1. Sasha Milov Focus on Multiplicity Bari June 17, 2004 1 dN ch /dη and dE T /dη at Mid-Rapidity from SIS to LHC Alexander Milov for the PHENIX collaboration June 17, 2004

2. Sasha Milov Focus on Multiplicity Bari June 17, 2004 2 Outline.  Apparatus, Measurements & Errors:  PHENIX detector  dN ch /dη and dE T /dη measurement in PHENIX  Centrality & Trigger efficiency analysis using NBD.  Results:  PHENX results  RHIC and lower energy results  Physics:  √s NN dependencies  Averaged /  Centrality shape  Theoretical Models from Experimental Point of View  Summary

3. Sasha Milov Focus on Multiplicity Bari June 17, 2004 3 USA Abilene Christian University, Abilene, TX Brookhaven National Laboratory, Upton, NY University of California - Riverside, Riverside, CA University of Colorado, Boulder, CO Columbia University, Nevis Laboratories, Irvington, NY Florida State University, Tallahassee, FL Florida Technical University, Melbourne, FL Georgia State University, Atlanta, GA University of Illinois Urbana Champaign, Urbana-Champaign, IL Iowa State University and Ames Laboratory, Ames, IA Los Alamos National Laboratory, Los Alamos, NM Lawrence Livermore National Laboratory, Livermore, CA University of New Mexico, Albuquerque, NM New Mexico State University, Las Cruces, NM Dept. of Chemistry, Stony Brook Univ., Stony Brook, NY Dept. Phys. and Astronomy, Stony Brook Univ., Stony Brook, NY Oak Ridge National Laboratory, Oak Ridge, TN University of Tennessee, Knoxville, TN Vanderbilt University, Nashville, TN Brazil University of São Paulo, São Paulo China Academia Sinica, Taipei, Taiwan China Institute of Atomic Energy, Beijing Peking University, Beijing France LPC, University de Clermont-Ferrand, Clermont-Ferrand Dapnia, CEA Saclay, Gif-sur-Yvette IPN-Orsay, Universite Paris Sud, CNRS-IN2P3, Orsay LLR, Ecòle Polytechnique, CNRS-IN2P3, Palaiseau SUBATECH, Ecòle des Mines at Nantes, Nantes Germany University of Münster, Münster Hungary Central Research Institute for Physics (KFKI), Budapest Debrecen University, Debrecen Eötvös Loránd University (ELTE), Budapest India Banaras Hindu University, Banaras Bhabha Atomic Research Centre, Bombay Israel Weizmann Institute, Rehovot Japan Center for Nuclear Study, University of Tokyo, Tokyo Hiroshima University, Higashi-Hiroshima KEK, Institute for High Energy Physics, Tsukuba Kyoto University, Kyoto Nagasaki Institute of Applied Science, Nagasaki RIKEN, Institute for Physical and Chemical Research, Wako RIKEN-BNL Research Center, Upton, NY Rikkyo University, Tokyo, Japan Tokyo Institute of Technology, Tokyo University of Tsukuba, Tsukuba Waseda University, Tokyo S. Korea Cyclotron Application Laboratory, KAERI, Seoul Kangnung National University, Kangnung Korea University, Seoul Myong Ji University, Yongin City System Electronics Laboratory, Seoul Nat. University, Seoul Yonsei University, Seoul Russia Institute of High Energy Physics, Protovino Joint Institute for Nuclear Research, Dubna Kurchatov Institute, Moscow PNPI, St. Petersburg Nuclear Physics Institute, St. Petersburg St. Petersburg State Technical University, St. Petersburg Sweden Lund University, Lund 12 Countries; 58 Institutions; 480 Participants* *as of January 2004

4. Sasha Milov Focus on Multiplicity Bari June 17, 2004 4 PHENIX Detector.  Pad Chamber Detectors:  MWPC with binary pad readout  2.5m and 5.0m from the IP  |η|< 0.35 Δφ = 90 0  σ φ = 1.4mrad (1.7mm PC1)  σ η = 0.7×10 -3 (3.6mm PC1)  Double Hit Resolution ~4cm  Electromagnetic Calorimeter:  Lead+Scintillator 18 X 0  5.1m from the IP  |η|< 0.38 Δφ = 90 0  σ E = 8.1%/√E[GeV] ×2.1%  Beam-Beam Counters:  64 Cherenkov Counters  3.1<|η|< 3.9 Δφ = 360 0  σ vertex = ~5mm (central)  σ t = ~100 ps

5. Sasha Milov Focus on Multiplicity Bari June 17, 2004 5 Multiplicity analysis.  Counting tracks on statistical basis:  Combine all hits in PC1 to hits in PC3  Project lines onto the plane through the beam pipe  Count tracks inside the acceptance  Subtract combinatorial background by event mixing.  Corrections:  Tracks outside acceptance and background subtraction4.3%±1%  Inactive regions15%±2.3%  Double hit resolution Hit losses2×7% Background subtraction 3.6% of bkg Uncertainty (in central)±3.6%  Particle in-flow and out-flow Low energy10%±5.5% Higher energy1% ±2% No Field

6. Sasha Milov Focus on Multiplicity Bari June 17, 2004 6 Transverse Energy analysis.  E T definition:  E T = E×sin(θ)  E T ≈ m T at Mid-Rapidity in C.M.S.  E is full E for leptons and mesons  E is E±m for (anti) baryons  EMCal energy scale:  Measures full energy of e ± and γ (π 0 )  Slow hadrons are fully absorbed.  Relativistic hadrons leave M.I.P. peak  EMCal measures >75% of energy  Systematic errors:  Energy response3.9%-4.7%  Noise in central:<0.5% in peripheral:3.5%-6.%  In-flow and out-flow3.0% AGS test RHIC data

7. Sasha Milov Focus on Multiplicity Bari June 17, 2004 7 Centrality and trigger analysis. N p using Glauber N ch using Generator N hits using Detector MC Match to the data N p, N c ε trigger Shape of η-profile Knowledge of N ch = f(N p ) Assumed N ch ~ N p

8. Sasha Milov Focus on Multiplicity Bari June 17, 2004 8 Centrality and trigger using NBD. N p using Glauber N ch using Generator N hits using Detector MC Match to the data N p, N c ε trigger Assumed N ch ~ N p Shape of η-profile Knowledge of N ch = f(N p ) Use N.B. statistics Uncorrelated N ch production Negative Binominal Distribution: is the statistics describing distribution of number of trials (n) which are necessary to get a number of successes, if the probability of success (μ) is known: P(n, ,k) =  (n + k) / (  (k) n!)  (  /k) n / (1 +  /k) n+k where k is a N.B.D. parameter related to the width of the distribution  in a following way: (  /  ) 2 = 1/k + 1/ 

9. Sasha Milov Focus on Multiplicity Bari June 17, 2004 9 d-Au example. N p using Glauber Match to the data N p, N c ε trigger Assumed N ch ~ N p & uncorrelated N ch production Use N.B. statistics

10. Sasha Milov Focus on Multiplicity Bari June 17, 2004 10 Other examples: Case|η|<0.353<|η|<4Comment d-Au 200 GeVNoYes Matches pp trigger and tagged spectrum Au-Au 200 GeVNoYes N p is the same as found using standard technique Au-Au 130 GeVNoN/A Au-Au 62.4 GeVYes/NoNo Preliminary gives the same trigger efficiency as standard Au-Au 19.6 GeVYesNoWorks well on central arm.

11. Sasha Milov Focus on Multiplicity Bari June 17, 2004 11 Results: The distributions.  Only part of the acceptance shown  “Classical” Shape: Peak, Valley, Edge.  Centrality classes shown.  Edge might be modified due to acceptance limitation

12. Sasha Milov Focus on Multiplicity Bari June 17, 2004 12 Results: Centrality curves.  Consistent behavior for E T and N ch  Both increase with energy  Both show steady rise from peripheral to central

13. Sasha Milov Focus on Multiplicity Bari June 17, 2004 13 Results: Systematic errors.  Three types of errors  All plotted as 1 standard deviation  Statistical error:  Point-by-point error (<1%). In all points is smaller than the marker size.  Systematic errors:  Band (correlated) allow to tilt points within the limit of the band. In peripheral (~20%) due to trigger uncertainty. In central (~4%) are due to DHR of the detectors  Scaling (correlated) allow to shift curves up and down.  Total systematic error is a quadratic sum of two. It is shown with the bars.

14. Sasha Milov Focus on Multiplicity Bari June 17, 2004 14 Results: Ratios at different energies.  R200/19.6 is larger for E T than for N ch  Both are flat within systematic errors  Both show steady rise from peripheral to central

15. Sasha Milov Focus on Multiplicity Bari June 17, 2004 15 Results: Ratios /.  Ratio / increases by ~20% from 19.6 GeV to 200 GeV and stays the same between 200 GeV and 130 GeV  Consistent with the average particle momentum increase between those two energies.  Ratio / is independent of centrality  Still a puzzle.  Same freeze-out conditions?  Since trigger and centrality related uncertainties cancel out, the flatness of the curves is quite precise statement.

16. Sasha Milov Focus on Multiplicity Bari June 17, 2004 16 Comparison to other RHIC results.  Spectacular agreement between all 4 RHIC experiments:  All measurements are absolutely independent (including human factor) besides similar approach of using Glauber model.  BRAHMS:Si detectors + tracking  PHENIX: PC at 2.5m and 5m  PHOBOS: Si detectors  STAR:Tracking in magnetic field.  Would allow to calculate averaged values and reduce systematic errors

17. Sasha Milov Focus on Multiplicity Bari June 17, 2004 17 Recalculation between systems.  In C.M.S.:  At Mid-Rapidity: E T ~m T  dE T /dy ≈ 1.25 dE T/ dη  In Lab:  dm T /dy ≈ 1.25 dE T /dy  dE T /dy ≈ dE T /dη  In C.M.S.:  dN ch /dy ≈ 1.25 dN ch/ dη  In Lab:  dN ch /dy ≈ 1.04 dN ch /dη  Recalculation parameters are “rather” independent on energy  A systematic error of 5% is assigned to any recalculated value

18. Sasha Milov Focus on Multiplicity Bari June 17, 2004 18  Good agreement between PHENIX measurements at 19.6 GeV and SPS measurements at 17.2 GeV in both measured values.  SPS spread of the data is larger than RHIC, but the same averaging should be possible to reduce the systematic errors. Comparison to other SPS results.

19. Sasha Milov Focus on Multiplicity Bari June 17, 2004 19  At intermediate SPS energy the energy spread between points is relatively large.  Using weighted average and error scaling by S-factor (see PDG)  S=1 if χ 2 /n.d.f. < 1  S=√χ 2 /n.d.f.if χ 2 /n.d.f. > 1  At lower SPS energy the data spread is even larger, a higher quality data is highly desirable.  At AGS energy the Centrality curve is deduced from a combined data. Comparison of SPS results.

20. Sasha Milov Focus on Multiplicity Bari June 17, 2004 20  Averaged SPS data at 17,3 GeV is in very good agreement to averaged RHIC data at 19.6 GeV (expected difference ~4%)  There is a continuous set of measurements from AGS to RHIC data. Comparison to other results.

21. Sasha Milov Focus on Multiplicity Bari June 17, 2004 21  PHENX suggested ln(s NN ) at QM01 and it works well with better and larger data-set.  Both in E T and in N ch show log-scaling.  Works even better on N ch for N p = 350. Band on the right is 2σ error!  Extrapolation to LHC dN ch /dη = (6.1±0.13)×(0.5Np).  Extrapolation to lowest energy gives:  for E T : √s 0 NN = 2.35 ± 0.2 GeV  for N ch : √s 0 NN = 1.48 ± 0.02 GeV √s NN dependence.

22. Sasha Milov Focus on Multiplicity Bari June 17, 2004 22  That’s what we see ln(√s NN ) 2a.m.u. N ch ETET -0.5 GeV +0.5 GeV FOPI  Energy conservation law.  What √s o NN mean? Caution: they are in GeV!  Now comes FOPI at <0.1 GeV kinetic energy!  Lower energy: √s o NN  /   Higher energy: / ~ constant √s o NN  N ch Low √s NN story

23. Sasha Milov Focus on Multiplicity Bari June 17, 2004 23 What happens to ?  At low √s NN :  E T is “produced” energy only.  N ch can benefit from pre-existing particles (baryons).  At higher √s NN :  Critical temperature T c =0.17GeV.  Assuming: =3/2T c ≈ 0.26 GeV ≈ 0.25 GeV = + ≈ 0.51 GeV / ≈ 1.6 ≈ 0.82 GeV  Prediction for LHC: 0.93±0.04 GeV  How does flow work?

24. Sasha Milov Focus on Multiplicity Bari June 17, 2004 24  Hard/Soft approach:  Might be deceiving: e.g. strangeness turn on.  Negatively correlated errors are huge.  N p α parameterizations:  assumes a power law  what does α mean?  Still large errors  PHOBOS as of June 2,2004 nucl-ex/0405027:  Bottom line: inconclusive! Centrality shapes.

25. Sasha Milov Focus on Multiplicity Bari June 17, 2004 25  three centrality bins divided by ln(√s NN )- parameterization.  Central bin N p = 350 is just consistent with 1 as expected  Mid-central bin N p =100 with large systematic errors is just an offset  Most peripheral: N p = 2 (pp) for a moment needs more data at low energy. Turns out to be quite difficult to get it right. Centrality shapes: basic approach

26. Sasha Milov Focus on Multiplicity Bari June 17, 2004 26 Bjorken energy.  Done at all three energies  STAR advocates another approach taking for overlap area S ~N p 3/2.  Difference to standard approach: area of the nuclei vs. area of the nucleons  Makes some difference at low N p  Recent STAR finding: (nucl-ex/03011017) dE T /dy / (0.5 N p ) decreases with N p ?!

27. Sasha Milov Focus on Multiplicity Bari June 17, 2004 27 Models: experimentalist’s view  Model vs. Generator:  Do you know why we are such in love with HIJING?  IMHO: Model is a precursor to the Generator.  Major difference besides completeness and ease of use: Generator does partial probabilities!  What happened to systematic errors?  How well defined a model is within itself?  Only Mini-Jet gives a band.  How should experimentalist compare models to data?  Thanks to all authors who sent us their data!

28. Sasha Milov Focus on Multiplicity Bari June 17, 2004 28 Models I LUCIFERHadronic cascade model, input fixed from lower energy. D.E.Kahana & S.H.Kahana, nucl-th/0208063. Minijet Multiphase transport model, includes both initial partonic and final hadronic interactions. S. Lee and X.N. Wang, Phys Lett B527, 85 (2002) EKRT K.J. Eskola, et al., Nucl. Phys. B570, 379 (2000), Phys Lett B497, 39 (2001). SSHM Saturation for Semi-Hard Minijetis. pQCD-based for semi-hard partonic interaction WNM for soft particle production. A.Accardi, Phys Rev C64, 064905 (2001). KLN D. Kharzeev and M. Nardi, Phys Lett B507, 121(2001), D. Kharzeev and E. Levin, Phys Lett B523, 79 (2001).

29. Sasha Milov Focus on Multiplicity Bari June 17, 2004 29 Models II DSM: Dual String Model, Dual Parton Model + strings. R. Ugoccioni, Phys Lett B49, 253 (2000). A. Capella et al, Phys Lett C236, 225 (1994). HIJING: pQCD for initial minijet production and the Lund string model for jet fragmentation and hadronization, +jet quenching +nuclear shadowing. X.N. Wang et al. PRC 68, 054902 (2003). LEXUS:Linear EXtrapolation of UltraRrelativsitic nucleon-nucleon scattering data to nucleus- nucleus collisions. S. Jeon and J. Kapusta, Phys Rew C63, 011901 (2001) AMPT:multiphase transport model +initial partonic and final hadronic interactions. Z. Lin et al. Phys Rew. C64, 011902 (2001). SFM:String Fusion Model string model, includes hard collisions, collectivity in the initial state (string fusion), and final state. N. Armesto Perez et al., Phys Lett B527, 92 (2002)

30. Sasha Milov Focus on Multiplicity Bari June 17, 2004 30 Models III

31. Sasha Milov Focus on Multiplicity Bari June 17, 2004 31 What else do we need.  We expect collaboration to fill the missing gaps in the paper and give it more physical impact:  what do parameters of the ln(√s NN )-scaling mean?  help with quality pp data at low energy  polish the model section 62 GeV data.  PPG19 draft to be released to collaboration today without 62 GeV  Michael Mendenhall from VU is working on the data.  We might have results + an analysis note in scope of weeks.  Impact on the paper:  for physics: minimal  for completeness: desirable  for future references: good  text/structure change to incorporate: minimal (~1 day)  If we have the data my suggestion is to bring it to convenor’s meeting to decide when it happens, if not too late.