ゆらぎで探る原子核物質の相図
原子核実験グループ 野中俊宏

2024/7/2

T. Nonaka, TCHoU member meeting1Outline• Introduction• Methodology• Experimental results• Net-proton 4th-order fluctuations from BES-I• New results from BES-II (A. Pandav, CPOD2024)• Summary

2024/7/2

T. Nonaka, TCHoU member meeting2Introduction
BES, STAR, Cumulant

2024/7/2

T. Nonaka, TCHoU member meeting3

“Conjectured” QCD phase diagram• Crossover at µB = 0 MeV• Y. Aoki et al, Nature 443,675(2006)• 1st-order phase transition at large µB?
• Critical point?

A. Bzdak et al, Phys.Rep.853 pp1-87 (2020)

2024/7/2

T. Nonaka, TCHoU member meeting4Beam Energy Scan Phase-I (BES-I)• Crossover at µB = 0 MeV• Y. Aoki et al, Nature 443,675(2006)• 1st-order phase transition at large µB?
• Critical point?
Fluctuations of conserved charges havebeen measured for BES-I data.

Complementary measurements at RHIC: BES-II, FXT (2019-2022)
2024/7/2

T. Nonaka, TCHoU member meeting5STAR detectors
FXT mode : μB=750 MeV @ 3GeV

2024/7/2

T. Nonaka, TCHoU member meeting6

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

2024/7/2

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

T. Nonaka, TCHoU member meeting7

Cumulants of conserved charges•

Measure event-by-event distributions of net-baryon,
net-charge, and net-strangeness number

STAR, 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
M.Cheng et al,
PRD79.074505(2009)2024/7/2

T. Nonaka, TCHoU member meeting8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• Initial 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)
A. Bzdak, V. Koch, V. Skokov, PRC87.014901(2013)

2024/7/2

T. Nonaka, TCHoU member meeting

9Methodology
Detector efficiency, Initial volume fluctuations, pileup corrections

2024/7/2

T. Nonaka, TCHoU member meeting10

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

STAR, PRL126.092301(2021), PRC104.024902(2021)
2024/7/2

T. Nonaka, TCHoU member meeting11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
2024/7/2

T. Nonaka, TCHoU member meeting12Impact parameter (b): 原子核の中心同士の距離
Npart: 衝突に参加した核子数
Nch: 生成粒子数

中心衝突度• ２つの原子核の重なり度合い。
• 中心（正面）衝突ほど多くの粒子が生成される。
• 生成粒子数分布を等分割して定義。

2024/7/2

T. Nonaka, TCHoU member meeting13

Initial volume fluctuation• Initial and final state variables are not one-to-one corresponding, which isreferred to as the initial volume fluctuations.
• How does it affect the cumulant measurements?

0-10%

UrQMD study fitted by
Glauber+two-component model

10-20%
20-30%

Npart

NpartT. Sugiura et al., PRC.100.044904(2019)2024/7/2T. Nonaka, TCHoU member meeting

14

Centrality Bin Width Correction (CBWC)
Centrality bin width for
cumulant calculations• Initial volume fluctuations can be partly
suppressed by CBWC.
X. Luo et al., J. Phys. G40.105104 (2013)• Purely data-driven, but cannot eliminate
initial volume fluctuations.
STAR, PRC.104.024902(2021)
2024/7/2

T. Nonaka, TCHoU member meeting15

Experimental results• 4th-order fluctuations from BES-I and BES-II

2024/7/2

T. Nonaka, TCHoU member meeting16Net-proton C4/C2
STAR, PRL126.092301(2021)

C4/C2

••
•

2024/7/2

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 noncritical baselines.
Qualitatively consistent with the model prediction
incorporating a critical point.

T. Nonaka, TCHoU member meeting17Collision energy dependence• 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 numberconservation.

2.4 GeV
3.0 GeV

HADES, PRC102.024914(2020)
STAR, PRL128.202303(2022), PRC107.024908(2023)
2024/7/2• The data implies that the QCD criticalregion could only exist at energies > 3GeV.

T. Nonaka, TCHoU member meeting18

BES-II datasets

2024/7/2

T. Nonaka, TCHoU member meeting19

Detector upgrades

2024/7/2

T. Nonaka, TCHoU member meeting20Centrality

2024/7/2

T. Nonaka, TCHoU member meeting21New results from BES-II

2024/7/2

T. Nonaka, TCHoU member meeting22Effect of centrality resolution

2024/7/2

T. Nonaka, TCHoU member meeting23Model comparison

2024/7/2

T. Nonaka, TCHoU member meeting24Summary• Net-proton C4/C2 (BES-II) significant deviation from model
expectations at ~20 GeV. Theoretical input is needed forinterpretation.
• Results from FXT (3.3<√sNN<4.5 GeV) will come in near future.

2024/7/2

T. Nonaka, TCHoU member meeting25Thank you for your attention

2024/7/2

T. Nonaka, TCHoU member meeting26

Detector efficiency for neutrons• Reconstruction efficiency for neutrons
is varied to see the statisticaluncertainties after efficiency correction.
• Statistical uncertainties for C4 and C6
drastically increase below <20%efficiency.
• More detailed requirement should bedetermined based on the required
precision on final results and event
statistics.

2024/7/2

T. Nonaka, TCHoU member meeting46