Z. Ch. - QM 2009, Knoxville, Tennessee, Mar 31, Zbigniew Chajcki, 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 (k10 & 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 , T with dN/d 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. Lisas 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. Lisas 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. Lisas 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 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 (4) system e.g. beam fragmentation probably not relevant to system emitting at midrapidity characteristic physical processes (strings etc): y ~ 12 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