Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions. Benjamin Lungwitz, IKF Universität Frankfurt for the NA49 collaboration

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1 Energy Dependence of Multiplicity Fluctuations in Heavy Ion Collisions Benjamin Lungwitz, IKF Universität Frankfurt for the NA49 collaboration

2 Outline Introduction Analysis of energy dependence Energy dependence of multiplicity fluctuations Acceptance scaling Model comparison Summary Benjamin Lungwitz, IKF Universität Frankfurt

3 Motivation Anomalies in energy dependence seen at low SPS energies -> hint for onset of deconfinement? Models predict large fluctuations near onset of deconfinement or critical point + / π + K. T (MeV) 3 + K?. p+p A+A: NA49 AGS RHIC s NN (GeV) p+p (p): K S + K s NN A+A: NA49 AGS RHIC (GeV) s NN (GeV) Benjamin Lungwitz, IKF Universität Frankfurt 3

4 A Centrality Selection VCAL Veto calorimeter E Veto (A - N P )*E kin N P Veto calorimeter -> projectile spectators, number of projectile participants N P Target spectators not measured in NA49! Benjamin Lungwitz, IKF Universität Frankfurt 4

5 Var(n)/<n>.5.5 System Size Dependence of n- Fluctuations negative p+p Pb+Pb 58A GeV targ P 4 3 Pb+Pb, 58 A GeV HSD UrQMD 5 5 see talk of M. Rybczynski PROJ N P N P experimentally fixed, N P Targ fluctuate 5 5 Targ Peripheral collisions: Large N P fluctuations may cause large in forward hemisphere (e.g. mixing) Central collisions: N P Targ fluctuations negligible t N proj P see talk of M. Gorenstein, V. Konchakovskyi et al. Phys. Rev. C 73 (6) 349 Benjamin Lungwitz, IKF Universität Frankfurt 5

6 Track Selection [GeV/c] p T A GeV φ [deg].4<y< y in cms system Only hadrons in a limited forward acceptance (projectile hemisphere) were selected (58A GeV: equal to M. Rybczynski) Safe acceptance (no problems with efficiency etc.) (p T, φ) cut: y-cut: C. Alt et al., Phys.Rev.C7:6493, 4 h - T p A 8A GeV: <y<y beam 58A GeV:.8<y<.57 y(π) Benjamin Lungwitz, IKF Universität Frankfurt 6

7 Experimental Acceptance p small standard..8.6 h s NN Strong energy dependence of experimental acceptance Difficult to compare different energies Small acceptance (<y<(y beam -)/+) used to study acceptance effects Benjamin Lungwitz, IKF Universität Frankfurt 7

8 Multiplicity Distributions 4A GeV h - at N P =95 58A GeV 6 4 data/poisson Pb+Pb data/poisson.5 Pb+Pb N(h ) N(h ) N(h ) N(h ) black: data red: Poisson distribution all data are preliminary! Multiplicity distributions for central collisions are significantly narrower than Poisson distribution! N(h ) data/poisson.8.6 p+p N(h ) Benjamin Lungwitz, IKF Universität Frankfurt 8

9 Centrality Dependence at all Energies A GeV. 3A GeV. 4A GeV.5.5 h N P N P N P A GeV N P A GeV N P Not corrected for resolution of veto calorimeter 9<N P < selected Benjamin Lungwitz, IKF Universität Frankfurt 9

10 Corrections and Biases Correction applied for finite size of centrality bins bw = n Var N P N P in the order of % Known uncorrected biases: fluctuations due to finite Veto calorimeter resolution (estimated to be <%) N P A possible N P Targ hemisphere -> They both increase fluctuations fluctuations contribution to projectile Benjamin Lungwitz, IKF Universität Frankfurt

11 Energy Dependence of n- Fluctuations s NN.3 h + h - h +- blue: Pb+Pb red: p+p s NN (GeV) (GeV) s NN (GeV) Note: different acceptance for different energies! only statistical errors shown Scaled variance for h+, h - smaller than for h+- < for low energies, + > for higher energies (p+p) (central Pb+Pb) at 58A GeV Benjamin Lungwitz, IKF Universität Frankfurt

12 Effect of Limited Acceptance Assuming no correlations in momentum space acc = 4 p acc (*) (4π) > <=> (acc) >, (4π) < <=> (acc) < (acc) Formula (*) not valid if more than one daughter particle of a decay is detected very few particles decay into h - many particles decay into h + and h p(acc) π + Benjamin Lungwitz, IKF Universität Frankfurt ρ π -

13 Acceptance Scaling for h A GeV 3A GeV h 4A GeV 8A GeV 58A GeV - <(4π)> small and standard acceptance p Data comparable with acceptance scaling and no (or weak) energy dependence of multiplicity fluctuations in 4π Benjamin Lungwitz, IKF Universität Frankfurt 3

14 Statistical Model AGS SPS RHIC Primordial GCE Final GCE Primordial CE Final CE 3 S NN -.4. h + h - h AGS SPS 4π acceptance! RHIC Primordial GCE Final GCE Primordial CE Final CE 3 S NN ch AGS SPS RHIC Primordial GCE Final GCE Primordial CE Final CE see talk of M. Gorenstein,V. Begin M. Hauer et. al. nucl-th/ S NN Grand canonical ensemble (no charge conservation): > for all energies Canonical ensemble (B,Q,S conserved): < for h + and h -, crosses for h +- Final state: resonance decays Benjamin Lungwitz, IKF Universität Frankfurt 4

15 Statistical Model and Data data canonical model grand canonical model s NN s NN Benjamin Lungwitz, IKF Universität Frankfurt 5.5 data h + h -. canonical model grand canonical model.5 (GeV) 4π values scaled down to exp. acceptance assuming no correlations in momentum space (eg. due to resonance decays) Grand canonical model overpredicts fluctuations Canonical model works better, but its fluctuations are also too high (energy conservation needed?) (GeV)

16 String Hadronic Models: Venus, HSD data Venus HSD.3 h +.5 data h -. Venus HSD s NN (GeV) s NN (GeV) HSD: V. Konchakovski, priv. com. HSD: works good for A 4A GeV, but overpredicts data at 8A and 58A GeV Venus overpredicts data for energies > A GeV Benjamin Lungwitz, IKF Universität Frankfurt 6

17 String Hadronic Models: Venus, HSD () data Venus HSD h s NN (GeV) All string hadronic models overpredict fluctuations of h +- for energies > A GeV Benjamin Lungwitz, IKF Universität Frankfurt 7

18 Summary Multiplicity fluctuations in central Pb+Pb collisions for h+, h - and h +- at, 3, 4, 8 and 58A GeV were analysed scales with p(acc) for h - at all energies -> weak energy dependence of in 4π [ (4π).3 ] + and - smaller than for all energies -> Grand canonical ensemble does not work! Canonical statistical model shows similar trend as the data but (data) < (CE) String hadronic models (Venus, HSD) work for lower energies (-4A GeV) but fail for higher (8-58A GeV) Benjamin Lungwitz, IKF Universität Frankfurt 8

19 Backup Benjamin Lungwitz, IKF Universität Frankfurt 9

20 Multiplicity Distributions 58A GeV. Pb+Pb central N P =78 Poisson NP =39 Pb+Pb semi-periph. Poisson p+p Poisson P(N neg ) N neg N neg N neg Used measure of fluctuations: scaled variance n = Var n n = n n n [ = for Poissonian distribution ] Benjamin Lungwitz, IKF Universität Frankfurt negative hadrons, N P fixed

21 Centrality and System Size Dependence Var(n)/<n>.8 58A GeV h -.6 ectile hemisphere p+p C+C Si+Si Pb+Pb NA49 preliminary N P /A P Var(n)/<n> increases with decreasing centrality Approximate scaling in N P /A Benjamin Lungwitz, IKF Universität Frankfurt

22 Different Extreme Reaction Scenarios N P Targ fluctuations contribute in target hemisphere (most string hadronic models) N P Targ fluctuations contribute in both hemispheres (most statistical models) N P Targ fluctuations contribute in projectile hemisphere spectators fluctuate spectators fixed selected phase space for analysis M. Gazdzicki, M. Gorenstein arxiv:hep-ph/558 Multiplicity fluctuations sensitive to reaction scenario Benjamin Lungwitz, IKF Universität Frankfurt

23 String Hadronic Models Var(n)/<n> Data: p+p Pb+Pb String hadronic models: HSD UrQMD HIJING NA49 preliminary 5 5 N P ectile hemisphere HSD, UrQMD: V. Konchakovskyi et al. Phys. Rev. C 73 (6) 349 HIJING: M. Gyulassy, X. N. Wang Comput. Phys. Commun. 83 (994) 37 Simulation performed by: M. Rybczynski String hadronic models shown (UrQMD, HSD, HIJING) belong to transparency class They do not reproduce data on multiplicity fluctuations h - Benjamin Lungwitz, IKF Universität Frankfurt 3

24 Reflection, Mixing and Transparency Var(n)/<n> NA49 preliminary h - ectile hemisphere.5.5 Data: p+p Pb+Pb statistical model: transparency mixing reflection 5 5 N P Model calculation: M. Gazdzicki, M. Gorenstein arxiv:hep-ph/558 Significant amount of mixing of particles produced by projectile and target sources Benjamin Lungwitz, IKF Universität Frankfurt 4