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PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed
particles in ALICE at the LHC
Alice Ohlson∗for the ALICE Collaboration
RuprechtKarlsUniversität Heidelberg
Email: alice.ohlson@cern.ch
The eventbyevent ﬂuctuations of identiﬁed particles in ultrarelativistic nucleusnucleus colli
sions give information about the state of matter created in these collisions as well as the phase
diagram of nuclear matter. In this proceedings, we present the latest results from ALICE on the
centrality and pseudorapidity dependence of netproton ﬂuctuations, which are closely related
to netbaryon ﬂuctuations, as well as netkaon and netpion ﬂuctuations. The effects of volume
ﬂuctuations and global baryon conservation on these observables are discussed. Furthermore, the
correlated ﬂuctuations between different particle species, quantiﬁed by the observable νdyn, are
also shown as functions of multiplicity and collision energy and are compared with Monte Carlo
models. These measurements are performed in Pb–Pb collisions at √sNN =2.76 TeV using the
novel Identity Method and take advantage of the excellent particle identiﬁcation capabilities of
ALICE.
Critical Point and Onset of Deconﬁnement
711 August, 2017
The Wang Center, Stony Brook University, Stony Brook, NY
∗Speaker.
c
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PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
1. Introduction
Ultrarelativistic collisions of heavy nuclei create a hot, dense, stronglyinteracting state of
matter in which quarks and gluons are deconﬁned. Studying the properties of this state, known
as the quarkgluon plasma (QGP), allows us to understand the hightemperature and highdensity
regime of the phase diagram of nuclear matter. Measurements of eventbyevent ﬂuctuations of
particle multiplicities probe the properties and phase structure of stronglyinteracting matter. These
quantities are of particular interest because they are related, under a set of assumptions, to the
thermodynamic susceptibilities of the medium.
The thermodynamic susceptibilities, χ, are a set of observables which characterize the prop
erties of a thermodynamic system by describing its response to changes in external conditions. Of
particular interest in this case are the nthorder derivatives of the reduced pressure (P/T4) with
respect to the reduced chemical potential (µN/T),
χN=B,S,Q
n=∂n(P/T4)
∂(µN/T)n,(1.1)
where Ndenotes an additive quantum number such as baryon number (B), strangeness (S), or
electric charge (Q) and the corresponding chemical potentials are µB,µS, and µQ, respectively.
The susceptibilities χB,S,Q
ncan be calculated in lattice quantum chromodynamics (lattice QCD,
or LQCD) within the grand canonical ensemble (GCE) where they are related to the central mo
ments of the multiplicity distribution of conserved charges. The relationships between the higher
moments and the susceptibilities χB,S,Q
ncan be given by
M=h∆Ni=V T 3χ1,
σ2=h(∆N−h∆Ni)2i=V T 3χ2,
S=h(∆N−h∆Ni)3i/σ3=V T 3χ3
(V T 3χ2)3/2,
κ=h(∆N−h∆Ni)4i/σ4−3=V T 3χ4
(V T 3χ2)2.
(1.2)
where ∆Nis the net number of charges (∆NB,S,Q=NB,S,Q−N¯
B,¯
S,¯
Q), Vis the volume of the system,
and Tis the temperature. If the volume and temperature are constant, then the factors of V T 3can
be eliminated by measuring products of the moments:
Sσ=χ3/χ2
κσ2=χ4/χ2.(1.3)
While LQCD calculations become difﬁcult where µBis nonzero, highenergy heavyion col
lisions at the Large Hadron Collider (LHC) probe the region of the phase diagram very close to
µB=0, and therefore studying eventbyevent netbaryon number ﬂuctuations in these collisions
allows us to test precise LQCD predictions. Additionally, these measurements also look for signs
of criticality which may persist even far from the phase transition.
However, there are multiple effects which cause the relationship between the theoretically
calculable quantities and the experimentallymeasurable observables to be inexact. First, the
1
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
experimentallyaccessible quantities are the number of particles of a given species, not the strangeness
or baryon number. Typically, unidentiﬁed charged particles (∆NQ=N+−N−) or charged pions
(∆Nπ=Nπ+−Nπ−) are used as proxies to study netcharge ﬂuctuations, charged kaons (∆NK=
NK+−NK−) are measured to access netstrangeness ﬂuctuations, and netproton (∆Np=Np−N¯p)
moments are used as a proxy for baryon number ﬂuctuations. Second, while in LQCD the volume
of the system can be ﬁxed thus allowing the Vterms to cancel in Eq. 1.3, the system volume is not
experimentally accessible and therefore volume ﬂuctuations are intrinsic to the measurement. Fur
thermore, when measurements are done within a ﬁxed pseudorapidity range (∆η) the system can
be viewed as sitting within a particle bath, but when ∆ηis large global conservation laws cause the
GCE approximation to break down. Each of these effects should be explored and taken into account
when interpreting experimental measurements and their comparison to theoretical calculations.
2. Experimental setup & Analysis technique
The measurements presented here were performed in Pb–Pb collisions at a centerofmass
energy per nucleonnucleon pair of √sNN =2.76 TeV at the LHC using the ALICE (A Large
Ion Collider Experiment) detector. The principle subsystems used in the following measurements
were the ITS (Inner Tracking System) and TPC (Time Projection Chamber) for charged particle
tracking, and the V0 detectors in the forward region (−3.7<η<−1.7 and 2.8<η<5.1) for
event centrality determination. Particle identiﬁcation was performed in the TPC from the speciﬁc
energy loss (hdE/dxi) of charged tracks. For more details on the ALICE experiment, see Ref. [1].
The results presented below were obtained using the Identity Method [2,3,4], which makes
it possible to calculate the moments of the identiﬁed particle multiplicity distribution even when
particle identiﬁcation is done on a statistical, i.e. not trackbytrack, basis. First, the full, inclusive
hdE /dxidistribution is obtained from a large sample of events. This allows the probability that
a given track corresponds to a particular particle species to be determined with high precision.
Each track is assigned a weight wπ,K,p,ebetween 0 and 1, which corresponds to the probability
that a particle is a pion, kaon, proton, or electron. The sum of all track weights in a particular
event, Wπ,K,p,e=∑wπ,K,p,e, is then calculated, and the distributions of Wπ,K,p,eare obtained. The
Identity Method then provides a mathematical formalism for unfolding the moments of the Wπ,K,p,e
distributions into the moments hNn
π,K,p,ei.
Traditional particle identiﬁcation techniques reduce contamination by using additional detec
tor information or rejecting altogether particles which fall in regions of phase space where the
identiﬁcation is unclear, thus lowering the detection efﬁciency of the particles of interest. On the
other hand, the Identity Method explicitly accounts for the effects of imprecise particle identiﬁca
tion without lowering the detection efﬁciency.
3. Netproton, netkaon, and netpion ﬂuctuations
Figure 1shows the measurement of the ﬁrst and second moments of the proton (κn=1,2(p))
2
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
centrality [%]
010 20 30 40 50 60 70
(Skellam)
2
κ)/p(p
2
κ
0.95
1
ratio, stat. uncert.
syst. uncert.
0 10 20 30 40 50 60 70
n
κ
10
20
30
40
50
= 2.76 TeV
NN
sALICE Preliminary, PbPb
 < 0.8η, c < 1.5 GeV/p0.6 <
Model arXiv:1612.00702
)p(p
2
κ
(Skellam)
2
κ
(p)
2
κ
)p(
2
κ
(p)
1
κ
)p(
1
κ
)p(p
2
κModel
(p)
2
κModel
ALIPREL122598
η∆
0.5 11.5
(Skellam)
2
κ
)p
(p 
2
κ
0.9
0.95
1
1.05
1.1
1.15
= 2.76 TeV
NN
sALICE Preliminary, PbPb
, centrality 05%c < 1.5 GeV/p0.6 <
ratio, stat. uncert.
syst. uncert.
baryon conserv. arXiv:1612.00702
syst. uncert. HIJING, AMPT
ALIPREL122602
Figure 1: (left) The ﬁrst (κ1) and second (κ2) moments of protons (p), antiprotons ( ¯p), and netprotons
(p−¯p) are measured as a function of centrality and compared with the Skellam expectation (κ2(Skell am) =
κ1(p) + κ1(¯p)). (right) The second moment of netprotons, compared to the Skellam expectation, is mea
sured as a function of the pseudorapidity acceptance of the measurement (∆η). The results in both ﬁgures
are compared with a model [5] which includes the effects of volume ﬂuctuations due to the experimental
centrality determination procedure as well as global baryon number conservation.
and antiproton (κn=1,2(¯p)) multiplicity distributions:
κ1(p) = hNpi,κ1(¯p) = hN¯pi(3.1)
κ2(p) = h(Np−hNpi)2i,κ2(¯p) = h(N¯p−hN¯pi)2i(3.2)
The measured second moment of the netproton multiplicity (∆Np=Np−N¯p) distribution, deﬁned
in Eq. 3.3, is also shown as a function of event centrality in Fig. 1.
κ2(p−¯p) = h(∆Np−h∆Npi)2i(3.3)
=h(Np−N¯p−hNp−N¯pi)2i(3.4)
=κ2(p) + κ2(¯p)−2(hNpN¯pi−hNpihN¯pi)(3.5)
If the multiplicity distributions of Npand N¯pare Poissonian and uncorrelated, then the distribution
of ∆Npis Skellam. The higher moments of a Skellam distribution are simply related to the ﬁrst mo
ments of the individual particles, in particular κ2(Skellam) = κ1(p) + κ1(¯p). In Fig. 1a deviation
from the Skellam baseline is observed. However, a model [5] which includes the effects of partici
pant ﬂuctuations on the experimental results shows good agreement with the data. The model takes
as input only the mean multiplicities, κ1(p)and κ1(¯p), and the experimental centrality determina
tion procedure, and reproduces κ2(p),κ2(¯p), and κ2(p−¯p)within a consistent framework without
the need of correlations or critical ﬂuctuations.
Furthermore, the same model ([5]) incorporates the effects of global baryon conservation
which can be observed in the dependence of the second moments on the pseudorapidity acceptance
of the measurement (∆η), also shown in Fig. 1. Within the model, the deviation from a Skellam
3
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
η∆
0.5 11.5
(Skellam)
2
κ
)

π 
+
π(
2
κ
0.8
0.9
1
1.1 = 2.76 TeV
NN
sALICE Preliminary, PbPb
, centrality 05%c < 1.5 GeV/p0.6 <
ratio, stat. uncert.
syst. uncert.
HIJING
ALIPREL122614
η∆
0.5 11.5
(Skellam)
2
κ
)

 K
+
(K
2
κ
0.8
0.9
1
1.1
1.2
= 2.76 TeV
NN
sALICE Preliminary, PbPb
, centrality 05%c < 1.5 GeV/p0.6 <
ratio, stat. uncert.
syst. uncert.
HIJING
ALIPREL122618
η∆
0.5 11.5
(Skellam)
2
κ
)p
(p 
2
κ
0.9
1
1.1 = 2.76 TeV
NN
sALICE Preliminary, PbPb
, centrality 05%c < 1.5 GeV/p0.6 <
ratio, stat. uncert.
syst. uncert.
HIJING
ALIPREL122606
Figure 2: The ∆ηdependence of the (left) netpion, (center) netkaon, (right) netproton second moments
in 05% central Pb–Pb collisions are compared to predictions from the HIJING Monte Carlo generator.
distribution can be parameterized by Eq. 3.6, where hNmeas
piis the number of protons within the
acceptance range ∆ηand hN4π
Biis the total number of baryons in the full 4πphasespace.
κ2(p−¯p)
κ2(Skell am)=1−hNmeas
pi
hN4π
Bi(3.6)
The factor hN4π
Biis obtained by extrapolating from the number of baryons within the acceptance,
hNacc
Bi, determined in Ref. [6]. The Monte Carlo generators HIJING and AMPT are used for the
extrapolation, and the small differences between the two generators are included in the systematic
uncertainties on the model. As was observed in the centrality dependence of κ2(p−¯p), the model
can also fully describe the ∆ηdependence as due to baryon conservation without the need of critical
ﬂuctuations.
In Fig. 2, the results on the centrality dependence of the second moments of netpion, netkaon,
and netproton distributions are compared with HIJING. While the pions show good agreement
with HIJING, the agreement with the kaons is marginal, and the protons show signiﬁcant disagree
ment. However, the production of pions and kaons from resonance decays contributes signiﬁcantly
to the measured κ2(π+−π−)and κ2(K+−K−), which also means that a Skellam distribution is
not the proper baseline for these measurements.
4. Identiﬁed particle ﬂuctuations
In addition to measuring the ﬂuctuations of particles and their antiparticles, the eventbyevent
correlated ﬂuctuations of different species are also investigated. The second moment of the relative
abundances between two particle types, Aand B, can be written with the variable ν, deﬁned in
Eq. 4.1.
ν=*NA
hNAi−NB
hNBi2+(4.1)
=hN2
Ai
hNAi2+hN2
Bi
hNBi2−2hNANBi
hNAihNBi−1
hNAi+1
hNBi(4.2)
4
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
Centrality (%)
0 10 20 30 40 50 60 70 80
]

+K
+
,K

π+
+
π [
dyn
ν
0
5
10
15
20
25
30
35
40
45
3−
10×
ALICE Data, stat. errors:
Systematic uncertainty
= 2.76 TeV
NN
sALICE Preliminary, PbPb
c<1.5 GeV/p<0.8, 0.2<η 
ALI−PREL−96315
Centrality (%)
0 10 20 30 40 50 60 70 80
]p,p+

π+
+
π [
dyn
ν
25−
20−
15−
10−
5−
0
3−
10×
ALICE Data, stat. errors:
Systematic uncertainty
= 2.76 TeV
NN
sALICE Preliminary, PbPb
c<1.5 GeV/p<0.8, 0.2<η 
ALI−PREL−96319
Centrality (%)
0 10 20 30 40 50 60 70 80
]

+K
+
,Kp [p+
dyn
ν
0
5
10
15
20
25
3−
10×
ALICE Data, stat. errors:
Systematic uncertainty
= 2.76 TeV
NN
sALICE Preliminary, PbPb
c<1.5 GeV/p<0.8, 0.2<η 
ALI−PREL−96323
Figure 3: The centrality dependence of (top left) νdyn [π,K], (top right) νdyn [π,p], and (bottom) νdyn[p,K]
is measured.
The ﬁnal term in Eq. 4.2 represents the independent statistical ﬂuctuations of NAand NB, and can
be subtracted to obtain a measure of the dynamical ﬂuctuations, called νdyn , deﬁned in Eq. 4.3.
νdyn =hN2
Ai
hNAi2+hN2
Bi
hNBi2−2hNANBi
hNAihNBi(4.3)
If NAand NBhave Poisson distributions and are uncorrelated, then νdyn =0.
Figure 3shows the results for the correlated ﬂuctuations of each combination of pions (π++
π−), kaons (K++K−), and protons (p+¯p): νdyn [π,K],νdyn [p,K], and νdyn[π,p]. The values of
νdyn are small in central events but grow in peripheral events. This deviation from the Poisson
expectation may have contributions from other sources of correlations such as jets and resonance
decays, but is also due to an intrinsic multiplicity scaling in the νdyn observable. This multiplicity
scaling is removed by multiplying by hdNch/dηi, as shown in Fig. 4, where it is observed that the
data still deviates from the Poisson baseline. Comparisons with the AMPT and HIJING model
show qualitative agreement with the data, but quantitative differences.
Finally, the ALICE results in the 05% centrality range at a centerofmass energy of √sNN =
2.76 TeV are compared with results from the STAR beam energy scan in Fig. 4. While a sign
change of νdyn [p,K], and νd yn[π,p]is observed, the evolution from RHIC to LHC energies is
generally smooth.
5. Conclusions
In this proceedings the latest results from ALICE on the ﬂuctuations of identiﬁed particles in
Pb–Pb collisions at the LHC are presented. The measurements exploit the excellent particle iden
5
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
/dNd
0 200 400 600 800 1000 1200 1400 1600
!/d
ch
Nd"]

+K
+
,K

#+
+
# [
dyn
$
0
2
4
6
ALICE Data, stat. errors
Systematic uncertainty
HIJING
AMPT, String melting OFF, Rescattering ON
AMPT, String melting ON, Rescattering OFF
AMPT, String melting ON, Rescattering ON
= 2.76 TeV
NN
sALICE, PbPb
/dNd
0 200 400 600 800 1000 1200 1400 1600
!/d
ch
Nd"]p,p+

#+
+
# [
dyn
$
2%
0
2
4
6
!/d
ch
Nd
0200 400 600 800 1000 1200 1400 1600
!/d
ch
Nd"]

+K
+
,Kp [p+
dyn
$
0
5
= 2.76 TeV
NN
sALICE Preliminary, PbPb
ALIPREL129629
(GeV)s
10 2
10 3
10
]

+K
+
,K

!+
+
! [
dyn
"
0
1
2
3
3#
10$
ALICE: 05% PbPb (Id. Method), stat. errors
Systematic uncertainty
c<1.5 GeV/p<0.8, 0.2<% 
STAR: 05% AuAu (TPC+TOF)
c<1.8 GeV/p0.2, &
T
p<1, K: % 
c<1.8 GeV/p0.2, &
T
p: !
c<3.0 GeV/p0.4, &
T
p p:
= 2.76 TeV
NN
s
ALICE, PbPb
(GeV)s
10 2
10 3
10
]p,p+

!+
+
! [
dyn
"
4#
2#
0
3
10$
(GeV)
NN
s
10 2
10 3
10
]

+K
+
,Kp [p+
dyn
"
4#
2#
0
3
10$
= 2.76 TeV
NN
sALICE Preliminary, PbPb
ALIPREL129633
Figure 4: (left) The measurements of νdyn [π,K],νdyn [π,p], and νdyn [p,K]are scaled by the multiplicity
hdNch/dηiand compared with HIJING and three conﬁgurations of AMPT. (right) The values of νdyn mea
sured in 05% Pb–Pb and Au–Au collisions are shown as a function of centerofmass energy.
tiﬁcation capabilities of the ALICE detector, and are performed with the Identity Method in order
to account for cases in which the particle identiﬁcation is unclear without lowering the detection
efﬁciency.
The ﬂuctuations of netprotons, netkaons, and netpions are of particular interest because
they are related to the susceptibilities of the QGP matter which can be calculated within LQCD.
The centrality and ∆ηdependence of the second moments of netprotons has been measured and
a deviation from the Skellam baseline is observed. However, a model including the effects of
volume ﬂuctuations and baryon number conservation is able to fully describe the difference without
needing additional ﬂuctuations, therefore indicating that these measurements agree with LQCD
predictions.
The crossspecies correlated ﬂuctuations of pions, kaons, and protons are also measured with
the observable νdyn and show qualitative, but not quantitative, agreement with Monte Carlo
models. While there is a sign change observed in νd yn[p,K]and νd yn[π,p]from RHIC to LHC
energies, the energy dependence shows a smooth behavior over the large range. Future
investigations and measurements of the higher moments in ALICE will more fully explore the
physics of the ﬂuctuations of conserved charges in heavyion collisions.
6
PoS(CPOD2017)031
Measurements of the ﬂuctuations of identiﬁed particles in ALICE at the LHC Alice Ohlson
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[5] P. BraunMunzinger et al., Nucl. Phys. A960 (2017) 114, arXiv:1612.00702 [hepph].
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