+2@(a) @(b) @(cde) + ...(10 combs)+@(a) @(bc) @(de) + ...(15 combs)
6@(a) @(bcde) + ...(5 combs)
2@(ab) @(cde) + ...(10 combs)+24@(abcde) ,Measurement of Sixth Cumulant of the Net-Proton
Multiplicity Distributions in Au+Au Collisions at√sNN = 200 GeV at the STAR Experiment(47)@ (a) @ (b) @ (c) @ (d) @ (e) @ (f ) = @(a) @(b) @(c) @(d) @(e) @(f )@(a) @(b) @(c) @(d) @(ef ) + ...(45 combs)+2@(a) @(b) @(c) @(def ) + ...(20 combs)
6@(a) @(b) @(cdef ) + ...(15 combs)
2@(a) @(bc) @(def ) + ...(60 combs)
92
show
thefinal+formulas
up to the sixth order as follows:@We@@...(15combs)(ab) (cd) (ef )+4@(abc) @(def ) + ...(10 combs)+6@(ab) @(cdef ) + ...(15 combs)+24@(a) @(bcdef ) + ...(6 combs)
120@(abcdefLattice QCD calculation predicts the phase transition at small μB is the smooth crossover.
Experimentally,
however, there is still no(48)direct evidence for).

Toshihiro Nonaka, for the STAR Collaboration
University of Tsukuba, CiRfSE⌦↵= willhq(1,1) ibec,the phase transition. The sixth order cumulant (C6) is predicted to probe the phase transition, Qthat
negative at the phase transition. In thisc
We define thelinear combinations
over all has
the acceptanceas⌦ 2at↵ theposter, the sixth order cumulant (C6) of net-proton
multiplicity
distribution
been measured
2 extended pT region (0.4 < pT < 2.0 GeV/c) withQ c = hq(1,1)
ic + hq(2,1) ic hq(2,2) ic ,efficiency correction in Au+Au collisions in √sNN = 200 GeV. Centrality, pT and rapidity
dependenceofC/C
arepresented.
62
⌦ ↵M
M87

Motivation

Smooth crossover at small μB
predicted by Lattice QCD

Q(a) ⌘89

Experimentally no evidence forthe phase transition

3X
Q3 c = hq(1,1)
ic + 2hq(3,3) ic
ai Ni , q(a) ⌘a i ni ,3hq(1,1) q(2,2) ic + hq(3,1) ic + 3hq(1,1) q(2,1) ic

3hq(3,2) ic ,(49)422qEfficiency correction
Q c = hq(1,1)
ic 6hq(1,1)
q(2,2) ic + 6hq(1,1)
q(2,1) ic+8hq
4hq(1,1) q(3,1) ic become
12hq(1,1) q(3,2)
ic 6hqby(1,1) q(3,3) ic +(2,2) qpower(2,1) ic•
Calculation
costforefficiency
correction
largeofwhere Ni and ni are the number of produced and measured particles at the 2ith acceptance,andaistheelectrici
2+3hq(2,2) ic + 3hq(2,1)
ic 6hq(4,4) ic + hq(4,1) ic 7hq(4,2) ic + 12hq(4,3) ic ,charge. Then we proceed similar procedures as showninEqs.
(27)
and(28).
efficiency bins with formulas based on the factorial moments (Bzdak⌦ 5↵533sixth order 2cumulant. 2and Koch, 2016),forQ cwhich= hq(1,1)
icis crucial
10hq(1,1)q(2,2)
ic +the10hq(1,1)q(2,1) ic + 20hq(1,1) q(3,3) ic + 15hq(2,2) q(1,1) ic
hQ(a) ic = hQ(a) ifc = hq(a/p) ifc = hq(a/p) ic ,(50)222+10hqEsumi
30hq(1,1) q(3,2)aic +15hq(2,1)
q(1,1) ic•Nonaka,
Kitazawa
andnewefficiency
correction.
c(1,1) q(3,1) ideveloped
2hQ2(a) ic = hQ2(a) ifc + hQ(a ) ifc = hq(a/p)
ifc + hq(a /p) ifc
30hq(1,1) q(2,1) q(2,2) ic 30hq(1,1) q(4,4) ic 20hq(2,2) q(3,3) ic + 5hq(1,1) q(4,1) ic
Calculation
cost
increases
linearlywith
thenumberofefficiencybins.
235hq(1,1) q(4,2) ic 10hq(2,2) q(3,1) ic + 60hq(1,1) q(51)(4,3) ic + 20hq(2,1) q(3,3) ic= hq(a/p)
ic hq(a /p ) ic + hq(a /p) ic ,•Inadditiontothepdependence,
acceptancenon-uniformityinphi+30hq
qi30hq
qi+10hq
q
i
T
ccc
(2,2)
(3,2)
(2,1)
(3,2)
(2,1)
(3,1)
3
hQ3(a) ic = hQ3(a) ifc + 3hQ(a) Q(a ) ifc + hQ(a ) ifc = hq(a/p)
ifc + 3hq(a/p)
q(a /p)i ifc 60hq
+ hq(a i/p)+i50hq
fc+24hq
15hq(5,2) ic + hq(5,1) ic ,c(5,5)(5,4) c(5,3) ic
direction
arecorrected.
3K. Fukushima and T. Hatsuda, Rept. Prog.
Phys. 74, 014001(2011)88X

1i=1⌦ 4↵
i=1

2

222

2

2= hq(a/p) ic

33

23hq(a/p) q(a2 /p2 ) ic + 2hq(a3 /p3 ) ic + 3 hq⌦ (a/p)
q 2 i↵ (a /p) c

Friman et al, Eur. Phys. J. C (2011)
Eur.orPhys.
J. C (2011) 71:1694
C6 < 0 (net-baryonnet-charge)
71:1694

6Q6 c = hq(1,1)
ichq(a3 /p2 ) ic + hq(a3 /p) i.

4415hq(1,1)
q(2,2) ic + 15hq(1,1)
q(2,1) ic

290hq(1,1)
q(2,2) q(2,1) ic(52)

32 7 of2 113Page+40hq(1,1)
q(3,3) ic + 45hqqi+20hqc(2,2) (1,1)(1,1) q(3,1) ic

360hq(1,1)
q(3,2) ic

2
223
M : # of efficiency bins
predicted at the phase transition+45hq(1,1)
q(2,1)
ic 90hq(1,1)
q(4,4) ic 120hq(3,3) q(2,2) q(1,1) ic 15hq(2,2)
ic
At the first qualities we used Eqs. (37)–(39), andn for
third qualities Eqs. (43)–(45) are used. For simplicity, we: # ofthe
particles
22+15hq
q
i60hq
q
q
i60hq
q(4,2) ic
cc
(4,1)
(1,1)
(2,2)
(3,1)
(1,1)
(1,1)
definethefollowing
expression.
C6p:
efficiency
6 → Cumulant ratio directly
22=+120hq(1,1) q(2,1) q(3,3) ic + 180hq(1,1)
q(4,3) ic + 45hq(2,2)
q(2,1) ic
a : electric charge
C2
2 connected to the susceptibilityM+180hqqqi45hq 2 qi45hq 2 qi
9091q(r,s) ⌘X arini .
spi=1 i(1,1) (2,2) (3,2) c(1,1) (4,2) c(2,1) (2,2) c

180hq(1,1) q(2,1) q(3,2) ic + 60hq(1,1) q(2,1) q(3,1) ic (53)
+ 15hq(2,1) ic

2+144hq(5,5) q(1,1) ic + 90hq(4,4) q(2,2) ic + 40hq(3,3)
ic + 6hq(5,1) q(1,1) ic

2→ Nonaka, Kitazawa andC6/C2 of net-proton distribution is+15hq(4,1) q(2,1) ic + 10hq(3,1)
ic 30hq(5,2) q(1,1) ic 15hq(4,1) q(2,2) ic
Esumi : in preparation+300hq(5,3) q(1,1) ic + 40hq(3,3) q(3,1) ic + 60hq(4,2) q(2,2) ic 360hq(5,4) q(1,1) ic
measured at √sNN = 200 GeV with90hq(4,4) q(2,1) ic 120hq(3,3) q(3,2) ic 180hq(4,3) q(2,2) ic
STAR detector to find the2+180hq(4,3) q(2,1) ic + 45hq(4,2) q(2,2) ic + 90hq(3,2)
ic
New Net-proton Analysis: Larger pT Acceptance
evidence of the phase transition
60hq(3,2) q(3,1) ic 60hq(4,2) q(2,1) ic 60hq(5,2) q(1,1) ic 45hq(4,2) q(2,1) ic390hq(6,4) ic + 180hq(6,3) ic 31hq(6,2) ic + hq(6,1) ic .
TOFLarger
is used forp/pbar in addition with TPC to extend the pT 120hq
coverage.
(6,6) ic + 360hq(6,5) ic
New Net-proton Analysis:
pTIdentify
AcceptanceFig. 5 The temperature dependence of the fourth, sixth and eighthcrossover temperature. The shaded area indicates the region of the chiB relative tocumulants
ofthenetbaryon
numberfluctuations
χral crossover transition at µq /T = 0. The calculations were done in theTOF
is usedorderfor Identify
p/pbarinaddition
with
TPC
to
extendAnalysistechniques
X. Luo and N. Xu, arXiv: 1701.02105 n the pT coverage.
the second order one. The temperature is given in units of the chiral
PQM model within
the FRG
Au+Au#approachprotons

Results400

qProton identification
0.4 < pT < 2.0 (GeV/c)|y| < 0.5
Au+Au # protons
11• Large and uniform acceptance with full azimuthal angles with |η|<1.0Ø (Right plot) pT and rapidity• At low pT region (0.4 < pT < 0.8 GeV/c) dE/dx measured by TPC is used.
Cumulants for P(NC) are
expressed
in terms of (mixed) cumulants of q. Since q is the linear combination for adependenceof/Cand
4 Eq.2 (53), the calculation cost is drastically reduced compared to the formulas proposed200
acceptance as shown in• At high pTNew
region(0.8 < pT < 2.0GeV/c) combinedwith TOF isNet-proton
Analysis:
Larger PID
pT Acceptance
0.8
0.8
TOF
weconsidered
above
thecaseofefficiency
correction
tothecumulantsof net-particle distribution withC6/CThoughatcentralcollisions.
2efficiency bins, exactly the same discussions can be applied to the efficiency correction on mixed cumulants
implemented.
TOF
probe correlations between di↵erent conserved quantities, e.g, net-baryon and net-strangeness, net-strangenes
TOF is used for Identify p/pbar in addition with TPC to extend the p coverage.
C4/C293
94
95

TOF

TOF96T

9798

TPC

TPC

Au+AuTPC
# protons⌦↵
0-5%
0net-charge, and so on. Below we show efficiency correction formulas for mixed cumulants
Q Q up to fourth
5-10%

0.6

Ø (Bottom plot)
TPCMerged resultofcentrality dependence of−200
C6/C2 between Run10 and 40
Run11.
20−400i
X

0.60-5%, eff.uncor
5-10%, eff.uncor

Run10 central trigger
11.5

jY

2

40

0.1

0.2

0.3

0.4

0.5

20

C6/C2

Acceptance:|y|≤0.5,0.4≤p≤2GeV/cT
Acceptance: |y| ≤ 0.5, TOF
0.4 ≤ pT ≤ 2 GeV/c0ü
Usedstatistics
Efficiency
corrections:
Efficiency
corrections:Fig. 6 Comparison of thetemperaturedependence of the ratios χ6B /χ2B and χ8B /χ2B for various µq /T corresponding to values at chemical
~region
TPC(0.4the≤ pchiral
0.8crossover
GeV/c): ε~=0.8−≤600−20TOF
T TPC (0.4≤ pT ≤ 0.8: ε0.8 of/T
0freeze-out
in heavy ion collisions
at RHIC.
TheGeV/c)shadedarea indicatesTPC
thetransition
atµTPCq
0-10%10-80%
TPC+TOF (0.8 ≤ pT ≤ 2 GeV/c): εTPCεTOF ~ 0.5
TPC+TOF (0.8 ≤ pT ≤ 2 GeV/c): εTPCεTOF ~ 0.5
0100
200−40TPC
TPC
Run10~160M~200M

0−20−40300−60 STAR Preliminary
N60
B . We also
Xiaofeng Luo determination
26/ 40CiRfSEχworkshop,
Jan.note
19, 2016@
Tsukuba
University.
qCentrality
XiaofengLuo
26 / −40
Run11~50M~450M
CiRfSE
workshop,
Jan.
19,
2016
@
Tsukuba
University.
cumulants
that
theseminima
becomemore
4Freeze-outandtheQCD
transition
partn0.1 0.2 0.3 0.4 0.5
1
1.52• Use charged particles
exceptin µorder
toavoidtheauto/T.
Infact,thestructureofpronounced
withprotons
increasingq
0.4 <thepT < X (GeV/c)|y| < X
The analysis of universal scaling functions that control
BB
correlation.
to that of |y|χ8 ≤at0.5,
large
e.g. R6,2 becomes similar
Acceptance:
0.4µ≤q /T
pT .≤This
2 GeV/cthermodynamics
inthevicinityofaphasetransition
intheis easily
understood Efficiency
in terms ofcorrections:
the Taylor expansion ofq Centrality bin widthcorrection
20universality
classof 3-dimensional O(4) symmetric theories
 TPC (0.4 ≤ p ≤ 0.8 GeV/c): εTPC ~ 0.8
B
the multiplicity
dominant
correction
atp averagenon-zeroµis ~ 0.5R6,2 , where• Calculatecumulants
ateachbinandtheminq /T(Sect. 2), of model (Sect. STAR3) and Preliminaryof lattice calculations [22,TPC+TOF(0.8≤≤2GeV/c):εε10
TPCTOFB,duetoχ
one centrality, which leads
to the supression of the volume36] suggest that10at vanishing baryon chemical potential the
8|y| < 0.5, 0.4 < pT < 2.0 (GeV/c)
Xiaofeng Luo
26 / 40 order cumulant of the net baryon number fluctuations
sixth
CiRfSE workshop, Jan. 19, 2016 @ Tsukuba University.
fluctuation.
B
B
isnegativeintheentire
high-temperaturephase.
In
fact,
theR
(µ/T)
=R(0)
q Statistical errors6,2: Bootstrap
q6,20O(4)scalingfunctionsforhighercumulants
turnnegative!
"• Make 0a new distribution by random
from the original
net2#$1 µq sampling=0)
criticaltemperalreadyinthevicinityofthechiral(mBB
B
q+
R8,2 (0) − R6,2 (0)R4,2 (0)proton distribution and calculate
cumulants.
2 Tature, i.e. below
the crossover temperature (mq > 0), which−10• This procedure is repeated with !!
300 times,"4 " and the statisticalis relevant for the transition at non-zero values of the lightµq cumulants.
Run10+Run11
errors are taken from the RMS
ofthequark masses. The regular terms
in the QCD free energy.
(21)+O
T

C6/C2

C6/C2T−10T−20

Run10,Central
may shift the onset of the negative
regimeto highertrigger
temperatures. However, model [35]as well as lattice [22, 36]
Binomial
This also makes it clear why for µq /T > 0 the location−30 that the regime
calculations suggestof negative sixth order
Summaryzero
B (µ /T ) is shifted to lower temperof the minimum of R6,2q
cumulants
startsbelow
butclosetotheQCD
crossovertranØ We present high statistics results of centrality, pT and rapidity
aturesrelativetothatofthechiralcrossovertemperature.
sition temperature.
−20−40dependenceofC/Cofnet-proton
multiplicity
distributions
fromB
6 2 1000200
0 chemical potential,
100 the temperature
200, the ratio R8,2 (µ300Similarly,
at non-zero µq /T
At non-zero baryonq /T ) shows√sNN = 200 GeV more
in Au+Au
collisions.
B , or equivalently R B (µ /T ), shrinks
intervalofnegativeχ
pronounced oscillations in the transition region, dueqv Systematic uncertainties
are under
66,2study.
partpartØ Results are consistent
with zero
within2σwithcurrent which
statistics.
and follows the crossover transition line. This is illustrated
to contributions
fromhigherorder
cumulants,
oscilin Fig. 7, which shows the temperature interval, closest tolate more rapidly in the transition region. The amplitude of
the hadronic phase, where the sixth and eighth order cuthe
maximumathightemperatures
becomescompatibleinToshihiro Nonaka
The STAR
Collaboration
mulantsof the net baryon number fluctuations are negative,
magnitude with that of the minimum.

Ntnonaka@rcf.rhic.bnl.gov

Ndrupal.star.bnl.gov/STAR/presentations300