Measurement of sixth order cumulantof net-proton multiplicity distribution
in Au+Au collisions at √sNN = 200 GeV
with the STAR detector
CiRfSE workshop
Jan. 25, 2017
Toshihiro Nonaka

Motivation✓ Lattice calculations predict a “smooth crossover” at μB=0.
Y. Aoki, Nature 443, 675(2006)✓ Theoretically sixth order cumulant of net-baryon and net-charge
fluctuation change sign near the chiral phase transition.
Friman et al, Eur. Phys. J. C (2011) 71:1694✓ Find the evidence for crossover with measurement of the sixthorder cumulant of net-proton multiplicity distribution.

✦ Can we observe thenegative value?

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

CiRfSE workshop, T. Nonaka2

STAR results✓ The STAR experiment measured C6/C2 at 0.4<pT<0.8 GeV/c without
efficiency correction at √sNN=200GeV of Run10 datasets (~240M events).
L. Chen (STAR collabration), NPA 904-905(2013)✓ Event statistics are very important for higher orders.
✓ We focus on √sNN=200GeV at Run10 and Run11 datasets which have
~500M and ~250M events, and measure C6/C2 at 0.4<pT<2.0 GeV/c withefficiency correction.

→ Run10, √sNN=200GeV, eff.uncorr
L. Chen (STAR collabration),
NPA 904-905(2013)

CiRfSE workshop, T. Nonaka

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Higher order fluctuation✦ Moments and Cumulants are mathematical measures of “shape”
of a histogram which probe the fluctuation of observables.
✓✓

Moments : Mean(M), sigma(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

Volume dependence
CiRfSE workshop, T. Nonaka

4Fluctuations of conserved quantities✦ 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→neutrons cannot be measured(2) Direct comparison with susceptibilities.
M. Cheng et al, PRD 79, 074505 (2009)

Volume dependence can be canceled by taking ratio.
CiRfSE workshop, T. Nonaka

5Event and track selection✓ DatasetAu+Au, √sNN=200GeV, mb trigger,
Run10 and Run11✓ Event selection|Vz|<30cm, |Vr|<2cm, |VpdVz-Vz|<3cm
Pileup rejection from tofmatched vs refmult✓ Track selection
DCA<1cm, nHitsFit>20,
nHitsFit/nFitPoss>0.52, nHitsDedx>5,|y|<0.5
PID cut
0.4<pT<0.8 : |nσproton|<20.8<pT<2.0 : |nσproton|<2 && 0.6<m2<1.2
CiRfSE workshop, T. Nonaka

6Analysis techniques
1. Centrality determination

χ2/NDF=1.9

Use charged particles except protons in order toavoid the auto correlation.
Analysis : |y|<0.5, p and pbar

DataGlauber

Centrality : |η|<1.0, exclude p and pbar

2. Centrality Bin Width Correction

Refmult3

Calculate cumulants at each multiplicity bin inorder to suppress the volume fluctuation.
X.Luo et al. J. Phys.G40,105104(2013)

3. Statistical error calculation : Bootstrap✓ Bootstrap✓ Delta theorem

4. Efficiency correction
B. Efron,R. Tibshirani, An introduction to the bootstrap,
Chapman & Hall (1993).

CiRfSE workshop, T. Nonaka7

Efficiency correction✓ Based on the assumption of binomial efficiency.
A.Bzdak and V. Koch PRC.86.044904

M.Kitazawa PRC.86.024904✓ Simple relationship between measured and true factorial moments.

✓ It can be extended to the case of multi-number of phase spaces.
A.Bzdak and V. Koch PRC.91.027901
X. Luo PRC.91.034907

CiRfSE workshop, T. Nonaka

8Calculation cost
✓ Efficiency drops at pT = 0.8 Gev/c region where TOF is included inproton identification.
✓ The number of efficiency bin is four. (p and pbar, low and high pT)✓ Calculation cost become ~4 times larger than fourth order.

• # of terms to be calculated per event for

0-5%•efficiency correction
increase by power of efficiency bins

C4C62+2225

784

4+44900

44100(GeV/c)CiRfSE workshop, T. Nonaka

9New development✦ M.Kitazawa and I developed a new correction formula via factorial cumulants,
which can drastically reduce the calculation time.
✦ It has been checked that the formulas below give exactly the same value with
Bzdak-Koch.
✦ About ~2000 times faster than usual Bzdak-Koch formulas in the case of 8bins.
Loops just increase with efficiency bin

Nonaka, Kitazawa, Esumi : paper in preparation
CiRfSE workshop, T. Nonaka

10Analytical calculation✓ Assume two distribution that have exactly the same shape (Cm) but
different efficiencies.
✓ Efficiency correction using averaged efficiency does not give a correct
value for any probability distributions other than Poisson.

Poisson : C1 = C2 = C3…. = Cm
→ ΔKm = 0

✓ Gaussian (Cm=0, m>=3)✓ Poisson — 5% deviation

Nonaka, Kitazawa, Esumi : paper in preparation

CiRfSE workshop, T. Nonaka

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pT integrated efficiency

PRL. 97. 152301 (2006)✦ Integrated using corrected pT spectra.
✦ One can obtain efficiency vs centrality.
✦ Translate centrality into <refmult3>.

pol3 fit

pol1 fit|y|<0.5

CiRfSE workshop, T. Nonaka

12phi dependent efficiency✦ TPC sectors are divided into 3 regions, dead, bad and good sectors.
✦ pT integrated efficiencies are calculated for each case.
→ Dead→ Bad→ GoodEfficiency

protonΦ

Efficiency

antiprotonΦ0.4<pT<2.0 GeV/cyCiRfSE workshop, T. Nonaka

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Acceptance dependence✦ pT and rapidity dependence at central collisions of C4/C2 and C6/C2✦ Large errors exist for C6/C2. More statistics are necessary.
0.4 < pT < 2.0 (GeV/c)

C6/C2C4/C2|y| < 0.5

systematic uncertainties
are understudy
0.4 < pT < X (GeV/c)|y| < X

CiRfSE workshop, T. Nonaka

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Centrality dependence✦ Central trigger is used for Run10 results at 0-10%.
✦ Other points are from minimum bias trigger.
✦ All the results except 40-50% (~3sigma) are consistent within
1~2sigma between Run10 and Run11.
√sNN = 200 GeV, |y| < 0.5, 0.4 < pT < 2.0 (GeV/c)

Run10Run11

Run10+Run110-10%systematic uncertainties
are understudy
CiRfSE workshop, T. Nonaka

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Comparison with theory✦ Lattice results predict -1~0.5 for C6/C2 at √sNN=200GeV (~166MeV)✦ Large errors exist for experiment and theory.
Run10+Run11

arXiv:1701.04325|y| < 0.5, 0.4 < pT < 2.0 (GeV/c)~166 MeV(√sNN = 200GeV)

More statistics are needed !!
CiRfSE workshop, T. Nonaka

16Summary and Outlook✓ Development of more efficient formulas forefficiency correction up to sixth order cumulant.
✓ C6/C2 of net-proton multiplicity distribution has

been measured in Au+Au collisions at √sNN =200 GeV.
✓ Use more Au+Au data.

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