Zbigniew Chaj ę cki, Mike Lisa Ohio State University

1. Z. Ch. & M. Lisa, PRC 78 064903 (2008) Z. Ch. & M. Lisa, PRC 79 034908 (2009) Z. Ch., arXiv:0901.4078 [nucl-ex] Z. Ch. & M. Lisa, to be published Do p+p Collisions Flow at RHIC?Understanding One- and Two-particle Distributions, Multiplicity Evolution, and Conservation Laws Zbigniew Chajęcki, Mike Lisa Ohio State University Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

2. Outline & Motivation • p+p as a reference to heavy ion collisions • Effect of the phase-space constraints due to energy and momentum conservation • Re-examining multiplicity-evolution of pT spectra, considering evolution of available phase space • postulate of unchanging parent distribution • Consistent treatment of the phase-space constraints and bulk in femtoscopy and spectra [hard sector] [soft sector] • Heavy ion collisions as a reference to p+p? • Summary Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

3. Small vs Big STAR, PRL93 (2004) 252301 STAR PRL 92 112301 (2004) Au+Au p+p Small system (p+p) Large system (Au+Au) Hard sector : p+p apparently different than Au+Au Soft sector : Is p+p a clear reference to Au+Au? Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

4. Phase-Space varies with multiplicity Phase-space factor: Hagedorn/Fermi Phase-space constraints Extreme case, N=3, easily calculable with Dalitz plot What about the effect for higher number of particles? Dalitz plot for a three-body final state. (p at 3 GeV), PDG 2008 Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

5. Correlations arising (only) from conservation laws (PS constraints) single-particle “parent” distribution w/o P.S. restriction what we measure no other correlations with P.S. restriction k-particle distribution (k<N) CLT approximation works best for N>10 & Ei< 23<E> Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

6. Phase-space effect on k-particle distribution k-particle distribution in N-particle system (in CMS frame) “distortion” due to PS constraints • Danielewicz et al, PRC38 120 (1988) • Borghini, Dinh, & Ollitraut PRC62 034902 (2000) • Borghini, Eur. Phys. J. C30:381-385, (2003) • Chajecki & Lisa, PRC 78 064903 (2008), PRC 79 034908 (2009) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

7. Phase-space effect on kinematic observables 1-particle PS effect 2-particle PS effect N=40 3-particle PS effect Borghini et al, PRC 66 014901 (2002) - also, Danielewicz, PLBB157:146 (1985) NA49 pions N. Borghini, PRC75:021904 (2007) Finite-particle constrains Z.Ch, M.Lisa, PRC 79 034908 (2009) N=5 CF (GenBod) EMCICs Z. Ch, M. Lisa, PRC 78 064903 (2008) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

8. 1-particle phase-space effect STAR PRL 92 112301 (2004) Then we would measure: measured Au+Au 0-5% Au+Au 60-70% “distortion” of single-particle spectra “matrix element” What ifthe only difference between p+p and A+A collisions was N? p+p minbias STAR PRL 92 112301 (2004) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

9. Multiplicity evolution of spectra - p+p to A+A (soft sector) STAR PRL 92 112301 (2004) N evolution of spectra dominated by PS “distortion” p+p system samples same parent distribution, but under stronger PS constraints Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

10. Kinematic scales of “the system” Fit results for p+p consistent with expectations from Maxwell-Boltzman equation, Blast-wave, Pythia, … • postulate of same parent consistent with all spectra • magnitude • pT dependence (shape) • mass dependence Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

11. By popular demand Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004. STAR PRL 92 112301 (2004) Almost universal “flow” & “temperature” parameters in a BlastWave fit Apparent changes in β, T with dN/dη caused by finite phase-space effect p+p Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

12. Blast-wave in p+p@200GeV: simultaneous description of spectra, HBT determined entirely by spectra STAR Preliminary See M. Lisa’s poster (STAR) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

13. Fits to pion CF in p+p by STAR Use parameters obtained from the fit to STAR femtoscopic correlation function and use them to “correct” spectra kT = [0.35,0.45] GeV/c STAR preliminary STAR Preliminary See M. Lisa’s poster (STAR) exp CF HBT HBT+ “conservation” Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

14. Combined fit: consistent flow-based description STAR Preliminary See M. Lisa’s poster (STAR) Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004. Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

15. Combined fit: consistent flow-based description “raw” (ignoring PS effets) p+p collisions show same flow signals as A+A collisions PS effects fixed by correlations Joint spectra/HBT BW fit PS effects free adjusted to spectra & fit to spectra PS effects fixed by correlations Joint spectra/HBT BW fit “raw” (ignoring PS effects) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

16. Summary STAR Preliminary exp CF HBT HBT+ “conservation” STAR PRL 92 112301 (2004) ? • Energy and momentum conservation induces phase-space constraint that has explicit multiplicity dependence • should not be ignored in (crucial!) N-dependent comparisons • significant effect on 2- (and 3-) particle correlations [c.f. Ollitrault, Borghini, Voloshin…] • …and single-particle spectra (often neglected because no “red flags”) • Femtoscopy & Spectra • in H.I.C., well understood, detailed fingerprint of flow • RHIC – first opportunity for direct comparison with p+p • accounting for finite phase-space effects  identical flow signals in p+p • Has A+A become the reference system for p+p in non-perturbative sector??? Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

17. “the system”… a nontrivial concept Characteristic scales of relevant system in which limited energy-momentum is shared • Not known a priori • should track measured quantities, but not be identical to them • N includes all primary particles (including unmeasured γ’s etc) • secondary decay (resonances, fragmentation) smears connection b/t <E2> and measured one • <E2> etc: averages of the parent distribution • “relevant system” almost certainly not the “whole” (4π) system • e.g. beam fragmentation probably not relevant to system emitting at midrapidity • characteristic physical processes (strings etc): Δy ~ 1÷2 • jets: “of the system” ?? • or just stealing energy from “the system?” • if “relevant system” ≠ “whole system”, then total energy-momentum will fluctuatee-by-e Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

18. Consistency check …. Characteristic scales of relevant system in which limited energy-momentum is shared Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

19. Heavy Ion Collisions : Explosive flow revealed through specific fingerprints on soft-sector observables Spectra v2 HBT calculable in hydrodynamics or toy “blast wave” models slow  fast  Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

20. Femtoscopy - direct evidence of flow Spectra v2 R (fm) space-momentum substructure mapped in detail STAR PRL 91 262301 (2003) HBT mT (GeV/c)  K Flow-dominated “Blast-wave” toy models capture main characteristics e.g. PRC70 044907 (2004) Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

21. Implication: A+A is just a collection of flowing 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 rather, p+p looks like a “little A+A” Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

22. EMCIC fit to STAR p+p data kT = [0.15,0.25] GeV/c kT = [0.25,0.35] GeV/c kT = [0.35,0.45] GeV/c kT = [0.45,0.60] GeV/c STAR preliminary Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

23. Average matrix element - factorization Probability for an n-particle final state: dynamics kinematics Single-particle spectrum R. Hagedorn, Relativistic Kinematics 1963 Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

24. … STAR PRC 2007 Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

25. World Systematics : R(pT/mT) in small systems STAR preliminary STAR preliminary from STAR talk at WWND 2009 non-STAR data taken from Z. Ch. arXiv:0901.4078 [nucl-ex] ** Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

26. Non-femto correlations Multiplicity increases Qx<0.2 GeV/c E766, PRD 49 (1994) 4373 OPAL, Eur. Phys. J. C52 (2007) 787-803 Qx<0.04 GeV/c NA23, Z. Phys. C43 (1989) 341 CLEO PRD32 (1985) 2294 NA22, Z. Phys. C71 (1996) 405 Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

27. Significant non-femto correlations, but little effect on “message” rather, “suggestion”: explosive flow in p+p? Ratio of (AuAu, CuCu, dAu) HBT radii by pp STAR preliminary Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

28. STAR ϕ spectra PLB 612 (2005) 181 99 (2007) 112301 folks use this one for p+p data … and this one for Au+Au data (looks better than the one to the left!) looks to me like the spectrum evolves… jetty starting ~ mT-m=1.5  pT=2.3 arXiv:0809.4737 these ones are recently submitted papers that replot the data from the above arXiv:0810.4979 submitted Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

29. phi agrees as well/poorly as pi/K/p from our paper Z. Chajecki & M. Lisa PRC 79 034908 (2009) as discussed in our paper, EMCICs alone is not enough to explain behavior beyond ~ 1GeV/c using same parameters as in our paper, multiplicity-dependence of phi is described, as well, and up to same pT, as pi/k/p Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

30. Phase-space effects in PYTHIA  correlation function from PYTHIA It’s likely that there are also other correlations in PYTHIA than just due to E&M correlations Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009

31. b Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 2009