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Mike Lisa Ohio State University

The multiplicity evolution of spectra at RHIC How different (really) are p+p and Au+Au collisions ?. Mike Lisa Ohio State University. Z. Chajecki & MAL, arXiv:0803.0022 [nucl-th]; Z. Chajecki & MAL arXiv:0807.3569 [nucl-th]. Outline.

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Mike Lisa Ohio State University

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  1. The multiplicity evolution of spectra at RHICHow different (really) are p+p and Au+Au collisions? Mike Lisa Ohio State University Z. Chajecki & MAL, arXiv:0803.0022 [nucl-th]; Z. Chajecki & MAL arXiv:0807.3569 [nucl-th]

  2. Outline • 2 Prime Discoveries in (heavy ion) collisions at RHIC: flow & RAA • Observed multiplicity evolution of spectra at RHIC (& conclusions derived) • EMCIC* effects • soft-sector implications • hard-sector speculations • Summary * EMCIC = “Energy and Momentum Induced Correlation/Constraint” mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  3. Perfect Press Releases 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 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 • Perfect or not, creation of a bulk system at RHIC is established – soft sector: flow • This system is very color dense and largely opaque to partons traversing it – hard sector: RAA • Are these statements unique to A+A collisions? mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  4. Spectra signals from hard & soft sectors • Jet “quenching” RAA • comparing “big” to “small” systems indispensible • clear evidence for suppression of fragmentation daughters mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland mike lisa - WPCF - Krakow - 11 Sept 2008

  5. Spectra signals from hard & soft sectors Spectra v2 HBT • Jet “quenching” RAA • comparing “big” to “small” systems indispensible • clear evidence for suppression of fragmentation daughters • Soft sector: evidence for collectivity • spectra • azimuthal correlations (v2) • femtoscopy (best probe…) • no reference to small system required? mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland mike lisa - WPCF - Krakow - 11 Sept 2008

  6. Spectra signals from hard & soft sectors Spectra v2 HBT • Jet “quenching” RAA • comparing “big” to “small” systems indispensible • clear evidence for suppression of fragmentation daughters • Soft sector: evidence for collectivity • spectra • azimuthal correlations (v2) • femtoscopy (best probe…) • no reference to small system required? • Central Au+Au collisions • T~105 MeV • <β> ~ 0.55 c • consistent with femtoscopy • Insensitive to space Can one have bulk collective behaviour in smaller systems? mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland mike lisa - WPCF - Krakow - 11 Sept 2008

  7. Spectra signals from hard & soft sectors Spectra v2 HBT • Jet “quenching” RAA • comparing “big” to “small” systems indispensible • clear evidence for suppression of fragmentation daughters • Soft sector: evidence for collectivity • spectra • azimuthal correlations (v2) • femtoscopy (best probe…) • no reference to small system required? NA22 Collaboration Z. Phys. C 71, 405–414 (1996) (hadron-hadron collisions) • Central Au+Au collisions • T~105 MeV • <β> ~ 0.55 c • consistent with femtoscopy • Insensitive to space OPAL Collaboration, Eur.Phys.J.C52:787-803,2007; arXiv:0708.1122 [hep-ex] [based on shape of C(q)…] Our data do not confirm the expectation from the string type model… A good description of our data is, however, achieved in the framework of the hydrodynamical expanding source model. Can one have bulk collective behaviour in smaller systems? E735 Collaboration, PRD48 1931 (1993) also PLB 2002 consistent with an expanding shell model. W. Kittel Acta Phys.Polon. B32 (2001) 3927 [Review article] R2tside , R2tout and, less markedly, R2long decrease with increasing kt . The presence of correlations between the particle production points and their momenta is an indication that the pion source is not static, but rather expands during the particle emission process. … and suggests the existence of an important “collective flow”, even in the system of particles produced in e+e− annihilation! A 1/√m T scaling first observed in heavy-ion collisions is now also observed in Z fragmentation and may suggest a “transverse flow” even there! mike lisa - WPCF - Krakow - 11 Sept 2008 mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland mike lisa - WPCF - Krakow - 11 Sept 2008

  8. Spectra signals from hard & soft sectors Spectra v2 HBT • Jet “quenching” RAA • comparing “big” to “small” systems indispensible • clear evidence for suppression of fragmentation daughters • Soft sector: evidence for collectivity • spectra • azimuthal correlations (v2) • femtoscopy (best probe…) • no reference to small system required? NA22 Collaboration Z. Phys. C 71, 405–414 (1996) (hadron-hadron collisions) • Central Au+Au collisions • T~105 MeV • <β> ~ 0.55 c • consistent with femtoscopy • Insensitive to space OPAL Collaboration, Eur.Phys.J.C52:787-803,2007; arXiv:0708.1122 [hep-ex] [based on shape of C(q)…] Our data do not confirm the expectation from the string type model… A good description of our data is, however, achieved in the framework of the hydrodynamical expanding source model. • RHIC: “comparison machine” • Vary size. All else fixed. • spectra • femtoscopy (Z. Chajecki) Can one have bulk collective behaviour in smaller systems? E735 Collaboration, PRD48 1931 (1993) also PLB 2002 consistent with an expanding shell model. W. Kittel Acta Phys.Polon. B32 (2001) 3927 [Review article] R2tside , R2tout and, less markedly, R2long decrease with increasing kt . The presence of correlations between the particle production points and their momenta is an indication that the pion source is not static, but rather expands during the particle emission process. … and suggests the existence of an important “collective flow”, even in the system of particles produced in e+e− annihilation! A 1/√m T scaling first observed in heavy-ion collisions is now also observed in Z fragmentation and may suggest a “transverse flow” even there! mike lisa - WPCF - Krakow - 11 Sept 2008 mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland mike lisa - WPCF - Krakow - 11 Sept 2008

  9. Multiplicity evolution of pT spectra Au+Au 0-5% Au+Au 60-70% p+p minbias STAR PRL 92 112301 (2004) mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  10. Blast-wave fit to spectra: • much less explosive flow, (& higher “temperature”) in low-multiplicity collisions (as per prejudice) mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  11. Blast-wave fit to spectra: • much less explosive flow, (& higher “temperature”) in low-multiplicity collisions (as per prejudice) • BUT: correlation studies (e.g. Chajęcki) clear finite-number effects. • Would that affect spectra? mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  12. energy-momentum conservation in n-body states statistics: “density of states” larger particle momentum more available states P conservation Induces “trivial” correlations (i.e. even for M=1) spectrum of kinematic quantity  (angle, momentum) given by n-body Phasespace factor Rn mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  13. Example of use of total phase space integral Hagedorn • In absence of “physics” in M : (i.e. phase-space dominated) • single-particle spectrum (e.g. pT): • “spectrum of events”: F. James, CERN REPORT 68-15 (1968) mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  14. Correlations arising (only) from conservation laws (PS constraints) single-particle “parent” distribution w/o P.S. restriction what we measure no other correlations k-particle distribution (k<N) with P.S. restriction mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  15. Simplification for “large” N-k (1) Numerator is the probability distribution of a sum of many (N-k) uncorrelated vectors (i.e. the probability that they will add up to P-Σi=1kpi) If (N-k) big Multivariate Central Limit Theorem Denominator is “just” a constant normalization (indep pi) mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  16. Using central limit theorem (“large* N-k”) N.B. relevant later k-particle distribution in N-particle system • Danielewicz et al, PRC38 120 (1988) • Borghini, Dinh, & Ollitraut PRC62 034902 (2000) • Borghini Eur. Phys. J. C30:381-385, (2003) • Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC * “large”: N > ~10

  17. k-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) mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  18. Effects on single-particle distribution • Finite-particle “distortion” • 1st, 2nd moments of parent <E>, <E2>, <pT2> • multiplicity N in this case, the index i is only keeping track of particle type, really mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  19. “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 primary particles (including unmeasured γ’s etc) • secondary decay (resonances, fragmentation) smears connection b/t <E2> and measured one • “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 only stealing energy from the system which then redistributes? • “relevant system” ≠ “whole system”,  total energy-momentum will vary somewhatevent-to-event – see definition above • <E2> etc: averages of the parent distribution mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  20. “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 • What to expect? mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  21. What drives the evolution? measured Au+Au 0-5% “matrix element” Au+Au 60-70% p+p minbias STAR PRL 92 112301 (2004)

  22. What drives the evolution? measured “matrix element” What ifthe only difference between p+p and A+A collisions was N? Then we would measure: mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  23. 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 K ~ unity. driven by conservation of discrete quantum #s (strangeness, etc)

  24. By popular demand… Almost universal “flow” & “temperature” parameters in a BlastWave fit Apparent changes in β, T with dN/dη caused by EMCICs* * EMCIC = Energy & Momentum Conservation Induced Constraint

  25. Kinematic scales of “the system”

  26. Multiplicity evolution of spectra - within p+p (soft sector) What if the only difference between multiplicity-selected p+p collisions was N? STAR, PRD74 032006 (2006) …Then we would measure: pion mass assumed mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  27. Multiplicity evolution of spectra - within p+p (soft sector) Account for “trivial” before inferring more “profound” messages unidentified particles  cannot conclude that EMCICs is the whole story… …but it appears to be most of it. STAR, PRD74 032006 (2006) pion mass assumed mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  28. Summary • E&M conservation induces phasespace constraints w/ explicit N dependence • obviously should not be ignored in (crucial!) N-dependent comparisons • significant effect on 2- (and 3-) particle correlations [c.f. Danielewicz, Borghini, Voloshin, Chajęcki…] • …and single-particle spectra (often neglected because no “red flags”) • Soft sector: • differences observed in pT spectra consistent with EMCIC “distortion” of unchanging parent distribution mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  29. Can we look at higher pT ? • Not quantitatively… • CLT approximation becomes unreliable for E > ~2÷3<E>c • also: jets – are they“of the system” ? • statistical energy-sharing questionable But do it anyways, just to see… CLT approx • Calculation shown: GENBOD program of Fred James (CERN 1968) • correlations due only to EMCICs • intrinsic “algorithmic” parent distribution

  30. Au+Au collisions • High multiplicity collisions suppressed at high pT, relative to low multiplicity: • NOT explained by phasespace restrictions (EMCICs) • parent (physics) drives the change mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  31. p+p collisions • High multiplicity collisions enhanced at high pT, relative to low multiplicity: • but not as enhanced as if only EMCICs were at play: Rpp mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  32. p+p collisions • High multiplicity collisions enhanced at high pT, relative to low multiplicity: • but not as enhanced as if only EMCICs were at play: Rpp • naively (!!) “correct” for EMCICs  R’pp • high-pT suppression in p+p ??? Calculation way too quantitatively (conceptually?) unreliable at this pT Conclude only that “trivial” effects might be large here, should be considered in addition to more profound physics conclusions mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  33. Summary • E&M conservation induces phasespace constraints w/ explicit N dependence • obviously should not be ignored in (crucial!) N-dependent comparisons • significant effect on 2- (and 3-) particle correlations [c.f. Danielewicz, Borghini, Voloshin, Chajęcki…] • …and single-particle spectra (often neglected because no “red flags”) • Soft sector (~quantitative): • differences observed in pT spectra consistent with EMCIC “distortion” of unchanging parent distribution • Hard sector (qualitative): • EMCICs do not explain N-dependence of spectra (RAA) – parent changes • EMCIC effects in p+p big, may modify physics conclusions mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

  34. Summary • E&M conservation induces phasespace constraints w/ explicit N dependence • obviously should not be ignored in (crucial!) N-dependent comparisons • significant effect on 2- (and 3-) particle correlations [c.f. Danielewicz, Borghini, Voloshin, Chajęcki…] • …and single-particle spectra (often neglected because no “red flags”) • Soft sector (~quantitative): • differences observed in pT spectra consistent with EMCIC “distortion” of unchanging parent distribution • Hard sector (qualitative): • EMCICs do not explain N-dependence of spectra (RAA) – parent changes • EMCIC effects in p+p big, may modify physics conclusions • “jet quenching” in p+p ?? • In terms of our “big physics” at RHIC, • How different (really) are p+p and A+A collisions? • flow in p+p? – spectral signal same as A+A • jet quenching in p+p? much less clear mike lisa - WPCF - 11-14 Sept 2008 - Krakow Poland

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