TCHoU Workshop (Quark-Nuclear Matters)

Fluctuation analysis in STAR BES-IIFan Si (司凡)University of Science and Technology of China
University of Tsukuba
March 29, 2024

Outline◦Introduction◦STAR BES and results◦Upgrades in BES-II◦Challenges in FXT◦Summary

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Introduction: QCD phase structure◦ Crossover at μB = 0◦ Expected by lattice QCD◦ T = (156 ± 1.5) MeV◦ 1st-order phase transition◦ At higher μB◦ Expected by QCD-based model◦ QCD critical point? Predicted!
◦ Existence and possible location◦ Experimental scan of QCD phase diagram◦ By varying collision energy sNN
STAR and CBM, arXiv:1609.05102; Y. Aoki, Nature 443, 675-678 (2006); HotQCD, PLB 795, 15-21 (2019)

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

3Introduction: experimental observables◦ Higher-order cumulants of net-particle multiplicities◦ Proxies for conserved charges (B, Q, S)◦ 𝜇𝑟 = 𝑁 − 𝑁 𝑟 : rth-order central moment𝑞= 𝑉𝑇 3 𝜒1
◦ 𝐶1 = 𝑀 = 𝑁3𝜒𝑞
22=𝑉𝑇
𝐶=𝜎=𝜇~𝜉◦ 222𝑞= 𝑉𝑇 3 𝜒3 ~ 𝜉 4.5◦ 𝐶3 = 𝑆𝜎 3 = 𝜇3𝑞= 𝑉𝑇 3 𝜒4 ~ 𝜉 7◦ 𝐶4 = 𝜅𝜎 4 = 𝜇4 − 3𝜇22𝑞= 𝑉𝑇 3 𝜒5 ~ 𝜉 9.5= 𝜇5 − 10𝜇3 𝜇2◦ 𝐶5𝑞◦ 𝐶6 = 𝜇6 − 15𝜇4 𝜇2 − 10𝜇32 + 30𝜇23 = 𝑉𝑇 3 𝜒6 ~ 𝜉12◦ Sensitive to correlation length (ξ)

Skewness S = μ3/σ3 → asymmetry

Gaussian: Cr = 0 (r > 2)
Skellam (Poisson − Poisson):
C3/C1 = C4/C2 = C5/C1 = C6/C2 = 1
Kurtosis κ = μ4/σ4 − 3 → sharpness𝑞◦ Directly connected to susceptibilities (𝜒𝑟 , q = B, Q, S)
𝑞◦𝐶3𝑞𝐶2𝑞= 𝑆𝜎 =𝑞

𝜒3 𝐶4𝑞𝜒2,𝑞𝐶2

Fan Si (USTC / Tsukuba)= 𝜅𝜎 2 =𝑞

𝜒4𝑞
𝜒2

κ>0
κ<0M. A. Stephanov, PRL 102, 032301 (2009)
M. Asakawa et al., PRL103, 262301 (2009)
M. A. Stephanov, PRL107, 052301 (2011)

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Introduction: predicted signals◦ Critical point◦ Crossover◦ Non-monotonic energy dependence◦ Negative C5 and C6of C4/C2 around baseline M. A. Stephanov, PRL 107, 052301 (2011)
A. Bzdak et al., Phys. Rept. 853, 1-87 (2020)

FRG
R51 = C5/C1
W.-j. Fu et al.,
PRD 104, 094047 (2021)

R62 = C6/C2

Lattice QCD

HotQCD,
PRD 101, 074502 (2020)

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Beam Energy Scan program◦ To map QCD phase diagram: BES-I 2010 – 2017; BES-II (including FXT) 2018 – 2021
sNN
(GeV)

# Events

Year 20xx(BES-I/II)

μB
(MeV)

sNN
(GeV)

# Events

Year 20xx(FXT)

μB
(MeV)

200

238M/138M/20B

10/19/23–2525

13.7

51M

21276

62.4

47M

1073

11.5

52M

21315

54.4

550M

1783

9.2

54M

21373

3986M

10112

7.7

51M/112M

19/20

420

2730M/555M

11/18

156

7.2

155M/317M/89M

18/20/21

440

19.6

15M/478M

11/19

206

6.2

118M

20

487

17.3

256M

21

230

5.2

103M

20541

14.6

324M

19262

4.5

108M

20

589

14.5

20M

14264

3.9

53M/117M

19/20

633

11.5

6.6M/235M

10/20

315

3.5

116M

20

666

9.2

162M

20373

3.2

201M

19699

7.7

3M/101M

10/21

420

3.0

258M/2.1B

18/21

720Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

6STAR detector system◦ Large acceptance◦ Excellent PID◦ Uniform efficiency◦ Upgraded since 2018

FXT setup◦ iTPC, eTOF, EPD

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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STAR published measurements (BES-I)◦ Non-monotonic energy dependence (3.1σ)◦ Qualitatively consistent with prediction
considering critical point◦ Deviates from non-critical models◦ Significant suppression at sNN = 3.0 GeV◦ Reproduced by UrQMD model(baryon-conservation driven)◦ Predominantly hadronic matter◦ Critical region could only
exist at sNN > 3.0 GeV
if created in HIC
Fan Si (USTC / Tsukuba)

STAR, PRL 126, 092301 (2021)
STAR, PRC 104, 024902 (2021)
STAR, PRL 128, 202303 (2022)
STAR, PRC 107, 024908 (2023)

TCHoU Workshop (Quark-Nuclear Matters)

8STAR published measurements (BES-I)
Rij = Ci/Cj
Lattice QCD

HotQCD, PRD 101, 074502 (2020)◦ C5/C1 (0-40% at sNN = 7.7 – 200 GeV) fluctuates around zero at all energies◦ Increasingly negative C6/C2 (0-40%) as collision energy sNN decreases down to 7.7 GeV◦ Trend consistent with LQCD calculation (UrQMD always positive or ~ 0)

◦ Positive C5/C1 & C6/C2 at 3.0 GeV, obviously different trend
Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

STAR, PRL 130, 082301 (2023)

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Upgrades in BES-II: energies and statistics
BES-II energies◦ Many new energies◦ From 3 to 27 GeV◦ Fine scan of μB◦ Much higher statistics◦ Smaller uncertainties expected in BES-II◦ Precision measurement for C4 and even higher orders
STAR Beam Use Request SN0773, SN0793

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Hyper-order cumulants: search for crossover◦ Hyper-order cumulants C5 – C8
◦ Sensitive to crossover◦ Vulnerable to backgrounds◦ Hungry for statistics◦ 2.1B events at sNN = 3.0 GeV (2021)◦ 20B events at sNN = 200 GeV (2023–2025)◦ May have precision measurements
in BES-IISTAR talk, sQM 2022
W.-j. Fu et al. PRD 104, 094047 (2021)

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Upgrades in BES-II: new detectors◦ iTPC (since 2019)◦ eTOF (since 2019)◦ Improves dE/dx measurement◦ Extends ηmax from 1.0 to 1.5◦ Forward rapidity coverage◦ Lowers pT cut-in from 125 to 60
MeV/c◦ For FXT, 1.52 < η < 2.24

◦ For FXT, ηmax from 2.0 to 2.5◦ Crucial in fixed-target program◦ PID at 1.05 < η < 1.50
◦ Provided by FAIR-CBM◦ EPD (since 2018)◦ 2.14 < |η| < 5.09
◦ Improves trigger◦ Better event plane reconstruction◦ Better centrality determination

iTPC: https://drupal.star.bnl.gov/STAR/starnotes/public/sn0619
eTOF: STAR and CBM eTOF Group, arXiv:1609.05102
EPD: J. Adams et al., NIMA 968, 163970 (2020)

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Proton acceptance plots in FXT mode
◦ Standard analysis window(red box)◦ 0.4 GeV/c < pT < 2 GeV/c◦ −0.5 < y < 0◦ TOF is required at highmomenta where proton
purity < 90%◦ Nearly full acceptanceat sNN up to 4.5 GeV◦ Limited mid-rapidity coverage at higher energies

STAR poster, QM 2023

◦ Crucial eTOF for proton identification at sNN from 3.5 GeV
Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Upgrades in BES-II: larger acceptance◦ For FXT sNN = 3.0 GeV in 2018 (published)(2018)◦ No iTPC installed◦ TPC coverage: −2.0 < ηlab < 0◦ Proton acceptance: −0.5 < y < 0◦ For FXT since 2019 (analysis ongoing)◦ Both iTPC and eTOF are installed◦ TPC including iTPC: −2.5 < ηlab < 0◦ For FXT sNN = 3.0 GeV in 2021 (2.1B events)Center-of-mass rapidity◦ Only half mid-rapidity window coveredbTOF

TPC◦ Possible proton measurement within −0.5 < y < 0.5◦ Red curve: expected acceptance boundary with iTPC and eTOF
STAR Beam Use Request SN0755

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Comparison between half/full mid-rapidity◦ From models for 3.0 GeV, clear
difference between calculations inhalf and full mid-rapidity windows◦ Necessary to learn the difference
between −0.5 < y < 0 and |y| < 0.5
in experiments
C4/C2Data (−0.5 < y < 0)

~ −1

UrQMD (−0.5 < y < 0)

~ −1

UrQMD (|y| < 0.5)

~ −4

Hydro (−0.5 < y < 0)~1

Hydro (|y| < 0.5)

~0Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

STAR, PRC 107, 024908 (2023)

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Upgrades in BES-II: larger acceptance◦ Acceptance is much larger thanks to iTPC

◦ Proton rapidity extension◦ |y| < 0.5 in BES-I, 0.7 may be available in BES-II◦ To observe correlations in larger system size

◦ Rapidity scan◦ Sensitive probe for critical region◦ Detailed scan for the QCD phase diagram

J. Brewer et al., PRC 98, 061901 (2018)

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

rapidity16

Upgrades in BES-II: better centrality resolution◦ For net-proton fluctuation measurements, centrality is determined by the reference
multiplicity excluding (anti)protons◦ To avoid auto-correlation◦ In BES-I, multiplicity (called RefMult3) is defined by π± and K± within |η| < 1.0◦ With the extended acceptance, RefMult3X is defined by π± and K± within |η| < 1.6◦ Better centrality resolution => smaller volume fluctuation => contribution to cumulants◦ Effect should be checked both in experiments and models

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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UrQMD simulation: volume fluctuation effect◦ Npart is a characterization of the system volume◦ Effect of volume fluctuation

STAR, PRC 107, 024908 (2023)◦ The centrality by reference multiplicity selects different events from the centrality by Npart◦ Npart varies even in each reference multiplicity bin
Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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UrQMD simulation: centrality resolution effectsNN = 7.7 GeV
0.4 < pT (GeV/c) < 2.0|y| < 0.5◦ Centrality resolution from worst to best: ○ < ● < □ < ■◦ Clear ordering: better resolution => lower cumulants/ratios (except C4/C2 at 0-5%)◦ Comparisons needed in experimental measurements
Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Challenges in FXT: pileup and timing issue◦ Pileup events: formed by multiple collisions in a short time (not separated by detector)◦ Higher pileup fraction in FXT than collider experiments◦ TOF has better timing precision and is faster than TPC◦ TPC reconstructs tracks from pileup events,
but TOF often misses them due to timing offset◦ TPC multiplicity for centrality◦ TPC+TOF for proton ID◦ A tail on the left-hand sideof proton number distribution
in central events
STAR talk, DNP 2023

Fan Si (USTC / Tsukuba)

0-5% centrality (TPC)(TPC+TOF)
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UrQMD simulation: pileup and timing issue◦ In experiments, we require TOF PID for tracks above a certain momentum◦ In UrQMD, we simulate pileup process and TOF PID◦ Instability of cumulants observed during variation of momentum threshold for TOF PID◦ Pileup events should be
carefully rejected if werequire TOF for PID

STAR talk, DNP 2023

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Challenges in FXT: η gap between b/eTOF◦ An acceptance gap between bTOF and eTOF
◦ 1.45 ≲ ηlab ≲ 1.55
◦ No TOF available for PID

Proton acceptance(pT – ylab) in FXT◦ Solutions◦ Check TPC proton purity in the gap◦ Test removing the gap from the acceptance◦ Model studies also needed for the effectSTAR and CBM, arXiv:1609.05102

Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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Summary◦ In BES-II, STAR has collected lots of data from sNN = 3.0 to 27 GeV◦ FXT mode: 3.0 – 13.7 GeV; collider mode: 7.7 – 27 GeV◦ Several upgrades in BES-II◦ New energies: 3.2 – 7.2, 9.2, 17.3 GeV; much higher statistics◦ New detectors, larger acceptance, and better centrality resolution◦ A few challenges in FXT◦ BES-II fluctuation measurements are ongoing.

Thank you for your attention!
Fan Si (USTC / Tsukuba)

TCHoU Workshop (Quark-Nuclear Matters)

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