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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, 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 p T 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]  Heavy ion collisions as a reference to p+p?  Summary [soft sector]

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Phase-Space varies with multiplicity 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 Phase-space factor: Hagedorn/Fermi

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Phase-space effect on k-particle distribution k-particle distribution in N-particle system (in CMS frame) –Danielewicz et al, PRC (1988) –Borghini, Dinh, & Ollitraut PRC (2000) –Borghini, Eur. Phys. J. C30: , (2003) –Chajecki & Lisa, PRC (2008), PRC (2009) “distortion” due to PS constraints

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

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

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

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, By popular demand 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 STAR PRL (2004) Blast-Wave Model: F. Retiere, M. Lisa, PRC70:044907,2004.

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Blast-wave in 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, Fits to pion CF in p+p by STAR HBT exp CF HBT+ “conservation” STAR preliminary k T = [0.35,0.45] GeV/c Use parameters obtained from the fit to STAR femtoscopic correlation function and use them to “correct” spectra STAR Preliminary See M. Lisa’s poster (STAR)

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Combined fit: consistent flow-based description “raw” (ignoring PS effets) “raw” (ignoring PS effects) 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 p+p collisions show same flow signals as A+A collisions

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Summary  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??? ? HBT exp CF HBT+ “conservation” STAR PRL (2004) STAR Preliminary

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, “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 1.N includes all primary particles (including unmeasured γ’s etc) 2.secondary decay (resonances, fragmentation) smears connection b/t and measured one 3. etc: averages of the parent distribution 4.“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 fluctuate e-by-e

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Spectra v2v2 HBT Heavy Ion Collisions : Explosive flow revealed through specific fingerprints on soft-sector observables calculable in hydrodynamics or toy “blast wave” models slow  fast 

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Femtoscopy - direct evidence of flow Spectra v2v2 HBT Flow-dominated “Blast-wave” toy models capture main characteristics e.g. PRC (2004)  K R (fm) m T (GeV/c) STAR PRL (2003) space-momentum substructure mapped in detail

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

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

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

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

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

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

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

Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, phi agrees as well/poorly as pi/K/p from our paper Z. Chajecki & M. Lisa PRC (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, 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, b