Energy Dependence of Multiplicity Fluctuations in Heavy Ion - PowerPoint PPT Presentation

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

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

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 ω 〉 T (MeV) + π + 〈 K / 300 〉 + K 〈 0.2 ? 200 0.1 A+A: NA49 100 A+A: AGS p+p ( p ): NA49 0 K AGS p+p RHIC S + RHIC K 0 2 2 1 10 10 1 10 10 s (GeV) s (GeV) √ s NN (GeV) NN NN 3 Benjamin Lungwitz, IKF Universität Frankfurt

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

System Size Dependence of n- Fluctuations 158A GeV Pb+Pb, 158 A GeV Var(n)/<n> 4 negative 2 HSD 1.5 UrQMD 3 1 targ P ω ω ω ω 2 p+p 0.5 Pb+Pb 1 0 50 100 150 PROJ N P 0 see talk of M. Rybczynski 0 50 100 150 200 proj N see talk of M. Gorenstein, P t V. Konchakovskyi et al. ● N P Proj experimentally fixed, N P Targ fluctuate Phys. Rev. C 73 (2006) 034902 ● Peripheral collisions: Large N P Targ fluctuations may cause large ω in forward hemisphere (e.g. mixing) ● Central collisions: N P Targ fluctuations negligible 5 Benjamin Lungwitz, IKF Universität Frankfurt

Track Selection 158 A GeV h - 2 [GeV/c] 2 1 T p 1.8 0 300 1.8 0.9 1.6 1.6 0.8 0 250 1.4 T 1.4 0.7 p 1.2 200 1.2 0.6 1 1 0.5 150 0.8 0.8 0.4 0.6 100 0.6 0.3 0.4 0.4 0.2 50 0.2 0.2 0.1 0 0 0 0 -4 -3 -2 -1 0 1 2 3 4 -150 -100 -50 0 50 100 150 y( π ) φ [deg] 1.4<y<1.6 y in cms system ● Only hadrons in a limited forward acceptance (projectile hemisphere) were selected (158A GeV: equal to M. Rybczynski) – Safe acceptance (no problems with efficiency etc.) ● (p T , φ) cut: ● y-cut: 20 A – 80 A GeV: 1<y<y beam C. Alt et al., 158A GeV: 1.08<y<2.57 Phys.Rev.C70:064903, 2004 6 Benjamin Lungwitz, IKF Universität Frankfurt

Experimental Acceptance 0.2 p 0.18 small 0.16 0.14 standard 0.12 0.1 h - 0.08 0.06 0.04 0.02 0 6 8 10 12 14 16 18 20 s NN ● Strong energy dependence of experimental acceptance – Difficult to compare different energies ● Small acceptance (1<y<(y beam -1)/2+1) used to study acceptance effects 7 Benjamin Lungwitz, IKF Universität Frankfurt

Multiplicity Distributions h - at N P Proj =195 40A GeV 158A GeV 2 800 2 data/poisson data/poisson 1600 Pb+Pb Pb+Pb 1.8 700 1400 1.6 1.5 600 1200 1.4 500 1.2 1000 1 1 400 800 0.8 300 600 0.6 0.5 200 400 0.4 100 200 0.2 0 0 0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 60 80 100 120 140 160 180 60 80 100 120 140 160 180 - - - - N(h ) N(h ) N(h ) N(h ) black: data all data are red: Poisson distribution 2 data/poisson preliminary ! 8000 p+p 1.8 7000 1.6 ● Multiplicity distributions for 6000 1.4 1.2 5000 central collisions are 1 4000 0.8 3000 significantly narrower than 0.6 2000 0.4 Poisson distribution ! 1000 0.2 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 - - N(h ) N(h ) 8 Benjamin Lungwitz, IKF Universität Frankfurt

Centrality Dependence at all Energies 1.2 1.2 1.2 ω ω ω h - 1.15 1.15 1.15 20A GeV 30A GeV 40A GeV 1.1 1.1 1.1 1.05 1.05 1.05 1 1 1 0.95 0.95 0.95 0.9 0.9 0.9 0.85 0.85 0.85 0.8 0.8 0.8 160 165 170 175 180 185 190 195 200 205 160 165 170 175 180 185 190 195 200 205 160 165 170 175 180 185 190 195 200 205 P P P N N N Proj Proj Proj ● Not corrected for 1.2 1.2 ω ω 80A GeV 158A GeV 1.15 1.15 resolution of veto 1.1 1.1 calorimeter 1.05 1.05 1 1 ● 190<N P Proj <200 0.95 0.95 0.9 0.9 selected 0.85 0.85 0.8 0.8 160 165 170 175 180 185 190 195 200 205 160 165 170 175 180 185 190 195 200 205 P P N N Proj Proj 9 Benjamin Lungwitz, IKF Universität Frankfurt

Corrections and Biases ● Correction applied for finite size of centrality bins  bw =〈 n 〉 Var  N P Proj  〈 N P Proj 〉 2 in the order of 2% ● Known uncorrected biases: – N P Proj fluctuations due to finite Veto calorimeter resolution (estimated to be <2%) – A possible N P Targ fluctuations contribution to projectile hemisphere -> They both increase fluctuations 10 Benjamin Lungwitz, IKF Universität Frankfurt

Energy Dependence of n- Fluctuations 1.3 ω 1.3 h + ω 1.3 ω h - h +- 1.25 1.25 1.25 1.2 1.2 1.2 1.15 1.15 blue: Pb+Pb 1.15 1.1 1.1 1.1 red: p+p 1.05 1.05 1.05 1 1 1 0.95 0.95 0.95 0.9 0.9 0.9 0.85 0.85 0.85 0.8 6 8 10 12 14 16 18 20 0.8 0.8 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 s (GeV) (GeV) (GeV) NN s s NN NN Note: different acceptance for different energies ! only statistical errors shown ● Scaled variance for h + , h - smaller than 1 ● ω for h +- < 1 for low energies, ω +− > 1 for higher energies ● ω (p+p) ≈ ω (central Pb+Pb) at 158A GeV 11 Benjamin Lungwitz, IKF Universität Frankfurt

Effect of Limited Acceptance ● Assuming no correlations in momentum space  acc = 4 ­ 1 ⋅ p  acc  1 (*) ● ω (4 π ) > 1 <=> ω (acc) > 1, ω (4 π ) < 1 <=> ω (acc) < 1 ● Formula (*) not valid if more than one daughter particle of a decay is 1.5 (acc) detected 1.4 ω 1.3 – very few particles decay into 2 h - 1.2 1.1 – many particles decay into h + and h - 1 0.9 0.8 0.7 0.6 π + 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p(acc) π - ρ 12 Benjamin Lungwitz, IKF Universität Frankfurt

Acceptance Scaling for h - 1.2 ω 20A GeV 1.15 h - 30A GeV 40A GeV <ω (4 π )> ≈ 0.3 1.1 80A GeV 158A GeV 1.05 1 small and standard 0.95 acceptance 0.9 0.85 0.8 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 p ● Data comparable with acceptance scaling and no (or weak) energy dependence of multiplicity fluctuations in 4 π 13 Benjamin Lungwitz, IKF Universität Frankfurt

Statistical Model 1.4 1.4 2 ch + - ω ω ω 1.8 1.2 1.2 1.6 RHIC 1 1 1.4 RHIC h + RHIC SPS SPS 1.2 0.8 0.8 1 0.6 SPS 0.6 0.8 AGS AGS h +- h - 0.6 0.4 Primordial GCE 0.4 Primordial GCE Primordial GCE AGS Final GCE Final GCE Final GCE 0.4 Primordial CE Primordial CE Primordial CE 0.2 0.2 0.2 Final CE Final CE Final CE 0 0 0 3 3 2 3 2 2 10 10 1 10 10 10 1 10 10 10 1 10 S S S NN NN NN 4 π acceptance ! see talk of M. Gorenstein,V. Begin M. Hauer et. al. nucl-th/0606036 ● Grand canonical ensemble (no charge conservation): – ω >1 for all energies ● Canonical ensemble (B,Q,S conserved): – ω <1 for h + and h - , ω crosses 1 for h +- ● Final state: resonance decays 14 Benjamin Lungwitz, IKF Universität Frankfurt

Statistical Model and Data 1.3 ω 1.3 ω h - 1.25 data 1.25 h + data canonical model 1.2 canonical model 1.2 grand canonical model grand canonical model 1.15 1.15 1.1 1.1 1.05 1.05 1 1 0.95 0.95 0.9 0.9 0.85 0.85 0.8 0.8 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 (GeV) (GeV) s s NN NN ● 4 π 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 ?) 15 Benjamin Lungwitz, IKF Universität Frankfurt

String Hadronic Models: Venus, HSD 1.3 1.3 ω ω h - h + 1.25 1.25 data data Venus Venus 1.2 1.2 HSD HSD 1.15 1.15 1.1 1.1 1.05 1.05 1 1 0.95 0.95 0.9 0.9 0.85 0.85 0.8 0.8 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 s (GeV) s (GeV) NN NN HSD: V. Konchakovski, priv. com. ● HSD: works good for 20A – 40A GeV, but overpredicts data at 80A and 158A GeV ● Venus overpredicts data for energies > 20A GeV 16 Benjamin Lungwitz, IKF Universität Frankfurt

String Hadronic Models: Venus, HSD (2) 1.7 ω h +- data 1.6 Venus 1.5 HSD 1.4 1.3 1.2 1.1 1 0.9 0.8 6 8 10 12 14 16 18 20 (GeV) s NN ● All string hadronic models overpredict fluctuations of h +- for energies > 20A GeV 17 Benjamin Lungwitz, IKF Universität Frankfurt

Summary ● Multiplicity fluctuations in central Pb+Pb collisions for h + , h - and h +- at 20, 30, 40, 80 and 158A GeV were analysed ● ω − scales with p(acc) for h - at all energies -> weak energy dependence of ω in 4 π [ ω(4π) ≈ 0.3 ] ● ω + and ω - smaller than 1 for all energies -> Grand canonical ensemble does not work ! ● Canonical statistical model shows similar trend as the data but ω (data) < ω (CE) ● String hadronic models (Venus, HSD) work for lower energies (20-40A GeV) but fail for higher (80-158A GeV) 18 Benjamin Lungwitz, IKF Universität Frankfurt

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