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How interesting is momentum conservation? (How important is it?)

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##### How interesting is momentum conservation? (How important is it?)

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**8**16 92 2 8 18 32 21 9 2 2 6 2 8 6 O S U Oxygen 15.9994 Sulfur 32.066 Uranium 238.02891 How interesting is momentum conservation?(How important is it?) Mike Lisa & Zbigniew Chajecki mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 (RAA) • clear signal of physical quenching AA versus pp • RAA versus Rpp • importance of conservation laws (EMCICs *) • “Conclusions” EMCICs: Energy and Momentum Conservation Induced Correlations mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 - flow • This system is very color dense and largely opaque to partons traversing it - RAA • Are these statements unique to A+A collisions? mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Spectra**v2 R (fm) space-momentum substructure mapped in detail STAR PRL 91 262301 (2003) HBT mT (GeV/c) Flow-dominated “Blast-wave” toy models capture main characteristics e.g. PRC70 044907 (2004) K mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**p+p: A clear reference system?**mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**RAA: the 2nd “crucial result” @ RHIC**what about soft sector comparisons? Importance of a p+p reference : “jet quenching” in hard sector STAR, nucl-ex/0305015 pQCD + Shadowing + Cronin high pT suppression pQCD + Shadowing + Cronin + Energy Loss Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200 e≈ 15 GeV/fm3(e.g. X.N. Wang nucl-th/0307036) mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Au+Au: central collisions**C(Qout) typical “Gaussian” fitting function C(Qside) C(Qlong) Obtaining 3D radii from 3D correlation functions • Au+Au: “Gaussian” radii capture bulk scales • (but c.f. talk of R. Lacey) • R(pT) consistent with explosive flow mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**The essence of CMB at a glance - decomposing WMAP survey**(average over m no “special” direction) mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Au+Au: central collisions**C(Qout) C(Qside) QLONG Q C(Qlong) QOUT QSIDE 3 “radii” by using 3-D vector q nucl-ex/0505009 & arXiv:0803.0022 [nucl-th] The essence of the 3D correlation function at a glance: SH decomposition • 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) also: Danielewicz,Pratt: nucl-th/0501003 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**simulated events**QLONG Q QOUT QSIDE nucl-ex/0505009 & arXiv:0803.0022 [nucl-th] The essence of the 3D correlation function at a glance: SH decomposition • Al,m coefficients encode strength and order of angular oscillations also: Danielewicz,Pratt: nucl-th/0501003 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**simulated events**simulated events EMCICs only nucl-ex/0505009 & arXiv:0803.0022 [nucl-th] The essence of the 3D correlation function at a glance: SH decomposition • Al,m coefficients encode strength and order of angular oscillations • ... for each |Q| ! also: Danielewicz,Pratt: nucl-th/0501003 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**simulated events**EMCICs only “full” 3D structure at a glance nucl-ex/0505009 & arXiv:0803.0022 [nucl-th] The essence of the 3D correlation function at a glance: SH decomposition • Al,m coefficients encode strength and order of angular oscillations • ... for each |Q| ! simulated events EMCICs only [Genbod; F. James 1968] • 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 also: Danielewicz,Pratt: nucl-th/0501003 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Au+Au: central collisions**C(Qout) typical “Gaussian” fitting function C(Qside) C(Qlong) Obtaining 3D radii from 3D correlation functions • Au+Au: “Gaussian” radii capture bulk scales • (but c.f. talk of R. Lacey) • R(pT) consistent with explosive flow mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Au+Au: central collisions**C(Qout) C(Qside) C(Qlong) Obtaining 3D radii from 3D correlation functions mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**STAR preliminary**d+Au peripheral collisions typical “Gaussian” fitting function Gaussian fit Obtaining 3D radii from 3D correlation functions • Au+Au: “Gaussian” radii capture bulk scales • (but c.f. talk of R. Lacey) • R(pT) consistent with explosive flow • p+p (d+A): strong non-femtoscopic correlations • not a “normalization” problem • not a “non-Gaussian effect” mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**STAR preliminary**d+Au peripheral collisions Gaussian fit Obtaining 3D radii from 3D correlation functions mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**We are not alone...**mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Qx<0.04 GeV/c**Qx<0.2 GeV/c CLEO PRD32 (1985) 2294 NA22, Z. Phys. C71 (1996) 405 OPAL, CERN-PH-EP/2007-025(submitted to Eur. Phys. J. C.) Non-femto correlations in B-E analysis through the years: We are not alone... mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**statistics: “density of states”**larger particle momentum more available states P conservation Induces “trivial” correlations (i.e. even for M=1) energy-momentum conservation in n-body states spectrum of kinematic quantity (angle, momentum) given by n-body Phasespace factor Rn mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Hagedorn**Example of use of total phase space integral • 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 - Winter Workshop on Nuclear Dynamics -12 april 2008**single-particle distribution**w/o P.S. restriction k-particle distribution (k<N) with P.S. restriction Correlations arising from conservation laws (PS constraints) what we measure no other correlations mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**N.B.**relevant later Using central limit theorem (“large N-k”) 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ﾐ385, (2003) • Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**exact expression:**• calculable numerically (iteratively) • correpondence with CLT discussed in detail in arXiv:0803.0022 [nucl-th] • (for “femtoscopic” correlations -others need individual study) N.B. relevant later Using central limit theorem (“large N-k”) 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ﾐ385, (2003) • Chajecki & MAL, arXiv:0803.0022 [nucl-th], sub PRC mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Effects on single-particle distribution**in this case, the index i is only keeping track of particle type, really mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Dependence on “parent” distrib f vanishes,**except for energy/momentum means and RMS k-particle correlation function 2-particle correlation function (1st term in 1/N expansion) mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**p+p minbias**mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**fem + non-fem**Improved fit with non-femto correlations included minbias p+p collisions • several treatments of non-femto tried • understood (still in progress) as due to conservation laws • worth it! - key probe of dynamics mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Zbigniew Chajecki QM05**Z0 decay @ LEP R Z(fm) DELPHI R (fm) K p STAR preliminary mT (GeV) mT (GeV) m, mT (GeV) hep-ph/0108194 femtoscopy in p+p @ STAR 1. Heisenberg uncertainty? • e.g. G. Alexander • “plausible” in z-direction • unlikely in transvrse 2. String fragmentation? (Lund) • p+p and A+A measured in same experiment, same acceptance, same techniques • unique opportunity to compare physics • what causes pT-dependence in p+p? • same cause as in A+A? 3. Resonance effects? • pT dependence maybe (??) • mass dependence probably no [Andersson, Moriond 2000] • e.g. Wiedemann & Heinz ‘97 • maybe, but will be significantly different effect than for Au+Au mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Ratio of (AuAu, CuCu, dAu) HBT radii by pp**• R(pT) 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”...) pp, dAu, CuCu - STAR preliminary mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**alternate non-femto**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 NEW fit w/ baseline parameterization Fit w/o baseline parameterization mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**pT spectra in soft sector: evidence against flow in p+p?**sNN = 200 GeV 0-5% Au+Au BUT! 70-80% Au+Au minbias p+p STAR PRL 92 112301 (2004) • Blast-wave fit to spectra: • much less explosive flow in p+p collisions mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**But remember!**measured “distortion” of single-particle spectra “matrix element” What if the only difference between p+p and A+A collisions was N? Then we would measure: mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Multiplicity evolution of spectra - p+p to A+A (soft sector)** 5% central Au+Au “corrected” minbias p+p scaled “corrected” minbias p+p minbias p+p N evolution of spectra dominated by PS “distortion” p+p system samples same parent distribution, but under stronger PS constraints mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Multiplicity evolution of spectra - within p+p (soft sector)**What if the only difference between multiplicity-selected p+p collisions was N? Then we would measure: STAR, PRD74 032006 (2006) pion mass assumed mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Multiplicity evolution of spectra - within p+p (soft sector)**STAR, PRD74 032006 (2006) soft sector: N evolution of spectra dominated by PS “distortion” pion mass assumed mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**Multiplicity evolution of spectra - within p+p (hard sector)**STAR, PRD74 032006 (2006) hard sector: N evolution of spectra NOT explained by PS “distortion” pion mass assumed mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**In fact, suggests high-pT tail in high multiplicity**collisions is suppressed relative to low-multiplicity (like AA) Multiplicity evolution of spectra - within p+p (hard sector) “Rpp” after dividing out EMCIC effects STAR, PRD74 032006 (2006) hard sector: N evolution of spectra NOT explained by PS “distortion” pion mass assumed mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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?! mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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 mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**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” (?) effectswith physics mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008**THEEND**mike lisa - Winter Workshop on Nuclear Dynamics -12 april 2008