Post on 25-Aug-2020
Recent Results on Cumulants of Net-Particle Distributions in Au+Au
Collisions at STAR
1
Toshihiro Nonaka for the STAR CollaborationUniversity of Tsukuba
Central China Normal University
Toshihiro Nonaka, QM2018, Venice, Italy
Outline
2
✓ Introduction- Observables
- Analysis methods
✓ Experimental results- Net-Λ cumulants
- Off-diagonal cumulants
- Sixth-order cumulants
✓Non-binomial efficiencies
Toshihiro Nonaka, QM2018, Venice, Italy
QCD phase diagram
3
✓ Higher-order fluctuations of net-particle distributions.
- Crossover at μB=0
- 1st-order phase transition at large μB?
- Critical point?
Toshihiro Nonaka, QM2018, Venice, Italy
Higher-order fluctuation
4
✓ Moments: mean (M), standard deviation (σ), skewness (S) and kurtosis (κ).✓ S and κ are non-gaussian fluctuations.
κ > 0
κ < 0
skewness→asymmetry kurtosis→sharpness
from wikipedia
✓ Cumulant ⇄ Moment ✓ Cumulant : additivity
proportional to volume
✦ Moments and cumulants are mathematical measures of “shape” of a distribution which probe the fluctuation of observables.
Toshihiro Nonaka, QM2018, Venice, Italy
Existing analysis methods
5
- X.Luo, J. Xu, B. Mohanty and N. Xu. J. Phys. G40,105104(2013)
✓ Efficiency correction on cumulants have been done assuming the binomial efficiencies.
- M. Kitazawa : PRC.86.024904, M. Kitazawa and M. Asakawa : PRC.86.024904- A. Bzdak and V. Koch : PRC.86.044904, PRC.91.027901, X. Luo : PRC.91.034907- T. Nonaka et al : PRC.94.034909, T. Nonaka, M. Kitazawa, S. Esumi : PRC.95.064912
✓Centrality bin width averaging is done for the reduction of the initial volume fluctuation.
✓Calculate the cumulants at each value of the multiplicity used for centrality, then weighted-average these in each centrality bin.
N1, N2 : lowest and highest multiplicity bin in the centralitynr : # of events in rth multiplicity bin
Toshihiro Nonaka, QM2018, Venice, Italy
Net-Λ cumulants
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✓ Strange hadrons freeze-out earlier than light flavor hadrons?✓ Net-Λ cumulants might provide additional constraints on freeze-out
conditions.
J. Noronha-Hostler, C. Ratti, P. Parotto, R. Bellwied, arXiv:1805.00088
HRG fit to STAR net-K using PDG16+
HRG fit to STAR net-p,Q (1403.4903)
STAR thermal fits ,p,K (1701.07065)
STAR thermal fits ,p,K, , , , ,Ks0 (1701.07065)
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B [MeV]
T[M
eV]
Toshihiro Nonaka, QM2018, Venice, Italy
Net-Λ cumulants
7
✓ Consistent with Poisson/NBD baselines.
✓ C1 and C2 are above UrQMD results.
✓ C3 shows better agreement with UrQMD.
>part<N50 100 150 200 250 300 350
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cumulantsΛnet -
Au + Au collisionsat STAR
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See N. Kulathunga, Poster #528
Toshihiro Nonaka, QM2018, Venice, Italy 8
✓ C2/C1 is close to HRG results (same kinematic range) with kaon freeze-out condition, and far away from those of charge and proton.
✓ The error on C3/C2 is presently too large to provide a meaningful constraint on the HRG model.
Net-Λ cumulants
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/M)
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/C 2C
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FO at charge/proton FO (HRG)ΛAssuming
Au + Au collisions
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(S 2/C 3
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Efficiency corrected.STAR Preliminary
Toshihiro Nonaka, QM2018, Venice, Italy
Off-diagonal cumulants of conserved charges will provide additional constraints on the freeze-out conditions.
9
• A. Majumder and B. Muller, Phy. Rev. C 74 (2006) • A. Bazavov et al. Phys. Rev. D86 (2012) 034509 • A. Chatterjee et al. J. Phys. G: Nucl. Part. Phys.
43 (2016) 125103• Z. Yang et al. Phys. Rev. C 95 014914 (2017)
✓ Covariance shows linear dependence with respect to the centrality and η acceptance.
✓ The correlation between net-protons and net-kaons changes from positive to negative with increasing beam energy.
See A. Chatterjee, Poster #534
Centrality dependence, |η|<0.5 η acceptance dependence, 0-5%
Efficiency corrected-0.5
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Efficiency correctedSTAR Preliminary
The 2nd-order off-diagonal cumulants
0.4<pT<1.6 (GeV/c)
Toshihiro Nonaka, QM2018, Venice, Italy 10
✓ Normalized p-k correlation is positive at low energies and negative at high energies, which are also consistent with UrQMD.
✓ Significant excess is observed in Q-k and Q-p with respect to the Poisson baseline and UrQMD.
✓ This excess increases with the beam energy in central collisions compared to peripheral collisions.
See A. Chatterjee, Poster #534
The 2nd-order off-diagonal cumulants
STAR Preliminary
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,k=(σ
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k=(σ
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2 k)
data 0-5%data 70-80%PoissonUrQMD 0-5%UrQMD 70-80%
Toshihiro Nonaka, QM2018, Venice, Italy 11
C.Schmidt,Prog.Theor.Phys.Suppl.186,563–566(2010) Cheng et al, Phys. Rev. D 79, 074505 (2009) Friman et al, Eur. Phys. J. C (2011) 71:1694
✓ There isn’t yet any direct experimental evidence for the smooth crossover at μB~0.✓ Sixth-order cumulants of net-charge and net-baryon distributions are predicted to
be negative if the chemical freeze-out is close enough to the phase transition.
Friman et al, Eur. Phys. J. C (2011) 71:1694 : O(4) scaling functions
Cheng et al, Phys. Rev. D 79, 074505 (2009) : Lattice QCD
Net-charge sixth-order cumulant
Predicted scenario for this measurement
Toshihiro Nonaka, QM2018, Venice, Italy 12
✓ The first result of C6/C2 of net-charge.✓ Net-charge has much larger errors than net-proton because the error strongly depends
on the standard deviation.✓ Results of net-charge C6/C2 are consistent with zero within large statistical errors.✓ Negative values are observed in net-proton C6/C2 systematically from peripheral to
central collisions.partN
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Toshihiro Nonaka, QM2018, Venice, Italy 13
✓ The detector efficiency may not be binomial, which would be due to the particle mis-identification, track splitting/merging effects, and many other reasons.
✓ Residual dependence of efficiency inside one multiplicity bin (for centrality) needs to be taken into account.
A. Bzdak, R. Holzmann, V. Koch : PRC.94.064907
A. Bzdak, R. Holzmann, V. Koch : PRC.94.064907
1. Experimental effects
√sNN = 200 GeV
"0lowp
= �0.00032
"0lowpbar
= �0.00033
"0highp
= �0.00025
"0highpbar
= �0.00023
STAR Preliminary
T. Nonaka, WPCF2017 Multiplicity
2. Multiplicity dependent efficiency
➡ One example of non-binomial distribution, Beta-binomial, is wider distribution than binomial
Non-binomial efficiencies
Toshihiro Nonaka, QM2018, Venice, Italy 14
✓ We performed MC simulations by embedding protons and antiprotons, e.g., Np=60 and Npbar=15 (which would be an extreme number), and see whether those particles can be reconstructed or not.
✓ The response matrix is close to the beta-binomial distribution, which is wider than binomial.
See T. Nonaka, Poster #453
➡ “Urn model” for beta-binomial distribution, where the parameter α controls the deviation from binomial.
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Non-binomial efficiencies
Toshihiro Nonaka, QM2018, Venice, Italy 15
√sNN = 19.6 GeV, 0-5% centrality, |y|<0.5, 0.4 < pT < 2.0, embedding simulation
Response matrices✓ The deviation from binomial would depend on the # of embedded protons and antiprotons.✓ 4-D response matrices are determined by embedding simulation, which can be directly
used for unfolding in order to reconstruct the distribution itself.
See T. Nonaka, Poster #453
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n pba
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np : # of reconstructed protons
R(np, npbar;Np, Npbar) Reversed response matrix
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Np : # of embedded protons
Npb
ar :
# of
em
bedd
ed a
ntip
roto
ns
R(Np, Npbar;np, npbar)
Toshihiro Nonaka, QM2018, Venice, Italy 16
✓ For unfolding, 2.5% centrality width averaging has been done.
✓ Systematic suppression is observed for C2 and C3 with respect to the results of efficiency correction assuming binomial efficiencies.
✓ C4, C3/C2 and C4/C2 are consistent within large systematic uncertainties limited by embedding samples.
See T. Nonaka, Poster #453
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C4/C2
Results of unfolding
Toshihiro Nonaka, QM2018, Venice, Italy
Summary
17
1. Net-Λ cumulants up to 3rd-order• Consistent with Poisson/NBD baselines.• The result of C2/C1 is closer to those of HRG with kaon freeze-out condition rather than light flavor hadrons.
2. Second-order off-diagonal cumulants• Q-k and Q-p correlations are in excess of the UrQMD results.
3. Sixth-order cumulant of net-charge and net-proton• Negative value is observed (although with extremely large uncertainties) in consistency with expectations
from O(4) scaling functions.4. Influence of non-binomial efficiencies
• One example of the response matrix is tested by embedding simulation, which is closer to beta-binomial than binomial.
• Unfolding has been applied at √sNN = 19.6 GeV in central collisions, where results show systematic suppression for C2 and C3 compared to the efficiency correction assuming binomial efficiencies, while C4, C3/C2 and C4/C2 are consistent within large systematic uncertainties limited by embedding samples.
Thank you for your attention
18
Back up
19
Toshihiro Nonaka, QM2018, Venice, Italy
Centrality definition
20
✓ In order to avoid the auto-correlation, the centrality is defined by using different paricle species or acceptance.
• Net-proton• Net-Λ
• Net-charge• Off-diagonal (π, K, p)
Charged paricles excluding (anti)protons in |η|<1.0
Charged paricles excluding (anti)protons in |η|>0.5
See : Phys. Rev. Lett. 113, 092301(2014) See : Phys. Rev. Lett. 112, 032302(2014)
Toshihiro Nonaka, QM2018, Venice, Italy
Lambda reconstruction
21
✓ Lambda is reconstructed event-by-event based on the decay topology.
2) GeV/c-π (P, invM1.08 1.1 1.12 1.14 1.16 1.18
Cou
nts
0
5
10
15
20
25
610×h_InvMass_UnFltd_0
Entries 5.788835e+08
Mean 1.128
Std Dev 0.02935
Signal
Background
39 GeV Au+Au Collisionsat STAR
)-πInv. mass (P,
STAR Preliminary
(p, π—)
(p, π—)Minv(p,⇡�) (GeV/c2)
Toshihiro Nonaka, QM2018, Venice, Italy
Lambda reconstruction
22
✓ The geometrical cuts were varied in order to obtain high pure (>90%) sample.
Minv(p̄,⇡+) (GeV/c2)
Toshihiro Nonaka, QM2018, Venice, Italy
Net-lambda distribution
23
Toshihiro Nonaka, QM2018, Venice, Italy 24
See A. Chatterjee, Poster #534Centrality dependence
-0.5
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Co-
varia
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1 )
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⟨Npart⟩
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Beam energy
0.4 < pT < 1.6 GeV/c|η| < 0.5
bars: syst. errorstat. error within the marker
α1x
⟨Npart⟩
7.7 GeV11.5 GeV14.5 GeV19.6 GeV
27 GeV
39 GeV62.4 GeV200 GeV
CLT
STAR Preliminary
2nd-order off-diagonal cumulants
Toshihiro Nonaka, QM2018, Venice, Italy 25
2nd-order off-diagonal cumulantsη acceptance dependence See A. Chatterjee, Poster #534
STAR Preliminary
Toshihiro Nonaka, QM2018, Venice, Italy
Unfolding methodology
26
✓ Difference between exp.meas and sim.meas is applied to sim.true to get the corrected distribution, which is repeated until cumulants converge.
A) Exp. true C) Sim. true
D) Sim. measB) Exp. meas
RMrev
C.F_rec = B) - D)
C.F_gen = RMrev x C.F_rec
C’) = C) + C.F_gen
run MC iteratively
Np
Npbar
Generatedcoordinate
Reconstructedcoordinate
S. Esumi et al : in preparation
Toshihiro Nonaka, QM2018, Venice, Italy
Test with non-binomial distributions
27
α1 2 3 4 5 6 7 8 9 10
Std.
Dev
1.3
1.4
1.5
1.6
1.7=0.6εN=10,
Beta-binomial
Hypergeometric
Binomial
n0 1 2 3 4 5 6 7 8 9 10
Hyp./Binom
ial
0.8
0.9
1
1.1
1.2
n0 1 2 3 4 5 6 7 8 9 10
Beta./Binom
ial
0.8
0.9
1
1.1
1.20 1 2 3 4 5 6 7 8 9 10
210
310
410
510
610
=1α
=3α
=5α
=10α
Binomial
N=10, ε=0.6
n0 1 2 3 4 5 6 7 8 9 10
Hyp./Binom
ial
0.8
0.9
1
1.1
1.2
n0 1 2 3 4 5 6 7 8 9 10
Beta./Binom
ial
0.8
0.9
1
1.1
1.2 0 1 2 3 4 5 6 7 8 9 10
410
510
610
=1α
=3α
=5α
=10α
Binomial
N=10, ε=0.6
Hypergeometric distributionDraw a ball from urn, if it is white, count particle. This is repeated without replacement.
Beta-binomial distributionDraw a ball from urn, if it is white, count particle. And return two white balls to urn (similar for black balls).
✓ Smaller α for Hypergeometric distribution, becomes narrower than binomial distribution.
✓ Smaller α for Beta-binomial distribution, becomes wider than binomial distribution.
✓ Both non-binomial distributions become close to the binomial with large α.
✓ The beta-binomial and hypergeometric distributions can be defined by the urn model, in which the parameter α controls the devitation from the binomial distribution.
Nw : white balls, Nb: black balls, ε: efficiency
Toshihiro Nonaka, QM2018, Venice, Italy
Response matrix from embedding simulation
28√sNN = 19.6 GeV, 0-2.5% centrality, 60 protons and 15 antiprotons are embedded2040608000.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991Np=1, Npbar=42040608000.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991Np=1, Npbar=82040608000.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991Np=1, Npbar=15
20 40 60 800
2
4
6
Np=7, Npbar=2
20 40 60 800
2
4
6
Np=15, Npbar=1
20 40 60 800
2
4
6
Np=15, Npbar=4
20 40 60 800
2
4
6
Np=30, Npbar=1
20 40 60 800
2
4
6
Np=30, Npbar=8
20 40 60 800
2
4
6
Np=30, Npbar=15
20 40 60 800
2
4
6
Np=60, Npbar=1
20 40 60 800
2
4
6
Np=60, Npbar=8
20 40 60 800
2
4
6
Np=60, Npbar=15
Binomial
Hypergeometric
Beta-binomial
α : closeness to the binomial
χ2/N
DF
20 30 40 50 60
5−10
4−10
3−10
2−10
1−10
20 30 40 50 600.80.91
1.11.21.3
np : # of reconstructed protonsda
ta/fi
t
χ2/NDF ~ 3.3χ2/NDF ~ 1.0
✓ Embed 60 protons and 15 antiprotons into the real data (which would be the extreme number), and see whether those particles can be reconstructed or not.
✓ The response matrix is wider than the binomial, and it is close to the beta-binomial distribution.
✓ More detailes can be found in the poster #453.
STAR Preliminary
STAR Preliminary
Toshihiro Nonaka, QM2018, Venice, Italy
Test with non-binomial distributions
29
✓ The beta-binomial distribution is wider than binomial, which can be defined by the urn model.
✓ The parameter α controls the devitation from the binomial distribution.
Nw : white balls, Nb: black balls, ε: efficiency
0 1 2 3 4 5 6 7 8 9 10
410
510
610
=1α
=3α
=5α
=10α
Binomial
N=10, ε=0.6
N