021.69 +/- 0.03 several treatments of non-femto tried understood (still in progress) as due to conservation laws worth it! - key probe of dynamics

32. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 32 femtoscopy in p+p @ STAR DELPHI Z 0 decay @ LEP m, m T (GeV) R (fm) R Z (fm) hep-ph/0108194   K p  STAR preliminary m T (GeV) 1. Heisenberg uncertainty? e.g. G. Alexander “plausible” in z-direction unlikely in transvrse 2. String fragmentation? (Lund) p T dependence maybe (??) mass dependence probably no [Andersson, Moriond 2000] 3. Resonance effects? e.g. Wiedemann & Heinz ‘97 maybe, but will be significantly different effect than for Au+Au Zbigniew Chajecki QM05 p+p and A+A measured in same experiment, same acceptance, same techniques unique opportunity to compare physics what causes p T -dependence in p+p? same cause as in A+A?

33. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 33 pp, dAu, CuCu - STAR preliminary Ratio of (AuAu, CuCu, dAu) HBT radii by pp R(p T ) taken as strong space-time evidence of flow in Au+Au clear, quantitative consistency predictions of BlastWave “Identical” signal seen in p+p cannot be of “identical” origin? (other than we “know it cannot”...)

34. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 34 Significant non-femto correlations, but little effect on “ message ” Ratio of (AuAu, CuCu, dAu) HBT radii by pp Fit w/o baseline parameterization NEW fit w/ baseline parameterization STAR preliminary alternate non-femto rather, “suggestion”: explosive flow in p+p?

35. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 35 AA versus pp: pT spectra in soft sector

36. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 36 p T spectra in soft sector: evidence against flow in p+p? STAR PRL 92 112301 (2004) minbias p+p 70-80% Au+Au 0-5% Au+Au  s NN = 200 GeV Blast-wave fit to spectra: much less explosive flow in p+p collisions BUT!

37. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 37 But remember! “distortion” of single-particle spectra What if the only difference between p+p and A+A collisions was N? measured “matrix element” Then we would measure:

38. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 38 Multiplicity evolution of spectra - p+p to A+A (soft sector) N evolution of spectra dominated by PS “distortion” p+p system samples same parent distribution, but under stronger PS constraints  5% central Au+Au  minbias p+p  “corrected” minbias p+p  “corrected” minbias p+p scaled

39. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 39 Multiplicity evolution of spectra - within p+p (soft sector) STAR, PRD74 032006 (2006) What if the only difference between multiplicity-selected p+p collisions was N? Then we would measure: pion mass assumed

40. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 40 Multiplicity evolution of spectra - within p+p (soft sector) soft sector: N evolution of spectra dominated by PS “distortion” STAR, PRD74 032006 (2006) pion mass assumed

41. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 41 Multiplicity evolution of spectra - within p+p (hard sector) hard sector: N evolution of spectra NOT explained by PS “distortion” STAR, PRD74 032006 (2006) pion mass assumed

42. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 42 pion mass assumed Multiplicity evolution of spectra - within p+p (hard sector) hard sector: N evolution of spectra NOT explained by PS “distortion” STAR, PRD74 032006 (2006) “R pp ” after dividing out EMCIC effects In fact, suggests high-pT tail in high multiplicity collisions is suppressed relative to low-multiplicity (like AA)

43. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 43 So you are saying that... There may be a bulk, collective system created in p+p, as A+A?? soft-sector signals: femtoscopy, spectra obscured if one ignores PS This bulk medium might suppress jets, similar to in A+A?? though P.S. effects make it appear opposite to A+A Whoever heard of such a stupid idea?!

44. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 44 So you are saying that... There may be a bulk, collective system created in p+p, as A+A?? soft-sector signals: femtoscopy, spectra obscured if one ignores PS This bulk medium might suppress jets, similar to in A+A?? though P.S. effects make it appear opposite to A+A Whoever heard of such a stupid idea?! Fig. 3

45. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 45 Does this maybe suggest......that the flow in A+A is nothing more than the individual p+p collisions flowing? (i.e. A+A is superposition of p+p) No! Quite the opposite. femtoscopically A+A looks like a big BlastWave not superposition of small BlastWaves A+A has thermalized globally spectra superposition of spectra from p+p has same shape as a spectrum from p+p! relaxation of P.S. constraints indicates A+A has thermalized globally

46. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 46 Does this maybe suggest......that the flow in A+A is nothing more than the individual p+p collisions flowing? (i.e. A+A is superposition of p+p) No! Quite the opposite. femtoscopically A+A looks like a big BlastWave not superposition of small BlastWaves A+A has thermalized globally spectra superposition of spectra from p+p has same shape as a spectrum from p+p! relaxation of P.S. constraints indicates A+A has thermalized globally anisotropic flow A+A shows increased signal over superposition of p+p is the p+p signal “flow” ??... that p+p looks like a “little A+A”? yes

47. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 47 Summary Collective motion: critical observable of bulk sector at RHIC bulk matter, “perfect liquid,” etc. evidence in AA from spectra, anisotropic flow, id and non-id femtoscopy apples::apples A+A::p+p invaluable to identify onset of bulk (or “new”) behaviour conservation laws can distort p+p, generating potentially misleading results p+p collisions may be more similar to A+A than usually thought collective flow? Rpp behaves “similar” to RAA? Danger of confusing “trivial” (?) effects with physics

48. mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008 48 THE END