Experimental Search for
QCD Phase Diagram

Toshihiro Nonaka
TCHoU member meeting 2020
Based on : arXiv:2001.02852 (STARCollaboration), submitted to Nature Physics

1Outline• Introduction• C4 measurement for critical point search• C6 measurement for crossover search• Future plan

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QCD phase diagram✓ Need to investigate the QCD phase structure in wide (μB,T) region.

- Crossover at μB = 0 MeV
Y. Aoki et al, Nature 443, 675(2006)- 1st-order phase transition at large
μ B?
- Critical point?

A. Bzdak et al, 1906.00936

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Beam Energy Scan
✓ Need to investigate the QCD phase structure in wide (μB,T) region.

- Crossover at μB = 0 MeV
Y. Aoki et al, Nature 443, 675(2006)- 1st-order phase transition at large
μ B?
- Critical point?

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Beam Energy Scan
✓ Need to investigate the QCD phase structure in wide (μB,T) region.
EEMC

Magnet

MTD

BEMC

TPC

TOF

iTPCEPD- Crossover at μB = 0 MeV
Y. Aoki et al, Nature 443, 675(2006)- 1st-order phase transition at large
μ B?
- Critical point?

HFT

STAR:
Has been a great experiment
Needs upgrades for the future
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Beam Energy Scan
✓ Need to investigate the QCD phase structure in wide (μB,T) region.

- Crossover at μB = 0 MeV
Y. Aoki et al, Nature 443, 675(2006)

20102014- 1st-order phase transition at large
μ B?
- Critical point?

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Higher-order fluctuations✦ Moments and cumulants are mathematical measures of “shape” of a distribution
which probe the fluctuation of observables.
✓✓

Moments: mean (M), standard deviation (σ), skewness (S) and kurtosis (κ).
S and κ are non-gaussian fluctuations.
skewness→asymmetry

κ>0kurtosis→sharpness

κ<0from wikipedia✓

Cumulant ⇄ Moment✓

Cumulant : additivity

proportional to volume

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Fluctuations of conserved quantities

PRL 105, 022302 (2010) :STAR Collaboration✦ Net baryon, net charge and net strangeness“Net” : positive - negative

No. of positively charged
particles in one collision

Fill in histograms
over many collisions

No. of negatively charged
particles in one collision(1) Sensitive to correlation length
59.5C5 =< ( N ) >c ⇡ ⇠612C6 =< ( N ) >c ⇡ ⇠→neutrons cannot be measured

M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009)
M. A. Stephanov, Phys. Rev. Lett. 107, 052301 (2011)
M︎Asakawa, S. Ejiri and M. Kitazawa, Phys. Rev. Lett. 103, 262301 (2009)(2) Direct comparison with susceptibilities.
M. Cheng et al, PRD 79, 074505 (2009)

M. Cheng et al, PRD 79, 074505 (2009)

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Net-proton multiplicity distributions✓ RAW distribution!

STAR Collaboration, arXiv:2001.02852, submitted to NP

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Efficiency correction✦ Efficiency follows binomial distribution.
✦ Factorial moments can be easily corrected.
- M. Kitazawa and M. Asakawa : PRC.86.069902 (2012)- A. Bzdak and V. Koch : PRC.86.044904 (2012), X. Luo : PRC.91.034907 (2016)- T. Nonaka, M. Kitazawa, S. Esumi : PRC.95.064912 (2017)
i kfik = "p "pbar Fik✦ Corrected cumulants are expressed in terms of measured factorial
moments and efficiency.
Measuredfactorial
momentTruefactorial
momentjust divideby efficiency

Measured
cumulant

True
cumulant

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C4/C2 for critical point searchSTAR Collaboration, arXiv:2001.02852, submitted to NP✓ κσ2 (C4/C2) shows a non-monotonic
behaviour. The trend is consistent
with the theoretical calculation.
✓ Enhancement at low beam energies
cannot be explained by baryon
number conservation.
!"

M.A. Stephanov, PRL107,052301 (2011)

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C4/C2 for critical point search

C4/C2✓ κσ2 (C4/C2) shows a non-monotonicbehaviour. The trend is consistent
with the theoretical calculation.
✓ Enhancement at low beam energies
cannot be explained by baryon
Shown in public since 2015
number conservation.
See : X. Luo, PoS CPOD2014 (2015) 019!"


M.A. Stephanov, PRL107,052301 (2011)

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C4/C2 for critical point searchSTAR Collaboration, arXiv:2001.02852, submitted to NP✓ κσ2 (C4/C2) shows a non-monotonicbehaviour. The trend is consistent
with the theoretical calculation.

✓ Enhancement at low beam energies
If efficiencies are not binomial,
theefficiency
correction
cannot be explained by baryon
method is no longer valid. number conservation.
- A. Bzdak et al : PRC.94.064907 (2016)!"✦Efficiencies are really binomial?
✦If not, how to correct?

σ model, M.A. Stephanov,PRL107, 052301 (2011)

T. Nonaka, TCHoU member meeting 202013Embedding simulation
T. Nonaka, NPA982 863-866 (2019)

EmbeddingBinomial
Beta-binomial✓ First results on detector
efficiency distributions,
reported in QM2018.
✓ Efficiencies follow betabinomial distribution.
✓ How much are final results
affected?

T. Nonaka, TCHoU member meeting 202014

Correction methods✓ Unfolding✓ Moment expansion method

S. Esumi and T. Nonaka, arXiv:2002.11253 (submitted to NIM)

T. Nonaka, M. Kitazawa, S. Esumi, NIM A906 10-17 (2018)C’) = C) + C.F_genrun MC
iterativelyD’)

NpbarC.F_gen = RMrev x C.F_rec

GeneratedcoordinateA) Exp. trueC) Sim. trueRMrev

Reconstructedcoordinate
C.F_rec = B) - D)B) Exp. meas

D) Sim. meas

Np

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Results✓ Results are consistent with those fromSTAR Collaboration, arXiv:2001.02852, submitted to NP binomial efficiency correction!
✓ STAR paper is in collaboration review..
Will be submitted to Nature Physics soon.

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C6/C2 for crossover search✓ There isn’t yet any direct experimental evidence for the smooth crossover at μB~0.
✓ C6/C2 < 0 is predicted at √sNN > 60 GeV.
✓ High-statistics data sets at √sNN = 54.4 and 200 GeV are analyzed to look for theexperimental signature of crossover transition.

A. Bazavov et al,
PhysRevD.95.054504 : LQCD

Friman et al, Eur. Phys. J. C (2011)
71:1694 : PQM model

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

negative signPredicted scenario for this measurementPositive sign is predicted in √sNN<60 GeV

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17Results
2200 GeV data taken in 2010 and 2011
54.4 GeV data taken in 2017

STAR Preliminary|y| < 0.5, 0.4< p (GeV/c) < 2.0T

1

C6/C 240-50%
0s NN = 54.4 GeV
s NN = 200 GeV

0-40%

UrQMD, s NN = 54.4 GeVUrQMD, s NN = 200 GeV−2LQCD, PRD.95.054504, (T = 160 MeV, µ = 0 MeV)B

C6/C2<0 at 200 GeV central
collisions could be an
experimental indication ofsmooth crossover at small μB.

LQCD, JHEP.10.205, (T = 160 MeV, µ = 0 MeV)
B

050

100〈Npart〉

T. Nonaka, QM2019

T. Nonaka, TCHoU member meeting 202018

Comparison with LQCD
✓ Consistent withLQCD for 3rd and 4th
net-proton(baryon)
fluctuations

Bazavov et al., Phys. Rev. D 101,074502 (2020)

T. Nonaka, TCHoU member meeting 202019

Comparison with LQCD
✓ C6/C2 < 0 is predictedfor √sNN > 39 GeV

Bazavov et al., Phys. Rev. D 101,074502 (2020)

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Acceptance dependence

Fluctuation✓ Which acceptance should be compared with LQCD calculations?
✓ Fluctuations should have minimum/maximum somewhere in acceptance size.

Poisson limit
104π limit?
Acceptance size
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Acceptance dependence at 200 GeV✓ Wide acceptance is crucial for fluctuation measurements!
p dependence, |y| < 0.5

Rapidity dependence, 0.4 < p < 2.0 (GeV/c)T1

100−1−2−3STAR PreliminarysNN = 200 GeV|y| < 0.1|y| < 0.2|y| < 0.3|y| < 0.4|y| < 0.5C6/C 2

C6/C 2T−1Net-Proton−2−3

0.4 < p < 0.8 GeV/c
T
0.4 < p < 1.1 GeV/c
T
0.4 < p < 1.4 GeV/c
T
0.4 < p < 1.7 GeV/c
T
0.4 < p < 2.0 GeV/c
T−4〈Npart〉

102−4〈Npart〉

102

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Future Plan
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2019-2021 : BES-II at RHIC
Au + Au Collisions at RHIC
0-5% centrality|y| < 0.5, 0.4 < pT < 2 (GeV/c)

4HighCMoments
gm/C422STAR Preliminary✓ Need to shrink the errors at low energies.
✓ BES-II has started this year.
✓ Map the QCD phase diagram 200 < μB < 420
MeVnet-protonanti-proton

3protonBES-II error for net-p
UrQMD

21025

102050100200Colliding Energy 3sNN (GeV)

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Beyond BES-II
Au + Au Collisions at RHIC
0-5% centrality|y| < 0.5, 0.4 < pT < 2 (GeV/c)

4High CMoments
4/C2 gm

2STAR Preliminary
net-protonanti-proton

3✓ Statistical uncertainties will bedramatically reduced.
✓ Can we measure a possible“peak” structure?

protonBES-II error for net-p
UrQMD

2

M.A. Stephanov, PRL107,052301 (2011)

1025102050

100200Colliding Energy 3sNN (GeV)
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FXT@STAR

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Beyond BES-II
Au + Au Collisions at RHIC
0-5% centrality|y| < 0.5, 0.4 < pT < 2 (GeV/c)

4STAR Preliminary

2High CMoments
4/C2 gm✓ Fixed-target experiment is alsoongoing.

net-protonanti-proton

3protonBES-II error for net-pUrQMD

21025102050100200

Colliding Energy 3sNN (GeV)
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Beyond BES-IIμB (MeV)
7106105103102✓ High beam intensity facilities
coming in 5~10 years

20Heavy Ion CollisionInteraction Rates (Hz)- CBM @FAIR (Germany)

FAIR SIS100 2025
HIAF 2025
HADESALICENICA 2023

sPHENIXSTAR FXT

Collider104200JPARC-HI

Fixed-Target

10400

STAR BES-II 2019 - 2021

10110//nxu/STAR/BE-II LoI/01nxu/kinematics/ratesvsenergy_hi_08Aug2018.kumac

108750- MPD @NICA (Russia)- HIAF (China)- JPARC-HI (Japan)✓ Huge statistics for critical pointsearch using higher orderfluctuations.

100Collision Energy 3sNN (GeV)
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Summary•

Higher-order fluctuations of net-particle distributions to search
for the QCD phase structure•

Non-monotonic beam energy dependence of C4/C2•

Negative value of C6/C2 at √sNN = 200 GeV central collisions•Future FXT experiments at √sNN < 10 GeV with higher beamintensity

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29Thank you for your attention

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