Measurements of net-particle fluctuations in Pb-Pb collisions at ALICE

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1 Measurements of net-particle fluctuations in Pb-Pb collisions at ALICE Alice Ohlson (Universität Heidelberg) for the ALICE Collaboration Observables of Hadronization and the QCD Phase Diagram in the Cross-over Domain Trento, 8 October 8

Fluctuations in heavy ion collisions Event-by-event fluctuations of particle multiplicities are used to study properties and phase structure of strongly-interacting matter In heavy-ion collisions at

2 Fluctuations in heavy ion collisions Event-by-event fluctuations of particle multiplicities are used to study properties and phase structure of strongly-interacting matter In heavy-ion collisions at the LHC: test lattice QCD predictions at µ B = look for signs of criticality l,disc /T HISQ/tree: N =6 N =8 N = asqtad: N =8 N = 4 T [MeV] A. Bazavov et al. PRD 85 () 5453, arxiv:.7 [hep-lat] Friman, B., et al. Eur. Phys. J. C 7 () 694, arxiv:3.35 [hep-ph] 8 October 8

3 Connecting theory to experiment Thermodynamic susceptibilities χ describe the response of a thermalized system to changes in external conditions, fundamental properties of the medium can be calculated within lattice QCD within the Grand Canonical Ensemble, are related to eventby-event fluctuations of the number of conserved charges Theory: susceptibilities ( ) χ B n = n P / T 4 µ B / T ( ) n particle bath Δη acceptance of the measurement Experiment: moments of particle multiplicity distributions ΔN B = N B N B 8 October 8 3

4 Connecting theory to experiment Thermodynamic susceptibilities χ describe the response of a thermalized system to changes in external conditions, fundamental properties of the medium can be calculated within lattice QCD within the Grand Canonical Ensemble, are related to eventby-event fluctuations of the number of conserved charges Theory: susceptibilities ( ) χ B n = n P / T 4 µ B / T ( ) n ΔN B = VT 3 χ B ( ΔN B ΔN B ) = VT 3 χ B = σ ( ΔN B ΔN B ) 3 σ 3 = VT 3 χ 3 VT 3 B χ B ( ) 3/ = S ( ΔN B ΔN B ) 4 σ 4 3 = VT 3 χ 4 VT 3 B χ B ( ) = κ Experiment: moments of particle multiplicity distributions ΔN B = N B N B 8 October 8 4

5 Connecting theory to experiment Thermodynamic susceptibilities χ describe the response of a thermalized system to changes in external conditions, fundamental properties of the medium can be calculated within lattice QCD within the Grand Canonical Ensemble, are related to eventby-event fluctuations of the number of conserved charges Theory: susceptibilities ( ) χ B n = n P / T 4 µ B / T ( ) n ΔN B = VT 3 B χ ( ΔN B ΔN Sσ B ) = VT χ B 3 B = σ 3 / χ κσ = χ B B 4 / χ ΔN B ΔN B VT 3 B χ ( ) 3 σ 3 = VT 3 χ 3 ( ) = S 3/ ( ΔN B ΔN B ) 4 σ 4 3 = VT 3 χ 4 VT 3 B χ B B ( ) = κ Experiment: moments of particle multiplicity distributions ΔN B = N B N B 8 October 8 5

6 Connecting theory to experiment Thermodynamic susceptibilities χ describe the response of a thermalized system to changes in external conditions, fundamental properties of the medium can be calculated within lattice QCD within the Grand Canonical Ensemble, are related to eventby-event fluctuations of the number of conserved charges Theory: fixed volume, particle bath in GCE ΔN B = VT 3 B / χ ( ΔN B ΔN B ) = / VT 3 χ B = σ ( ΔN B ΔN B ) 3 σ 3 = VT 3 χ / 3 VT 3 B χ B ( ) 3/ = S ( ΔN B ΔN B ) 4 σ 4 3 = VT 3 χ / 4 VT 3 B χ B ( ) = κ Experiment: event-by-event volume fluctuations, global conservation laws 8 October 8 6

7 Experimental Challenges. Event-by-event particle identification. Event-by-event efficiency correction We know how to correct the first moments, but what about the higher moments? 8 October 8 7

8 The challenge: event-by-event PID (arb. units) TPC de/dx ALI PERF 3849 e K p d π 8/5/ Pb-Pb =.76TeV p (GeV/c) TPC 8dE/dx Signal TPC de/dx Signal (a.u.) Traditional method: count number of pions (N π ), kaons (N K ), protons (N p ) in each event # tracks N p = i find moments of distributions of N π, N K, N p,... counts (a.u.) counts (a.u.) ALI PREL particle i is a proton particle i is not a proton ALICE Preliminary, Pb-Pb =.76 TeV ALICE Preliminary, Pb-Pb s =.76 TeV Generalised NN Gauss function: Data K -( x-µ /σ) Total Fit Generalised Gauss Ae function: (+Erf(S(x-µ)/σ )) K -( x-µ /σ) Electron Ae (+Erf(S(x-µ)/σ η <.8,.33<p<.35 )) GeV/c Pion η <.8,.33<p<.35 GeV/c Kaon Data Total Elect Pion Kaon 8 October 8 8

9 Traditional method (arb. units) TPC de/dx e K p d 8/5/ Pb-Pb =.76TeV counts (a.u.) counts (a.u.) 5 5 ALICE ALICE Preliminary, Preliminary, Pb-Pb Pb-Pb =.76 =.76 TeV TeV Data Data Total Total Fit Fit.<η<.3,.<η<.3,.73<p<.75.73<p<.75 GeV/c GeV/c Electron Electron 4 4 Pion Pion Generalised Generalised Gauss Gauss function: function: x-µ β x-µ β Kaon Kaon - - σ σ (x-µ) (x-µ) Ae Ae +erf +erf α α Proton Proton σ σ π ALI PERF 3849 p (GeV/c) TPC TPC de/dx de/dx Signal Signal (a.u.) (a.u.) ALI PREL 53 What if PID is unclear? use other detector information or reject phase space bin results in lower efficiency 8 October 8 9

10 Identity method (arb. units) TPC de/dx e K p d 8/5/ Pb-Pb =.76TeV counts (a.u.) counts (a.u.) 5 5 ALICE ALICE Preliminary, Preliminary, Pb-Pb Pb-Pb =.76 =.76 TeV TeV Data Data Total Total Fit Fit.<η<.3,.<η<.3,.73<p<.75.73<p<.75 GeV/c GeV/c Electron Electron 4 4 Pion Pion Generalised Generalised Gauss Gauss function: function: x-µ β x-µ β Kaon Kaon - - σ σ (x-µ) (x-µ) Ae Ae +erf +erf α α Proton Proton σ σ π ALI PERF 3849 p (GeV/c) TPC TPC de/dx de/dx Signal Signal (a.u.) (a.u.) ALI PREL 53 As a function of the PID variable m, determine probability w that particle is of a given species Calculate event-by-event sum of weights W π, W K, W p,... # tracks W p = w p (m i ) i M. Gazdzicki et al., PRC 83 () 5497, arxiv:3.887 [nucl-th] M. I. Gorenstein, PRC 84, () 49, arxiv: [nucl-th] A. Rustamov et al., PRC 86 () 4496, arxiv:4.663 [nucl-th] M. Arslandok and A. Rustamov, arxiv: [hep-ex] Using knowledge of inclusive m distributions, unfold moments of W distributions to get moments of N Contamination is accounted for, full phase space can be used 8 October 8

11 Efficiency corrections: several ideas Simple scaling of moments using HIJING and/or AMPT Correction of factorial moments assuming binomial track loss A. Bzdak and V. Koch, Phys. Rev. C86, 4494 (), arxiv:6.486 [nucl-th]. extension to Identity Method C. Pruneau, Phys. Rev. C96 (7) 549, arxiv: [physics.data-an] Correction using moments of detector response matrix T. Nonaka et al., Nucl. Inst. Meth. A 96 (8), arxiv:85.79 [physics.data-an] Full unfolding of moments A. Bzdak and V. Koch, Phys. Rev. C9, 79 (5), arxiv: [nucl-th]. All correction methods rely on different assumptions, which must be assessed and tested carefully! 8 October 8

12 Net-proton fluctuations A. Rustamov for ALICE, QM7 κ n ALICE Preliminary, Pb-Pb.6 < p <.5 GeV/c, η <.8 =.76 TeV κ (p-p) κ κ κ κ κ κ κ ( p) = N p κ ( p p) = N p N p N p N p ( ) ( p) = N p N p ( ) ( ) = κ ( p) +κ ( p) N p N p N p N p κ (p-p)/κ.95 ALI-PREL-59 ratio, stat. uncert. syst. uncert centrality [%] κ ( Skellam) = κ p correlation term If multiplicity distributions of protons and anti-protons are Poissonian and uncorrelated Skellam distribution for net-protons ( ) +κ ( p) 8 October 8

13 Net-proton fluctuations A. Rustamov for ALICE, QM7 κ n ALICE Preliminary, Pb-Pb.6 < p <.5 GeV/c, η <.8 =.76 TeV κ (p-p) κ κ κ κ κ κ κ ( p) = N p κ ( p p) = N p N p N p N p ( ) ( p) = N p N p ( ) ( ) = κ ( p) +κ ( p) N p N p N p N p κ (p-p)/κ.95 ALI-PREL-59 ratio, stat. uncert. syst. uncert centrality [%] κ correlation term κ (p-p) shows deviation from Skellam prediction due to correlation term? are protons and antiprotons Poissonian? ( Skellam) = κ ( p) +κ ( p) 8 October 8 3

14 Net-proton fluctuations κ n κ (p-p)/κ ALI-PREL-598 ALICE Preliminary, Pb-Pb =.76 TeV.6 < p <.5 GeV/c, η <.8 Model arxiv:6.7 κ (p-p) κ κ κ κ κ Model κ (p-p) Model κ ratio, stat. uncert. syst. uncert centrality [%] A. Rustamov for ALICE, QM7 Modeling the effects of participant fluctuations P. Braun-Munzinger et al., NPA 96 (7) 4, arxiv:6.7 [nucl-th] Inputs to the model: κ, κ, centrality determination procedure Model gives a consistent picture of κ, κ and κ (p-p) without need of correlations or critical fluctuations see talk by A. Rustamov 8 October 8 4

15 Global conservation laws acceptance of the measurement κ (p - p) κ.5..5 ALICE Preliminary, Pb-Pb A. Rustamov for ALICE, QM7 =.76 TeV.6 < p <.5 GeV/c, centrality -5% ratio, stat. uncert. syst. uncert. baryon conserv. arxiv:6.7 syst. uncert. HIJING, AMPT Small Δη Poissonian fluctuations, ratio to Skellam ~ Large Δη global baryon number and strangeness conservation effects, ratio to Skellam < ALI-PREL-6.95 Δη dependence consistent with effects of baryon number conservation P. Braun-Munzinger et al., NPA 96 (7) 4, arxiv:6.7 [nucl-th] η see talk by A. Rustamov 8 October 8 5

16 Net-pion and net-kaon fluctuations κ (π + - π ) κ -. ALICE Preliminary, Pb-Pb =.76 TeV.6 < p <.5 GeV/c, centrality -5% ratio, stat. uncert. syst. uncert. HIJING κ (K - K ) κ ALICE Preliminary, Pb-Pb =.76 TeV.6 < p <.5 GeV/c, centrality -5% A. Rustamov for ALICE, QM7 ratio, stat. uncert. syst. uncert. HIJING.9.9 ALI-PREL η ALI-PREL η Pions show good agreement with HIJING Production of pions and kaons from resonance decays contributes significantly to the measurement Skellam distribution is not a proper baseline for net-pions and net-kaons 8 October 8 6

17 From net-π, K, p to net-λ moments Explore correlated fluctuations of baryon number and strangeness Establish baseline for future measurements of higher moments in the strangeness sector Improve understanding of net-baryon fluctuations different contributions from resonances, etc, than in netproton measurement Λs can be added to net-proton or net-kaon results to get closer to net-baryon and net-strangeness fluctuations 8 October 8 7

18 Identity method for invariant mass For any value of m inv, the probability that a πp pair comes from the decay of a Λ baryon is known Apply Identity Method for four species : Λ, Λ, combinatoric π - p, combinatoric π + p - (GeV/c ) (/N ev ) dn/dm inv Pb Pb, ALICE Preliminary = 5. TeV, %.3 < p <.4 GeV/c, η <.5 T,Λ Λ background fit interpolated bkg. w Λ, w bkg.4 ALICE Preliminary..8.6 Pb Pb, = 5. TeV, %.3 < p <.4 GeV/c, η <.5 T,Λ Λ w Λ.4 w bkg ALI PREL 5779 m (GeV/c inv ) ALI PREL 577 m (GeV/c inv ) 8 October 8 for ALICE, QM8 8

19 Net-Λ fluctuations C n C (Λ-Λ)/C ALI PREL 5773 ALICE Preliminary Pb Pb, = 5. TeV < p < 4 GeV/c, η <.5 T,Λ Λ C C C C C (Λ Λ) Centrality (%) C C ( Λ) = N Λ C for ALICE, QM8 ( ) ( Λ) = N Λ N Λ ( Λ Λ) = ( N Λ N Λ N Λ N Λ ) = C ( Λ) + C ( Λ) ( N Λ N Λ N Λ N Λ ) Small deviations from Skellam baseline correlation term? non-poissonian Λ or Λ distributions? critical fluctuations? effects of volume fluctuations and global conservation laws? 8 October 8 9

20 Comparison to net-protons C n 5 4 ALICE Preliminary Pb Pb, = 5. TeV < p < 4 GeV/c, η <.5 T,Λ Λ κ n ALICE Preliminary, Pb-Pb.6 < p <.5 GeV/c, η <.8 =.76 TeV κ (p-p) κ κ κ κ κ C (Λ-Λ)/C ALI PREL October 8 C C C C C (Λ Λ) Centrality (%) κ (p-p)/κ.95 ALI-PREL-59 ratio, stat. uncert. syst. uncert centrality [%] Qualitatively similar results for net-protons different kinematic range, different contributions from resonance decays

21 Comparison to HIJING C n C (Λ-Λ)/C ALI PREL ALICE Preliminary Pb Pb, = 5. TeV < p < 4 GeV/c, η <.5 T,Λ Λ C C C C C (Λ Λ) HIJING C C C C C (Λ Λ) HIJING Centrality (%) for ALICE, QM8 HIJING does not describe strangeness production well underestimates C and C by factor ~4 However, C (Λ-Λ)/C ratio agrees with data coincidence? or due to description of fluctuations and resonance contributions in HIJING? 8 October 8

22 Δη dependence of net-λ fluctuations Small Δη Poissonian fluctuations, ratio to Skellam ~ Large Δη global baryon number and strangeness conservation effects, ratio to Skellam < Systematic uncertainties are highly correlated point-to-point Δη dependence consistent with effects of baryon number conservation strangeness conservation should also be considered consistency also with HIJING C (Λ-Λ) C (Λ-Λ)/C ALICE Preliminary Pb Pb, = 5. TeV, % < p < 4 GeV/c T,Λ Model from Nucl. Phys. A 96 (7) ALI PREL HIJING for ALICE, QM8 η 8 October 8

23 Higher moments Deviations from unity and signs of criticality are greatly enhanced for the higher moments (4 th, 6 th, 8 th,...) µ q /T= χ B 4 /χb χ B 6 /χb.6.8. Τ/T pc µ q /T=.6.8. Τ/T pc Friman, B., et al. Eur. Phys. J. C 7 () 694, arxiv:3.35 [hep-ph] But huge statistics are needed and experimental effects must be carefully controlled χ B 4 /χb χ B 8 /χb 8 October 8 3

24 First higher moments from ALICE! ( p) C ALI PREL p = p - p.4 < p <. GeV/c T η <.8 Boxes: sys. errors ALICE Preliminary Pb-Pb = 5. TeV =.76 TeV Centrality (%) ( p) C 4 /C.4 p = p - p ALICE Preliminary < p <. GeV/c s.4 T NN = 5. TeV η <.8 =.76 TeV. Skellam Boxes: sys. errors Centrality (%) ALI PREL Pb-Pb Measured with traditional (cut-based) PID method Consistent results between =.76 TeV and 5. TeV within statistical and systematic uncertainties In central events, consistency with Skellam baseline (C 4 /C = ) N. Behera for ALICE, QM8 8 October 8 4

25 First higher moments from ALICE! ( p) C ALI PREL p = p - p.4 < p <. GeV/c T η <.8 Boxes: sys. errors ALICE Preliminary Pb-Pb = 5. TeV =.76 TeV Centrality (%) ( p) C 4 /C ALI PREL 596 p = p - p Boxes: sys. errors ALICE Preliminary Pb-Pb ( - %).4 < p <. GeV/c T η <.8 STAR [PRL, 33 (4)] Au-Au ( - 5%).4 < p <.8 GeV/c T y <.5 3 (GeV) Measured with traditional (cut-based) PID method Consistent results between =.76 TeV and 5. TeV within statistical and systematic uncertainties In central events, consistency with Skellam baseline (C 4 /C = ) at LHC energies N. Behera for ALICE, QM8 8 October 8 5

26 First higher moments from ALICE! ( p) C ALI PREL p = p - p.4 < p <. GeV/c T η <.8 Boxes: sys. errors ALICE Preliminary Pb-Pb = 5. TeV =.76 TeV Centrality (%) ( p) C 4 /C ALI PREL 596 p = p - p Boxes: sys. errors ALICE Preliminary Pb-Pb ( - %).4 < p <. GeV/c T η <.8 STAR [PRL, 33 (4)] Au-Au ( - 5%).4 < p <.8 GeV/c T y <.5 3 (GeV) Higher statistics and improved understanding of systematics are needed to obtain the precision needed for LQCD comparisons Coming soon! improved statistical precision with December 8 dataset comparison to the Identity Method 8 October 8 N. Behera for ALICE, QM8 6

27 Conclusions Event-by-event fluctuations of identified particles yield information on properties of the QGP medium test lattice QCD predictions at µ B = allow us to look for effects of criticality Effects of imprecise particle identification under control Identity Method Effects of volume fluctuations and global baryon number conservation are assessed Net-proton and net-λ fluctuations: no deviations from Skellam baseline observed after accounting for baryon number conservation, agreement with LQCD predictions 8 data needed for precise measurements of 4 th moments, Run 3 needed for 6 th and 8 th moments 8 October 8 7

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29 Centrality dependence κ (p - p) κ. ALICE Preliminary, Pb-Pb =.76 TeV.6 < p <.5 GeV/c, centrality -5% ratio, stat. uncert. syst. uncert. HIJING κ (p - p) κ. ALICE Preliminary, Pb-Pb =.76 TeV.6 < p <.5 GeV/c, centrality 3-4% ratio, stat. uncert. syst. uncert. HIJING.9.9 ALI-PREL η ALI-PREL η Deviations from Skellam can be attributed to global baryon number conservation, more significant in more peripheral collisions Disagreement with HIJING 8 October 8 A. Rustamov for ALICE, QM7 9

Measurement of sixth order cumulant of net-proton multiplicity distribution in Au+Au collisions at s NN = 200 GeV with the STAR detector

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