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Higher-order transverse momentum fluctuations in heavy-ion collisions

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Somadutta Bhatta at Stony Brook University
Somadutta Bhatta
Chunjian Zhang at Stony Brook University
Chunjian Zhang
Jiangyong Jia
Jiangyong Jia
Jiangyong Jia
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In relativistic heavy-ion collisions, the event-by-event mean transverse momentum fluctuations are sensitive to overlap area and energy density fluctuations in the initial state. We present a framework to calculate p T fluctuations up to fourth order using standard and subevent methods, which is validated using the HIJING model. We observe a power-law dependence for cumulants of all orders as a function of charged particle multiplicity N ch, consistent with a simple independent source picture. The fluctuation in p p collisions is observed to be larger than for p+ Pb, Pb+ Pb, and Xe+ Xe collisions at the same N ch due to bias in the number of contributing sources. The short-range correlations are greatly suppressed in the subevent method in comparison to calculations based on the standard method. This paper provides a baseline for transverse momentum fluctuations without the presence of final-state effects.
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PHYSICAL REVIEW C 105, 024904 (2022)
Higher-order transverse momentum fluctuations in heavy-ion collisions
Somadutta Bhatta ,1Chunjian Zhang ,1and Jiangyong Jia 1,2,*
1Department of Chemistry, Stony Brook University, Stony Brook, New York 11794, USA
2Physics Department, Brookhaven National Laboratory, Upton, New York 11976, USA
(Received 8 December 2021; accepted 26 January 2022; published 7 February 2022)
In relativistic heavy-ion collisions, the event-by-event mean transverse momentum fluctuations are sensitive
to overlap area and energy density fluctuations in the initial state. We present a framework to calculate pT
fluctuations up to fourth order using standard and subevent methods, which is validated using the HIJING model.
We observe a power-law dependence for cumulants of all orders as a function of charged particle multiplicity
Nch, consistent with a simple independent source picture. The fluctuation in pp collisions is observed to be larger
than for p+Pb, Pb +Pb, and Xe +Xe collisions at the same Nch due to bias in the number of contributing
sources. The short-range correlations are greatly suppressed in the subevent method in comparison to calculations
based on the standard method. This paper provides a baseline for transverse momentum fluctuations without the
presence of final-state effects.
DOI: 10.1103/PhysRevC.105.024904
I. INTRODUCTION
Heavy-ion collisions at ultrarelativistic energies creates a
hot and dense QCD matter whose space-time evolution is
well described by relativistic viscous hydrodynamics [1,2].
Fluctuations of the position of participating nucleons lead to
large event-by-event fluctuations in the initial state of the col-
lision. As the system expands, initial-state fluctuations survive
various stages of system evolution and influence the final-state
observables [3–5]. Within hydrodynamic model framework,
the average transverse momentum pTin each event depends
on the initial energy density and is inversely related to the
size of overlap region area [6–9]. The variance of the pTand
the initial overlap size Ris expected to have a simple rela-
tion σ(pT)/pT=(pT−pT)2/pT∝σ(R)/R[10].
The pTfluctuations can be quantified by its cumulants, such
as mean, variance, skewness, and kurtosis. But so far, only
the mean and variance have been measured experimentally
[11–16]. Recently Ref. [8] predicted that the skewness of pT
fluctuations should be significantly larger than expectation
from the independent source scenario, and they can be used to
probe nuclear deformation effects [9,17]. But no experimental
measurement has been carried out for skewness and kurtosis.
The cumulants of pTfluctuations are intensive quantities.
Within the independent source picture, such as that imple-
mented in the HIJING model, each collision is composed
of superposition of independent pp-like collisions and in-
teraction between the sources are ignored [18]. Under these
conditions, the nth-order cumulant is expected to scale as
∝1/Ns(n−1), where Nsis the number of sources often taken
to be Npart (number of participating nucleons) or Nch (charged
particle multiplicity) [8,19,20]. However, the dynamics of
*Corresponding author: jjia@bnl.gov
evolution and final-state interaction can lead to a deviation
from this power-law behavior. Indeed, experimental measure-
ments of pTvariance in Au +Au collisions at √sNN =
200 GeV and Pb +Pb collisions at √sNN =2.76 TeV have
reported the power to be ≈0.81 instead of the expected value
of 1. This clear deviation from the baseline of the independent
source picture in the experimental data indicates the presence
of long-range collective correlations and significant final-state
effects [13,15,21].
The direct calculation of higher-order cumulants in heavy-
ion collisions are computationally expensive, we provide a
framework based on the standard and subevent methods to
ease this calculation [22,23]. We use the HIJING model to
extract the baseline in which pTfluctuations arise mostly from
superposition of contributions from independent sources. The
contribution from each source contains both long-range cor-
relations associated with strings and short-range correlations
from jets and resonance decays [18]. The short-range corre-
lations can be suppressed using rapidity-separated subevent
methods, which are widely used in previous flow analyses
[21,23–28]. To test the power-law scaling and its system size
dependence, we repeated the study using Pb +Pb, Xe +Xe,
p+Pb, and pp collisions at similar center-of-mass energy
around 5 TeV.
The paper is organized as follows. Section II provides the
formulas for calculating pTcumulants in both standard and
subevent methods and describes the setup for the HIJING
model. The main results are presented in Sec. III. Section IV
gives a summary.
II. METHODOLOGY AND MODEL SETUP
We first provide the framework for mean-pTcumulants
following the approach prescribed in Refs. [23,29]. The
2469-9985/2022/105(2)/024904(5) 024904-1 ©2022 American Physical Society
BHATTA, ZHANG, AND JIA PHYSICAL REVIEW C 105, 024904 (2022)
2
10 3
10
0.54
0.55
0.56
0.57
²²
T
p¢¢
|<2.5KHIJING, |
< 2.0 GeV
T
0.2 <p
Pb+Pb 5.02 TeV
Xe+Xe 5.44 TeV
2
10 3
10
5
10
4
10
²
2
c¢
0.001rb = 1.009
0.001rb = 1.010
b
)
ch
Fit fn.:a/(N
2
10 3
10
ch
N
9
10
7
10
²
3
c¢
0.019rb = 2.218
0.015rb = 2.132
b
)
ch
Fit fn.:a/(N
2
10 3
10
ch
N
12
10
9
10
2
²
2
c¢ - 3²
4
c¢
0.084rb = 2.920
0.083rb = 3.124
b
)
ch
Fit fn.:a/(N
FIG. 1. The pTcumulants without normalizing by pT for particles in 0.2<pT<2 GeV as a function of Nch in Pb +Pb and Xe +Xe
collisions. The solid lines show the fit of the data to a/(Nch)b.
n-particle pTcorrelator in one event is defined as
cn=
i1=···=in
wi1···win(pT,i1−pT)···(pT,in−pT)
i1=···=in
wi1···win
,
(1)
where wiis the weight for particle i. Following Ref. [23]
and denoting p≡pT, this relation can be expanded alge-
braically into a simple polynomial function of the following
quantities:
pmk =
i
wk
ipm
i
i
wk
i,τ
k=
i
wk+1
i
i
wik+1,
¯p1k≡p1k−pT,
¯p2k≡p2k−2p1kpT +  pT2,
¯p3k≡p3k−3p2kpT + 3p1kpT2−pT3,
¯p4k≡p4k−4p3kpT + 6p2kpT2
−4p1kpT3+pT4.(2)
Note there pT = p11 is the mean-pTaveraged over the
event ensemble.
Using these auxiliary variables, the correlator in
Eq. (1) in the standard method can be expressed
as
c2=¯p2
11 −¯p22
1−τ1
,c3=¯p3
11 −3¯p22 ¯p11 +2¯p33
1−3τ1+2τ2
,
c4=¯p4
11 −6¯p22 ¯p2
11 +3¯p2
22 +8¯p33 ¯p11 −6¯p44
1−6τ1+3τ2
1+8τ2−6τ3
(3)
where particles are taken from |η|<2.5 and only unique
particle combinations in the event are considered.
In the subevent method (2sub), particle combinations are
chosen from two rapidity separated subevents a(−2.5<
η<−0.75) and c(2.5>η>0.75). The gap between the
subevents reduce short-range correlations. The correlators in
this case are given by
c2,2sub =(¯p11 )a(¯p11)c,c3,2sub1 =¯p2
11 −¯p22a(¯p11 )c
1−τ1a
,
c3,2sub2 =¯p2
11 −¯p22c(¯p11 )a
1−τ1c
,
c4,2sub =¯p2
11 −¯p22a¯p2
11 −¯p22c
(1 −τ1a)(1 −τ1c),(4)
where the lettered subscripts in Eq. (5) denote the subevents
from which particles are taken. Note that there are two differ-
ent ways of calculating two-subevent c3, and the final results
are calculated as average, i.e., 2c3,2sub =c3,2sub1 +c3,2sub2.
The validity of these formulas is confirmed by comparison
with results obtained from direct loop calculations.
The cumulants are then calculated by averaging cnover
a given ensemble of events. In practice, they are calculated
over a unit Nch bin and are then combined over wider bins. In
024904-2
HIGHER-ORDER TRANSVERSE MOMENTUM FLUCTUATIONS … PHYSICAL REVIEW C 105, 024904 (2022)
2
10 3
10
ch
N
5
10
4
10
3
10
2
10
2
k
Standard method
Two-subevent method
< 5.0 GeV
T
0.2 < p
2
10 3
10
ch
N
0.2
0.3
2sub/std
2
10 3
10
ch
N
7
10
6
10
5
10
4
10
3
k
HIJING Pb+Pb 5.02 TeV
|<2.5K|
2
10 3
10
ch
N
0.6
0.7
0.8
2sub/std
2
10 3
10
ch
N
9
10
8
10
7
10
6
10
5
10
4
10
4
k
2
10 3
10
ch
N
0.6
0.8
1
2sub/std
FIG. 2. The variance (left), skewness (middle), and kurtosis (right) in Pb +Pb collisions using the standard (solid points) and two-subevent
method (open points) for charged particles in 0.2<pT<5.0 GeV as a function of Nch.
this paper, we use the following dimensionless definition for
cumulants (also called scaled cumulants),
k2=c2
pT2,k3=c3
pT3,
k4=c4−3c22
pT4,k2,2sub =c2,2sub
pTapTc
,
k3,2sub1 =c3,2sub1
pT2
apTc
,k3,2sub2 =c3,2sub2
pTapT2
c
,
k4,2sub =c4,2sub−2c2,2sub 2−c2ac2c
pT2
apT2
c
.(5)
Note that c2aand c2cdenote the c2obtained from the
standard method in subevents aand c, respectively. The final
skewness is taken as 2k3,2sub =k3,2sub1 +k3,2sub2.
For HIJING simulation, we generate pp,p+Pb, and
Pb +Pb collisions at √sNN =5.02 TeV and Xe +Xe
collisions at √sNN =5.44 TeV. The particles are chosen from
|η|<2.5 and two pTranges: 0.2<pT<2 and 0.2<pT<
5 GeV. The lower pTrange is less sensitive to contribution
from short-range correlations. To facilitate direct comparison
with experimental measurements, the calculations are carried
out as a function of Nch consisting only of charged hadrons
within |η|<2.5 and 0.5<pT<5 GeV. The Nch range, thus,
obtained is consistent with the choice used in the ATLAS
Collaboration experiment [27].
III. RESULTS
Figure 1shows the pTcumulants without the normalization
by pT in Pb +Pb and Xe +Xe collisions as a function of
Nch. A double-logarithmic scale is used to show clearly the
power-law dependence is as a function of Nch. The extracted
power-law index from a simple fit of the form a/(Nch )bgives
the value of bthat is very close to (n−1) expected for the
0 2000 4000
ch
N
7
10
6
10
5
10
4
10
3
10
2
k
HIJING Pb+Pb 5.02 TeV
|<2.5K|
< 2.0 GeV
T
0.2 < p
std
= 0K'2sub
= 0.5K'2sub
= 1.0K'2sub
= 2.0K'2sub
= 3.0K'2sub
0 2000 4000
ch
N
0
0.1
0.2
0.3
0.4
2,std
/k
K'2,2sub
k
FIG. 3. (Left) The variance obtained for the standard method and two-subevent method with various rapidity separations in Pb +Pb
collisions for 0.2<pT<2 GeV as a function of Nch. (Right) Ratio of results from two-subevent method to those obtained from the standard
method.
024904-3
BHATTA, ZHANG, AND JIA PHYSICAL REVIEW C 105, 024904 (2022)
0.55
0.6
²²
T
p¢¢
HIJING
< 2.0 GeV
T
|<2.5, 0.2 < pK|
3
10
2
k
2
10 ch
N
5
10
4
10
3
k
Pb+Pb 5.02 TeV
Xe+Xe 5.44 TeV
p+Pb 5.02 TeV
p+p 5.02 TeV
2
10 ch
N
7
10
6
10
5
10
4
k
FIG. 4. The pTcumulants compared between different collision systems as a function of Nch.
nth-order cumulant. This confirms that the pTfluctuations in
HIJING originate from superposition of independent sources.
Figure 2compares knbetween the standard and the
subevent calculations to estimate the influence of short-range
correlations. The k2,2sub is suppressed by a factor of 3 in
comparison to k2from the standard method, suggesting the
scaled variance in the HIJING model is dominated by the
short-range correlations. The influence for k3and k4are signif-
icantly smaller. This is consistent with the expectation that the
short-range correlations have smaller impact for higher-order
cumulants.
Figure 3shows how the scaled variance k2depends on
the rapidity separation between the two subevents. Most of
the decrease is obtained between the subevent method and
the standard method. Further decrease is observed when one
increases the separation between the two subevents. Beyond
the edge gap of 0.5 unit, however, the values of k2do not
change further. This residual signal probably reflects the gen-
uine long-range correlations associated with strings in the
HIJING model.
Figure 4compares the pTcumulants among pp,p+Pb,
Xe +Xe, and Pb +Pb collisions as a function of Nch.In
HIJING, we expect fluctuations to decrease with increasing
system size in accordance with increase in the number of
sources. The magnitude of pT shows a clear system size
ordering, whereas for higher-order cumulants, only pp has a
higher magnitude than those for p+Pb, Xe +Xe, and Pb
+Pb collisions. The latter is expected since the number of
sources in pp is small, and the events with large Nch are domi-
nated by fluctuations in the particle production in each source,
i.e., from minijets, instead of fluctuations in the number of
sources.
IV. SUMMARY
To summarize, we provide a framework for calculating the
higher-order dynamical pTcumulants up to fourth order using
the standard and subevent methods. In the HIJING model, the
higher-order cumulants are found to follow a simple power-
law scaling as a function of charged particle multiplicity
Nch as expected from a simple superposition of independent
sources. The subevent method is found to effectively suppress
short-range correlations that dominates the variance of the pT
fluctuations; such short-range correlations have smaller influ-
ence on skewness and kurtosis of the pTfluctuations. The pT
cumulants are found to follow a common scaling as a function
of Nch, except in the pp collisions where they are influenced
by fluctuations of particle production within each source. Our
paper provides a useful baseline for pTfluctuations that is
based on simple superposition of independent sources and
short-range correlations but without final-state effects.
ACKNOWLEDGMENT
This work was supported by DOE Grant No.
DEFG0287ER40331.
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024904-5
... The temperature fluctuations associated with phase transition in the QCD phase diagram can manifest themselves in event-wise mean transverse momentum (⟨p T ⟩) fluctuations of the final-state particles [15]. ⟨p T ⟩ is sensitive to the initial energy density and inversely proportional to the size of the overlap region [16,17], while it is also influenced by collective behavior, fluctuations in the participant nucleons, and other final-state effects [18]. ...
... Recently, higher-order ⟨p T ⟩ fluctuations have also been investigated in experiments to uncover the intricate mechanisms underlying the observed fluctuations. The ALICE experiment reports a positive skewness in ⟨p T ⟩ fluctuations in minimum-bias pp collisions and across all centralities in large collision systems [4], consistent with hydrodynamic simulation predictions [18,29,30]. Furthermore, the kurtosis of ⟨p T ⟩ fluctuations in most central Pb+Pb collisions aligns with that of Gaussian distribution, suggesting the formation of a locally thermalized system [4]. ...
... Similarly, the AMPT model, particularly with the string-melting version demonstrates good agreement with experimental measurements at the LHC energy [26,27,44]. In higher-order ⟨p T ⟩ fluctuations, HI-JING simulations exhibit a power-law scaling on charged particle multiplicity in both skewness and kurtosis, con-sistent with a superposition of independent sources [18]. Moreover, hydrodynamic calculations can explain the measurements of both skewness and kurtosis quantitively from semicentral to central collisions at LHC energy [4,30]. ...
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Full-text available
  • Jun 2024
The thermal fluctuations in the QGP medium formed in heavy ion collisions present themselves as event-wise mean transverse momentum ([pT]) fluctuations in the final state. Recent studies have shown that the fluctuations are sensitive to radial flow, random thermal motion, and nuclear deformation. They can provide constraints on the extent of thermalization of the QGP droplet. Recently, correlations of [pT] with flow harmonic coefficients (vn) also gained interest, as they were found to be sensitive primarily to the initial state fluctuations. This talk presents precise measurements of up to 3rd order [pT] cumulants as a function of multiplicity and centrality with an emphasis on ultra-central collisions. These results have strong implications for understanding the impacts of the initial condition, medium thermalization, and medium properties on final state [pT] fluctuations.
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Transverse momentum fluctuation in ultra-central Pb+Pb collision at the LHC
Article
Full-text available
  • Jun 2024
The ATLAS collaboration has recently observed that the variance of the transverse momentum per particle ([pt]), when measured as a function of the collision multiplicity (Nch) in Pb+Pb collisions, decreases by a factor 2 for the largest values of Nch, corresponding to ultra-central collisions. We show that this phenomenon is naturally explained by invoking impact parameter (b) fluctuations, which contribute to the variance, and gradually disappear in ultracentral collisions. It implies that Nch and [pt] are strongly correlated at fixed b, which is explained by the local thermalization of the QGP medium.
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Longitudinal Flow Decorrelations in Xe + Xe Collisions at s N N = 5.44 TeV with the ATLAS Detector
Article
Full-text available
  • Mar 2021
The first measurement of longitudinal decorrelations of harmonic flow amplitudes vn for n=2–4 in Xe+Xe collisions at sNN=5.44 TeV is obtained using 3 μb−1 of data with the ATLAS detector at the LHC. The decorrelation signal for v3 and v4 is found to be nearly independent of collision centrality and transverse momentum (pT) requirements on final-state particles, but for v2 a strong centrality and pT dependence is seen. When compared with the results from Pb+Pb collisions at sNN=5.02 TeV, the longitudinal decorrelation signal in midcentral Xe+Xe collisions is found to be larger for v2, but smaller for v3. Current hydrodynamic models reproduce the ratios of the vn measured in Xe+Xe collisions to those in Pb+Pb collisions but fail to describe the magnitudes and trends of the ratios of longitudinal flow decorrelations between Xe+Xe and Pb+Pb. The results on the system-size dependence provide new insights and an important lever arm to separate effects of the longitudinal structure of the initial state from other early and late time effects in heavy-ion collisions.
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Correlations of azimuthal anisotropy Fourier harmonics with subevent cumulants in p Pb collisions at s N N = 8.16 TeV
Article
Full-text available
  • Jan 2021
Event-by-event long-range correlations of azimuthal anisotropy Fourier coefficients (vn) in 8.16 TeV pPb data, collected by the CMS experiment at the CERN Large Hadron Collider, are extracted using a subevent four-particle cumulant technique applied to very low multiplicity events. Each combination of four charged particles is selected from either two, three, or four distinct subevent regions of a pseudorapidity range from −2.4 to 2.4 of the CMS tracker, and with transverse momentum between 0.3 and 3.0 GeV. Using the subevent cumulant technique, correlations between vn of different orders are measured as functions of particle multiplicity and compared to the standard cumulant method without subevents over a wide event multiplicity range. At high multiplicities, the v2 and v3 coefficients exhibit an anticorrelation; this behavior is observed consistently using various methods. The v2 and v4 correlation strength is found to depend on the number of subevents used in the calculation. As the event multiplicity decreases, the results from different subevent methods diverge because of different contributions of noncollective or few-particle correlations. Correlations extracted with the four-subevent method exhibit a tendency to diminish monotonically toward the lowest multiplicity region (about 20 charged tracks) investigated. These findings extend previous studies to a significantly lower event multiplicity range and establish the evidence for the onset of long-range collective multiparticle correlations in small system collisions.
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Thermodynamics of hot strong-interaction matter from ultrarelativistic nuclear collisions
Article
Full-text available
  • Jun 2020
  • NAT PHYS
Collisions between heavy atomic nuclei at ultrarelativistic energies are carried out at particle colliders to produce the quark–gluon plasma, a state of matter where quarks and gluons are not confined into hadrons, and colour degrees of freedom are liberated. This state is thought to be produced as a transient phenomenon before it fragments into thousands of particles that reach the particle detectors. Despite two decades of investigations, one of the big open challenges¹ is to obtain an experimental determination of the temperature reached in a heavy-ion collision, and a simultaneous determination of another thermodynamic quantity, such as the entropy density, that would give access to the number of degrees of freedom. Here, we obtain such a determination, utilizing state-of-the-art hydrodynamic simulations². We define an effective temperature, averaged over the spacetime evolution of the medium. Then, using experimental data, we determine this temperature and the corresponding entropy density and speed of sound in the matter created in lead–lead collisions at the Large Hadron Collider. Our results agree with first-principles calculations from lattice quantum chromodynamics³ and confirm that a deconfined phase of matter is indeed produced.
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Fluctuations of anisotropic flow in Pb+Pb collisions at sNNsNN \sqrt{{\mathrm{s}}_{\mathrm{NN}}} = 5.02 TeV with the ATLAS detector
Article
Full-text available
  • Jan 2020
  • J HIGH ENERGY PHYS
A bstract Multi-particle azimuthal cumulants are measured as a function of centrality and transverse momentum using 470 μ b − 1 of Pb+Pb collisions at sNN \sqrt{s_{\mathrm{NN}}} s NN = 5 . 02 TeV with the ATLAS detector at the LHC. These cumulants provide information on the event-by-event fluctuations of harmonic flow coefficients v n and correlated fluctuations between two harmonics v n and v m . For the first time, a non-zero four-particle cumulant is observed for dipolar flow, v 1 . The four-particle cumulants for elliptic flow, v 2 , and triangular flow, v 3 , exhibit a strong centrality dependence and change sign in ultra-central collisions. This sign change is consistent with significant non-Gaussian fluctuations in v 2 and v 3 . The four-particle cumulant for quadrangular flow, v 4 , is found to change sign in mid-central collisions. Correlations between two harmonics are studied with three- and four-particle mixed-harmonic cumulants, which indicate an anti-correlation between v 2 and v 3, and a positive correlation between v 2 and v 4 . These correlations decrease in strength towards central collisions and either approach zero or change sign in ultra-central collisions. To investigate the possible flow fluctuations arising from intrinsic centrality or volume fluctuations, the results are compared between two different event classes used for centrality definitions. In peripheral and mid-central collisions where the cumulant signals are large, only small differences are observed. In ultra-central collisions, the differences are much larger and transverse momentum dependent. These results provide new information to disentangle flow fluctuations from the initial and final states, as well as new insights on the influence of centrality fluctuations.
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Measurement of flow harmonics correlations with mean transverse momentum in lead–lead and proton–lead collisions at sNN=5.02 TeV\sqrt{s_{\mathrm{NN}}} = 5.02~\hbox {TeV}sNN=5.02TeV with the ATLAS detector
Article
Full-text available
  • Dec 2019
To assess the properties of the quark–gluon plasma formed in ultrarelativistic ion collisions, the ATLAS experiment at the LHC measures a correlation between the mean transverse momentum and the flow harmonics. The analysis uses data samples of lead–lead and proton–lead collisions obtained at the centre-of-mass energy per nucleon pair of 5.02 TeV, corresponding to total integrated luminosities of 22~\upmu \text {b}^{-1} and 28 nb−128~\text {nb}^{-1}, respectively. The measurement is performed using a modified Pearson correlation coefficient with the charged-particle tracks on an event-by-event basis. The modified Pearson correlation coefficients for the 2nd-, 3rd-, and 4th-order flow harmonics are measured in the lead–lead collisions as a function of event centrality quantified as the number of charged particles or the number of nucleons participating in the collision. The measurements are performed for several intervals of the charged-particle transverse momentum. The correlation coefficients for all studied harmonics exhibit a strong centrality evolution, which only weakly depends on the charged-particle momentum range. In the proton–lead collisions, the modified Pearson correlation coefficient measured for the 2nd-order flow harmonics shows only weak centrality dependence. The lead-lead data is qualitatively described by the predictions based on the hydrodynamical model.
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Shape of atomic nuclei in heavy ion collisions
Article
  • Jan 2022
In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flows vn are linearly related to the strengths of the multipole shape of the distribution of nucleons in the transverse plane, ɛn: vn∝ɛn. The ɛn, for n=1,2,3,4, are sensitive to the shapes of the colliding ions, characterized by the quadrupole β2, octupole β3, and hexadecapole β4 deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, 〈ɛn2〉=an′+bn′βn2, for events in a fixed centrality. The 〈ɛ12〉 has a contribution from β3 and β4, and 〈ɛ32〉 from β4. In ultracentral collisions, there are little cross contributions between β2 and ɛ3 and between β3 and ɛ2, but clear cross contributions are present in noncentral collisions. Additionally, 〈ɛn2〉 are insensitive to nonaxial shape parameters such as the triaxiality. This is good news because the measurements of v2, v3, and v4 can be used to constrain simultaneously the β2, β3, and β4 values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical an′, to obtain a simple equation that relates the βn of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale (<10−24s) much shorter than probed by low-energy nuclear structure physics (<10−21s), which ultimately may provide information complementary to that obtained in the nuclear structure experiments.
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Skewness of mean transverse momentum fluctuations in heavy-ion collisions
Article
  • Feb 2021
We propose the skewness of mean transverse momentum 〈pt〉 fluctuations as a fine probe of hydrodynamic behavior in relativistic nuclear collisions. We describe how the skewness of the 〈pt〉 distribution can be analyzed experimentally, and we use hydrodynamic simulations to predict its value. We predict, in particular, that 〈pt〉 fluctuations have positive skew, which is significantly larger than if particles were emitted independently. We elucidate the origin of this result by deriving generic formulas relating the fluctuations of 〈pt〉 to the fluctuations of the early-time thermodynamic quantities. We postulate that the large positive skewness of 〈pt〉 fluctuations is a generic prediction of hydrodynamic models.
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Transverse momentum fluctuations and their correlation with elliptic flow in nuclear collisions
Article
  • Sep 2020
We propose observables v0 and v0(pT) which quantify the relative fluctuations in the total transverse momentum at fixed multiplicity. We first study the factorization of the fixed multiplicity momentum-dependent two-particle correlation function into a product of v0(pTa) and v0(pTb) within realistic hydrodynamic simulations. Then we present computations of v0(pT) for different particle types. We determine the relation between the integrated v0 and previously measured observables and compare results from a hybrid hydrodynamics-based model to experimental data. The effects of bulk viscosity and an initial pre-equilibrium stage on the results are quantified. We find that v0 is strongly correlated with the initial state entropy per elliptic area, S/A. Using this result, we explain how the observed correlations between the elliptic flow and the transverse momentum (both in simulations and experiment) reflect the initial state correlations between 1/A and ellipticity ɛ2 at fixed multiplicity. We argue that the systematic experimental study of v0, with the same sophistication as used for the other vn, can contribute significantly to our understanding of quark gluon plasma properties.
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Relativistic Fluid Dynamics in and out of Equilibrium: And Applications to Relativistic Nuclear Collisions
Book
  • May 2019
Cambridge Core - Theoretical Physics and Mathematical Physics - Relativistic Fluid Dynamics in and out of Equilibrium - by Paul Romatschke
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Collision-energy dependence of p t correlations in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider
Article
  • Apr 2019
We present two-particle pt correlations as a function of event centrality for Au+Au collisions at sNN=7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These results are compared to previous measurements from CERES at the Super Proton Synchrotron and from ALICE at the Large Hadron Collider. The data are compared with UrQMD model calculations and with a model based on a Boltzmann-Langevin approach incorporating effects from thermalization. The relative dynamical correlations for Au+Au collisions at sNN=200 GeV show a power-law dependence on the number of participant nucleons and agree with the results for Pb+Pb collisions at sNN=2.76TeV from ALICE. As the collision energy is lowered from sNN=200 to 7.7 GeV, the centrality dependence of the relative dynamical correlations departs from the power-law behavior observed at the higher collision energies. In central collisions, the relative dynamical correlations increase with collision energy up to sNN=200 GeV in contrast to previous measurements that showed little dependence on the collision energy.
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