Proton-Number Fluctuations in HADES: Reconstruction of higher moments

Transcription

1 Hosan Proton-Number Fluctuations in : Reconstruction of higher moments Romain Holzmann, GSI Helmholtzzentrum Darmstadt, for the collaboration SIS 18 energy regime: beam energies 1-2 GeV/u moderate T, high μ B baryon dominated Outline: : Au+Au at 1.23 GeV/u at GSI Net proton nb. fluctuations - efficiency corrections - volume fluct. effects - fragments, ie bound protons Summary & Outlook:

2 Fluctuations probe features of QCD phase diagram M. Stephanov M. Stephanov CPOD2014 κ 3 /κ 2 density Crossing features of the QCD phase-diagram (phase boundaries, CEP) is expected to result in: diverging susceptibilities & correlation length extra fluctuations of conserved quantities (e.g. baryon nb, charge, strangeness) observable discontinuities of the higher moments of particle number distributions, visible e.g. in a beam energy scan! increasing s decreasing μ b (see e.g. B. Friman et al, EPJC 71 (2011) 1694) 2

3 Fluctuations probe features of QCD phase diagram M. Stephanov M. Stephanov CPOD2014 κ 4 /κ 2 density Crossing features of the QCD phase-diagram (phase boundaries, CEP) is expected to result in: diverging susceptibilities & correlation length extra fluctuations of conserved quantities (e.g. baryon nb, charge, strangeness) observable discontinuities of the higher moments of particle number distributions, visible e.g. in a beam energy scan! increasing s decreasing μ b STAR/NA61 (see e.g. B. Friman et al, EPJC 71 (2011) 1694) Needs high-statistics data! 3

4 The detector at GSI large acceptance 2-3% mom resolution hadron & lepton PID up to 50 khz trigger rate RPC High Acceptance DiElectron Spectrometer + segmented diamond Start + plastic scint. FW (covering θ = 0. 5 o 7.5 o ) evt characterization (centrality & event plane) 4

5 Particle ID in Velocity vs. p Hadron ID based on ToF Momentum de/dx Hadron mass spectrum MDC & TOF de/dx de/dx vs. p

6 Proton distributions in Au+Au at s = 2.41 GeV y p t coverage for protons Proton mt spectra Δy = 0.1 preliminary Proton multiplicity distributions y cm = 0.74 Analysis based on Au+Au evts divided into 4 centrality classes 6

7 (I) Efficiency corrections Note that efficiency = acc x det. eff x rec. eff! 1. Correct the cumulants A. Bzdak & V. Koch, PRC 86 (2012); X. Luo, PRC 91 (2015); M. Kitasawa, PRC 93 (2016) 2. Correct measured distributions (bayesian unfolding) Garg et al., J. Phys. G: Nucl. Part. Phys. 40 (2013) we have investigated both methods 1. in simulations based on UrQMD evts filtered with full response 2. in real Au+Au data 7

8 efficiency Hades efficiencies vs. p t, y, centrality & N track /sector p t centrality = 30% - 40% efficiency vs. detector occupancy centrality = 0% - 10% y lab N track /sector p t Efficiency drops by up to 15% with occupancy, need to do a dynamic efficiency correction! Model ε = ε N track, sector to correct evt-by-evt! y lab We verified this correction scheme in full detector simulations using 54 separate acc. bins (Δy Δp t sector). 8

9 Method 1: Evt-by-evt efficiency correction of κ n Efficiency depends on particle, centrality, pt & y correct by phase-space bin and evt-wise! Bzdak & Koch, PRC 91 (2015) Tang & Wang, PRC 88 (2013) Xiaofeng Luo, PRC 91 (2015) Masakiyo Kitasawa, PRC 93 (2016) (1) (2) local factorial moments (3) correct evt-by-evt with dynamic ε=ε(n) 9

10 recons Method 2: Unfold the multiplicity distribution Response matrix of the system: (obtained from simul) N recons = A N input A A -1 in Tested on simulated proton spectra accepted in. All moments reproduced within statistical error bars! input unfolded + 10

11 Unfolding in a nutshell: regularize A Literature: G. D Agostino, Nucl. Instr. Meth. A 362 (1995) 487. S. Schmitt, J. Instr. 7 (2012) T P. Garg et al., J. Phys. G 40 (2013) Problem: y = A x x = true signal, A = response matrix, y = measured signal Knowing y and A, find x. Unfortunately, A is often quasi-singular and can not be inverted (ill-conditioned problem!). Solution: Minimize via least-squares procedure the Lagrangian L(x,λ): minimization Tikhonov regularization ROOT implementation: TUnfold, TUnfoldSys, TUnfoldDensity area constraint 11

12 (II) Volume fluctuations effects Effect of volume fluctuations due to centrality selection on (reduced) cumulants of the net baryon number discussed by Skokov, Friman & Redlich in PRC 88 (2013): volume fluctuations centrality bins in k n baryon number cumulants c n volume affected cumulants v n volume fluctuations cumulants Take volume fluctuations v n from model, e.g. Glauber or transport, adjusted to observable used to define centrality in a given experiment, and correct data. Effect of centrality selection investigated with UrQMD simul by G. Westfall in PRC 92 (2015) Discussed in more detail by PBM, Rustamov & Stachel NPA 960 (2017)

13 Volume fluctuation effects on cumulants Glauber simulation of N wounded + Negative Binomial model of particle production Braun-Munzinger, Rustamov & Stachel, Nucl. Phys. A 960 (2017) 114 s NN = 7.7 GeV Skokov formulas: 39 GeV 2.76 TeV κ 1 = c 1 κ 2 = c 2 κ 1 2 v 2 κ 3 = c 3 3 κ 2 κ 1 v 2 κ 1 3 v 3 κ 4 = c 4 4κ 3 κ 1 + 3κ 2 2 v 2 6κ 2 κ 1 2 v 3 κ 1 4 v 4 At large s, odd terms cancel! partial cancellation of volume terms at large N w? 13

14 Choice of phase-space bite for fluctuation analysis s NN = 2.41 GeV y p t coverage for protons rapidity gap = 1.5 units! Need to select a phase-space bite which avoids spectators and stays within the acceptance, but far enough from Poisson limit! phase-space bite used in fluctuation analysis: y = y 0 ± 0. 2 and p t = GeV/c 14

15 Checking the Poisson limit: κ n vs. Δy Expect to approach Poisson limit for narrow enough phase-space bin! Shown here for our Au+Au proton data with unfolding & volume correction: Poisson preliminar y preliminar y Poisson phase-space bin: y acc = y 0 ± Δy p t = GeV/c S σ 1 and κ σ 2 1 for Δy 0 ok! 15

16 volume corr. Fully corrected scaled moments vs. centrality 1.23 GeV/u Au+Au proton moments: ω = κ 2 κ 1 Sk σ = κ 3 κ 2 κ σ 2 = κ 4 κ 2 preliminar y 20-20% 20-30% 0-10% 30-40% 20-30% 30-40% 30-40% 10-20% 0-10% 0-10% preliminary preliminary Error bands correspond to 5% systematic error on proton efficiencies. < > < > Scaled cumulants deviate from Poisson with centrality Volume corrections on κ 4 /κ 2 smallest for most central 16

17 Comparison with STAR BES-I STAR analysis: Xiaofeng Luo et al., PoS (CPOD2014) 019 arxiv: v2 preliminary preliminary red/black = unfolding (preferred method) + vol. flucs. corr. green = evt-by-evt eff correction of factorial moments + vol. flucs. corr. 17

18 (III) What about bound protons? Systematics of d/p from STAR collaboration (QM2017) 1.23 GeV/u Au+Au data d/p (analysis in progress) Sizeable fraction of protons are bound in fragments: d, t, He, etc. How do they contribute to baryon-number fluctuations? Should they be taken into account in a beam-energy scan? Deuteron nb. fluctuations in Au+Au 18

19 d / 4 He separation in MDC via de/dx 19

20 volume corr. Fully corrected scaled moments of N p + N d (ongoing analysis...) 1.23 GeV/u Au+Au proton+deuteron moments: ω = κ 2 κ 1 Sk σ = κ 3 κ 2 κ σ 2 = κ 4 κ % 20-30% 0-10% 30-40% 20-30% 30-40% 10-20% 30-40% 0-10% 0-10% in work in work in work < > < > < > - efficiency corr. via unfolding - volume flucs. corr. - error bands = 5% uncertainty on particle eff. 20

21 Summary and Outlook Analyzed proton nb fluctuations in hi-stat Au+Au evt sample at s NN = 2.41 GeV 1 st time this kind of analysis has been done at low energies Systematic study of experimental & instrumental effects: use of fine grained y-pt bins for eff. corr. evt-by-evt changes of efficiency large volume fluctuations due to centrality selection Started to investigate contribution of bound protons interpretation of results needs help from theory (e.g. Bzdak-Koch couplings?) To be continued in future runs at FAIR (phase 0 and beyond) 21

22 Thrift Shop

23 Proton cumulants κ n vs N part in 1.23 GeV/u Au+Au Proton cumulants from unfolding + volume corrections 23

24 Proton & deuteron coverage 24

25 Fully corrected scaled moments of deuterons (ongoing analysis...) volume corr GeV/u Au+Au deuteron moments: ω = κ 2 κ 1 Sk σ = κ 3 κ 2 κ σ 2 = κ 4 κ % 20-20% 20-30% 0-10% 30-40% 20-30% 10-20% in work 30-40% 0-10% in work in work 0-10% < > < > < > - efficiency corr. via unfolding - volume flucs. corr. - error bands = 5% uncertainty on deuteron eff. 25

26 deuterons compared with STAR net p (ongoing analysis...) STAR analysis: Xiaofeng Luo et al., PoS (CPOD2014) 019 arxiv: v2 in work in work : - efficiency corr. via unfolding - volume flucs. corr. - no realistic errors yet! 26

27 p+d compared with STAR net p (ongoing analysis...) STAR analysis: Xiaofeng Luo et al., PoS (CPOD2014) 019 arxiv: v2 in work in work : - efficiency corr. via unfolding - volume flucs. corr. - no realistic errors yet! 27

28 N part from Glauber fits to hit/track observables adjusted to hit distribution in TOF & RPC: adjusted to track distribution in MDC: 4 centrality bins used within LVL1 trigger used as estimate for FW selection N part fluctuations, also called volume fluctuations, must be corrected for in the data! 28

29 Pion production in 1.23 GeV/u Au+Au centrality: Glauber calc π Pseudo-scalar mesons measured in via photon conversion: preliminary π 0, η 2 γ e + e e + e very hi-stat π sample! π 0 consistent with ½ π + + π π 0 preliminary preliminary 29

30 Pion production vs. centrality selection method charged pion distributions: pion moments: skewness (within 15%), kurtosis (within 30%) expect very similar N part distributions for 3 selection methods 30

31 Volume corrections (choice of centrality selection) 31

32 Volume corrections (evt-by-evt vs. unfolding) 32

33 Poisson limit (w/o corr. volume flucs.) Expect to approach Poisson limit for narrow enough phase-space bin! Checked on Au+Au proton data with the unfolding method: Poisson Poisson preliminary preliminary phase-space bin: y acc = y 0 ± Δy Sk σ 1 and κ σ 2 1 for Δy 0 33