Fluctuations of Conserved Charges (EX)Toshihiro Nonaka, University of Tsukuba

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

1Outline• Introduction• Experimental challenges• New results• Future prospect• SummaryExperimental results are mostly taken from published papers
since QM2019, or from new results in QM2022

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

2

“Conjectured” QCD phase diagram• Crossover at µB = 0 MeV• Y. Aoki et al, Nature 443,675(2006)• 1st-order phase transition atlarge µB?
• Critical point?
Fluctuations of conserved charges
are sensitive to the phase structure
A. Bzdak et al, Phys.Rep.853 pp1-87 (2020)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

3

Higher-order fluctuation• Moments and cumulants are mathematical measures of “shape” of a
distribution, which probes fluctuations of an observable.
Skewness (S) → asymmetry• Cumulant ↔ Central moment

2022/4/9, QM2022@Krakow

Kurtosis (κ) → sharpness• Cumulants have additivity :proportional to the system volume

T. Nonaka "Fluctuations of Conserved Charges"

4

Cumulants of conserved charges• Measure event-by-event distributions of netbaryon, net-charge, and net-strangeness number

STAR Collaboration, PRL105.022302(2010)(1) Sensitive to the correlation length

M. A. Stephanov, PRL102.032301(2009), PRL107.052301(2011)
M. Asakawa, S. Ejiri, and M. Kitazawa, PRL103262301(2009)(2) Comparison with susceptibilities

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

M.Cheng et al,
PRD79.074505(2009)5Baselines• Skellam distribution• “Statistical” baseline:• (Poisson) – (Poisson) = (Skellam)• C1 = C3 = C5 = µ1 - µ2
C /C = C /C = C /C = 1• C2 = C4 = C6 = µ1 + µ2 3 1 4 2 6 22022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

6Baselines• Skellam distribution• “Statistical” baseline:• (Poisson) – (Poisson) = (Skellam)• C1 = C3 = C5 = µ1 - µ2
C3/C1 = C4/C2 = C6/C2 = 1• C2 = C4 = C6 = µ1 + µ2

• Non-critical baseline• Volume fluctuation, baryon number
conservation...
P.Braun-Munzinger et al, NPA982.307(2019), NPA1008.122141(2021)
A. Bzdak et al, EPJC77(2017)5.288, A. Bhattacharyya et al, PRC90.034909(2014)

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

7Baselines• Skellam distribution• “Statistical” baseline:• (Poisson) – (Poisson) = (Skellam)• C1 = C3 = C5 = µ1 - µ2
C3/C1 = C4/C2 = C6/C2 = 1• C2 = C4 = C6 = µ1 + µ2

• Non-critical baseline• Volume fluctuation, baryon number
conservation… +proton clustering
P.Braun-Munzinger et al, NPA982.307(2019), NPA1008.122141(2021)
A. Bzdak et al, EPJC77(2017)5.288, A. Bhattacharyya et al, PRC90.034909(2014)

Apr. 6th, 4:40 pm, Anar Rustamov

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

8Probe the phase structure
Critical point : nonmonotonic beamenergy dependence of net-baryon C4/C2
w.r.t the baseline

Crossover : Negative sign of C5 and C6
B. Friman et al, Eur. Phys. J. C (2011)
71:1694

W. Fu et al,
PRD104.094047(2021)

A. Bazavov et al,
PRD95.054504(2017)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

9

Raw net-proton multiplicity distribution• Need to consider various experimental effects.

STAR, PRL126.092301(2021),
PRC104.024902(2021)
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

10Experimental Challenges
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

11Experimental challenges• Detector efficiency correction• Binomial distribution••

M. Kitazawa and M. Asakawa, PRC86.024904(2012), A. Bzdak and V. Koch, PRC86.044904(2012), X. Luo, PRC91.034907(2016),
T. Nonaka, M. Kitazawa, S. Esumi, PRC95.064912(2017), X. Luo and T. Nonaka, PRC99.044917(2019)••T. Nonaka, M. Kitazawa, S. Esumi, NIMA906 10-17(2018)
S. Esumi, K. Nakagawa, T. Nonaka, NIMA987.164802(2021)• Non-binomial distribution• Initial volume fluctuation•••

M. I. Gorenstein and M. Gaździcki, PRC84.014904 (2011), V. Skokov, B. Friman, and K. Redlich, PRC88,034911 (2013)
X. Luo, J. Xu, B. Mohanty, N. Xu, J. Phys. G40.105104 (2013), P. Munzinger, A. Rustamov, and J. Stachel, NPA960.114 (2017)
T. Sugiura, T. Nonaka, and S. Esumi, PRC100.044904 (2019)• Pileup events••

S. Sombun et al, J.Phys.G45.025101(2018), P. Garg and D. Mishra, PRC96.044908(2017)
T. Nonaka, M. Kitazawa, S. Esumi, NIMA984.164632(2020), Y. Zhang, Y. Huang, T. Nonaka, X. Luo, NIMA1026.166246(2022)• Identity method•••

M. Gaździcki, K. Grebieszkow, M. Maćkowiak, and S. Mrówczyński, PRC83.054907 (2011)
A. Rustamov and M. I. Gorenstein, PRC86.044906 (2012), M. I. Gorenstein, PRC84.024902 (2018)
M. Arslandok and A. Rustamov, NIMA946.162622 (2019)• More to be resolved…

• Net-proton≠net-baryon, purity correction, acceptance dependence for comparison with theory, ….

*Not all important studies are listed here
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

12Detector efficiency correction• Efficiency correction depends on the efficiency distributions.
The simplest scenario is the binomial distribution.
p: efficiency
N: generated particles
n: reconstructed particles

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

HADES, PRC102.024914(2020)13

Detector efficiency correction• Efficiency correction depends on the efficiency distributions.
The simplest scenario is the binomial distribution.
p: efficiency
N: generated particles
n: reconstructed particles

Efficiency distribution fromembedding simulations at STAR

Comparison between binomial andbeta-binomial efficiency corrections

Reconstructed protons
STAR, PRC.104.024902(2021), PRL126.092301(2021)
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

HADES, PRC102.024914(2020)14

Detector efficiency correction• Efficiency correction depends on the efficiency distributions.
The simplest scenario is the binomial distribution.

Response matrices constructedfrom HADES detector simulations
with IQMD

Results from different methods for efficiency corrections

p: efficiency
N: generated particles
n: reconstructed particles• Effects of non-binomial efficiencies need to be carefully
studied for each experimental group.
Efficiency distribution fromembedding simulations at STAR

Comparison between binomial andbeta-binomial efficiency corrections

Reconstructed protons
STAR, PRC.104.024902(2021), PRL126.092301(2021)
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

HADES, PRC102.024914(2020)15

Effect of pT acceptance cut• Baryon-charge ratio at 2nd-order shows significantly lower temperature than chemical freeze-out
temperature → effect of resonance decays?
• pT acceptance correction plays an important role on baryon-charge ratio at 2nd-order.
• Effect on for higher-order fluctuations?

Apr. 6th, 3:40pm, Masakiyo Kitazawa
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

16Initial volume fluctuation:
Centrality Bin Width Correction (CBWC)
STAR, PRC104.024902(2021)• Initial geometry and final-state multiplicity are
not one-to-one corresponding: initial volume
fluctuation.

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

17Initial volume fluctuation:
Centrality Bin Width Correction (CBWC)
STAR, PRC104.024902(2021)

Centrality bin width for
cumulant calculations• Initial geometry and final-state multiplicity are
not one-to-one corresponding: initial volume
fluctuation

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

18

Initial volume fluctuation:
Centrality Bin Width Correction (CBWC)
STAR, PRC104.024902(2021)

Centrality bin width for
cumulant calculations• Initial geometry and final-state multiplicity are
not one-to-one corresponding: initial volume
fluctuation• Volume fluctuations can be partly suppressed by
CBWC.
• Purely data-driven, but cannot eliminate volume
fluctuations.

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

19Initial volume fluctuation:
Volume Correction

HADES, PRC102.024914(2020)• One can define/determine initial volume distributions andtheir cumulants by using model simulations, which can beeliminated from measurements based on correction formulas.
κn = const. w.r.t. Npart :independent particle production

2022/4/9, QM2022@Krakow

κn : cumulant normalized by Npart
κ~n : volume-affected cumulant

T. Nonaka "Fluctuations of Conserved Charges"

20Initial volume fluctuation:
Volume Correction

HADES, PRC102.024914(2020)• One can define/determine initial volume distributions andtheir cumulants by using model simulations, which can beeliminated from measurements based on correction formulas.
κn = const. w.r.t. Npart :independent particle production

κn : cumulant normalized by Npart
κ~n : volume-affected cumulant
κn slope is taken into account2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

21

Initial volume fluctuation:
Volume Correction

HADES, PRC102.024914(2020)• One can define/determine initial volume distributions andtheir cumulants by using model simulations, which can beeliminated from measurements based on correction formulas.
κn = const. w.r.t. Npart :independent particle production

κn : cumulant normalized by Npart
κ~n : volume-affected cumulant
κn slope is taken into account

There is no established way to correctfor initial volume fluctuations.

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

22Initial volume fluctuation:
Volume Correction

HADES, PRC102.024914(2020)• One can define/determine initial volume distributions andtheir cumulants by using model simulations, which can beeliminated from measurements based on correction formulas.
κn = const. w.r.t. Npart :independent particle production

κn : cumulant normalized by Npart
κ~n : volume-affected cumulant
κn slope is taken into account

There is no established way to correctfor initial volume fluctuations.

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

Cumulants are least affected for most central
collisions because of the maximum number
23
of nucleons (394 for Au+Au).

Pileup correction
Toy model : 5% pileup

C3

2022/4/9, QM2022@Krakow

C4

Event pileups: superposition of more than one single-collision events.
It is difficult to remove pileup events completely in experiment.

• Pileup events are crucial in fixed-target experiments,
which could make an artificial enhancement ofhigher-order cumulants in central collisions.

T. Nonaka "Fluctuations of Conserved Charges"

24Pileup correction
Toy model : 5% pileup

C3

C4

Event pileups: superposition of more than one single-collision events.
It is difficult to remove pileup events completely in experiment.

• Pileup events are crucial in fixed-target experiments,
which could make an artificial enhancement ofhigher-order cumulants in central collisions.
• Pileup correction can be applied for residual pileups.

m : reference multiplicity

T. Nonaka, M. Kitazawa, S. Esumi, NIMA984.164632(2020)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

25

Pileup correction
Toy model : 5% pileup

C3

C4

Event pileups: superposition of more than one single-collision events.
It is difficult to remove pileup events completely in experiment.

• Pileup events are crucial in fixed-target experiments,
which could make an artificial enhancement ofhigher-order cumulants in central collisions.
• Pileup correction can be applied for residual pileups.
STAR data : 0.46% pileup

m : reference multiplicity

STAR Collaboration,
arXiv:2112.00240

T. Nonaka, M. Kitazawa, S. Esumi, NIMA984.164632(2020)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

26

Experimental Results
Experimental results are mostly taken from published papers
since QM2019, or from new results in QM2022

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

27Net-proton fluctuations from ALICE
Net-proton 2nd-order cumulant
normalized by Skellam

ALICE, PLB807.135564(2020)2022/4/9, QM2022@Krakow••

Net-proton 2nd-order (normalized) cumulant
decreases with widening the rapidity acceptance.
Results are explained by global baryon number
conservation, which implies long range
correlation in data.
P.B.Munzinger, A. Rustamov, J. Stachel, NPA960.114130(2017)
A. Bzdak, V. Koch, V. Skokov, PRC87.014901(2013)

T. Nonaka "Fluctuations of Conserved Charges"

28

Canonical ensemble + rapidity correlations
Net-proton 2nd-order cumulant
normalized by Skellam

ALICE, PLB807.135564(2020)••

Net-proton 2nd-order (normalized) cumulant
decreases with widening the rapidity acceptance.
Results are explained by global baryon number
conservation, which implies long range
correlation in data.
P.B.Munzinger, A. Rustamov, J. Stachel, NPA960.114130(2017)
A. Bzdak, V. Koch, V. Skokov, PRC87.014901(2013)•

The data are best described with new
implementation of rapidity correlation between
baryons and antibaryons with Δycorr=12.
Apr. 6th, 4:40 pm, Anar Rustamov

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

29Net-lambda fluctuation• Both baryon and strangeness conservations play
an important role for net-lambda fluctuations.

STAR, PRC102.024903(2020)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

30Poster session 1 T07_1,
Jonathan Ball

Net-lambda fluctuation• Both baryon and strangeness conservations play
an important role for net-lambda fluctuations.

3GeV
STAR, PRC102.024903(2020)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

31

Deuteron number fluctuation

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

Apr. 6th, 3pm, Debasish Mallick

32

Deuteron number fluctuation

Apr. 6th, 3pm, Debasish Mallick

Coalescencemodel

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

Thermal model (=1)

33

Deuteron number fluctuation

Apr. 6th, 3pm, Debasish Mallick

Coalescence
model

Thermal model (=1)

Correlated p-n
production
Independentp-n production

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

34

(Anti)Deuteron number fluctuation• Collision energy dependence is qualitatively
reproduced by UrQMD+coalescence and CE
thermal models.
Deuteron

Apr. 6th, 3pm, Debasish Mallick
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

35

(Anti)Deuteron number fluctuation• Collision energy dependence is qualitatively
reproduced by UrQMD+coalescence and CE
thermal models.

Proton vs Deuteron

Apr. 6th, 3pm, Debasish Mallick
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

36

(Anti)Deuteron number fluctuation• Collision energy dependence is qualitatively
reproduced by UrQMD+coalescence and CE
thermal models.

• Cumulant ratio is consistent with Poisson baseline and SHM.
• Negative correlation rules out a coalescence model withcorrelated production of (anti)protons and (anti)neutrons.
Anti-deuteron

Apr. 6th, 3pm, Debasish Mallick
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

Anti-proton vs anti-deuteron

Apr. 7th, 6:50pm, Sourav Kundu
37

Net-charge fluctuation from NA61/SHINE• Two-dimensional scan in systemsize and collision energy.
• No structure indicating criticalpoint.
Apr. 5th, 2:45pm, Antoni Marcinek

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

38Net-proton C4/C2 : critical point searchin BES-I
STAR, PRL126.092301(2021)

2022/4/9, QM2022@Krakow• Non-monotonic beam energy dependence (3.1σ)of net-p C4/C2 in Au+Au central collisions.

T. Nonaka "Fluctuations of Conserved Charges"

39Net-proton C4/C2 : critical point searchin BES-I
STAR, PRL126.092301(2021)

2022/4/9, QM2022@Krakow• Non-monotonic beam energy dependence (3.1σ)of net-p C4/C2 in Au+Au central collisions.
• Enhancement at ~7.7 GeV is not reproduced by
non-critical baselines.

T. Nonaka "Fluctuations of Conserved Charges"

40Net-proton C4/C2 : critical point searchin BES-I
STAR, PRL126.092301(2021)

2022/4/9, QM2022@Krakow• Non-monotonic beam energy dependence (3.1σ)of net-p C4/C2 in Au+Au central collisions.
• Enhancement at ~7.7 GeV is not reproduced by
non-critical baselines.
• Qualitatively consistent with the model
prediction incorporating a critical point.

T. Nonaka "Fluctuations of Conserved Charges"

41Net-proton C6/C2 for crossover search• C6/C2 values are progressively
negative from peripheral to central
collisions at 200 GeV, which isconsistent with LQCD calculations.
• Could suggest a smooth crossovertransition at top RHIC energy.
STAR, PRL127.262301(2021)

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

42

Isobaric collisions• Ratios approach LQCD calculations with increasing the multiplicity, which imply
that the created system approach thermalized medium at high multiplicity region.

Apr. 7th, 10:20am, Ho-San Ko
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

43

FXT from HADES and STAR
• No clear enhancement is observed for 2.4 and
3.0 GeV data from HADES and STAR.
• Negative value at 3GeV is reproduced by
UrQMD, which incorporates baryon number
conservation.
2.4 GeV• The data implies that the QCD critical region
could only exist at energies > 3GeV.

HADES, PRC102.024914(2020)
STAR, arXiv:2112.00240
2022/4/9, QM2022@Krakow

Apr. 5th, 4:30pm, Yu Zhang
T. Nonaka "Fluctuations of Conserved Charges"

44

Future Prospect
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

45

Probe magnetic field in HIC• 2nd order mix-cumulants among conserved charges aresuggested to be sensitive to the magnetic field.
• Difference between Zr+Zr and Ru+Ru?

LQCD: H-T.Ding et al, EPJA57.202(2021)
2022/4/9, QM2022@Krakow

Apr. 7th, 3:40pm, Jun-Hong Liu
T. Nonaka "Fluctuations of Conserved Charges"

46

Probe magnetic field in HIC

UrQMD: Z. Yang et al, PRC95.014914(2017)• 2nd order mix-cumulants among conserved charges aresuggested to be sensitive to the magnetic field.
• Difference between Zr+Zr and Ru+Ru?
• Hyperons have an important role for B-S correlations.

LQCD: H-T.Ding et al, EPJA57.202(2021)
2022/4/9, QM2022@Krakow

Apr. 7th, 3:40pm, Jun-Hong Liu
T. Nonaka "Fluctuations of Conserved Charges"

47

Probe magnetic field in HIC

UrQMD: Z. Yang et al, PRC95.014914(2017)• 2nd order mix-cumulants among conserved charges aresuggested to be sensitive to the magnetic field.
• Difference between Zr+Zr and Ru+Ru?
• Hyperons have an important role for B-S correlations.

Invariant mass reconstruction: Signal and BG
particles cannot be identified for track-by-track basis

LQCD: H-T.Ding et al, EPJA57.202(2021)
2022/4/9, QM2022@Krakow

Apr. 7th, 3:40pm, Jun-Hong Liu
T. Nonaka "Fluctuations of Conserved Charges"

STAR PRC102.034909(2020)

48

Hyperon number fluctuation• Direct measurement of event-by-event fluctuation is not possible due to backgrounds
under the signal peak.
• Identity method and purity corrections are available.
Identity method

Purity correctionmSN=mS+mN
mS

mR,1 mR,2

A. Ohlson, QM2018, NPA982.299(2019)2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

mN

mR,3 mR,4

T. Nonaka, arXiv:2202.06953
49

Crossover searchSTAR, PRL127.262301(2021)

Hint of a crossover at RHIC top energy• There will be several opportunities at RHIC
and LHC to establish the nature of the phasetransition at small μB region.
STAR BUR for Run22, STAR NOTE #0773

RHIC Au+Au 200 GeV 2023-2025

ALICE, LHC Run3

Poster session 1 T07_1,
Ashish Pandav

Challenge forC7 and C8

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

50Critical point search
HADES, PRC102.024914(2020)
STAR, arXiv:2112.00240• More data will come from BES-II and FXT at
STAR to fill the gap in 3<√sNN<20 GeV.
• More precise study will be carried out by
CBM@FAIR, MPD@NICA, HIAF, and JPARC-HI.

H. Caines, “RHIC BES and Beyond”

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

51

Summary : Where we are?
Courtesy of Nu Xu• Several hints on QCD phase structures
have been obtained throughmeasurements of fluctuations ofconserved charges.
• LQCD indicates critical point is not likely
to exist for µB/T < 2.5.
Apr. 6th, 11:30am, Dennis Bollweg• Precise data will come from CBM@FAIR,MPD@NICA, HIAF, and JPARC-HI forlarge μB region.
2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

522022 Yagi Award
https://ithems.riken.jp/en/about/yagi-award“Kohsuke Yagi Quark Matter Award” (Yagi Award) isbased on the donation to iTHEMS from bereaved familyof late Professor Kohsuke Yagi who was a renowned
Japanese nuclear physicist. Responding to the family
request, the award aims to support early career scientists
with Japanese nationality, to promote and expand
country's nuclear physics research field. It will beawarded to junior Japanese physicists under age of 40
who give plenary talk at the “Quark Matter: International
Conference on Ultra-relativistic Nucleus-Nucleus
Collisions” held in every 1.5 years.

2022/4/9, QM2022@Krakow

Prof. Kohsuke Yagi (1934-2014)
Quark Matter 1997, Chair

T. Nonaka "Fluctuations of Conserved Charges"

53

Acknowledgements
ShinIchi Esumi, Masakiyo Kitazawa, Ho-San Ko, Xiaofeng Luo,
Debasish Mallick, Bedangadas Mohanty, Risa Nishitani, Ashish
Pandav, Nu Xu, Yu Zhang (alphabetic), high-energy nuclear experiment group in University of Tsukuba, and all colleagues for interesting/important studies/papers in this field

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

54

Thank you for your attention

2022/4/9, QM2022@Krakow

T. Nonaka "Fluctuations of Conserved Charges"

55