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ATLAS CONF NoteATLAS-CONF-2019-055

November 3, 2019

Longitudinal flow decorrelations in Xe+Xe collisionsat √sNN = 5.44 TeV with the ATLAS detector

The ATLAS Collaboration

First measurement of longitudinal decorrelations of harmonic flow vn for n = 2, 3 and 4 inXe+Xe collisions at √sNN = 5.44 TeV is obtained using the ATLAS detector at the LHC. Thedecorrelation signal for v3 and v4 is found to be nearly independent of collision centrality andtransverse momentum, pT, but for v2 a strong centrality and pT dependence is seen. Whencompared to the results from Pb+Pb collisions at √sNN = 5.02 TeV, the decorrelation signalin mid-central Xe+Xe collisions is found to be larger for v2, but smaller for v3. Currenthydrodynamic models, which reproduce the ratio of vn between Xe+Xe and Pb+Pb, fail todescribe the magnitudes and trends of the ratios of flow decorrelations between Xe+Xe andPb+Pb. These results provide new insights on the longitudinal structure of the initial-stategeometry in heavy-ion collisions.

© 2019 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

High-energy heavy-ion collisions create a new state of matter known as Quark-Gluon Plasma (QGP), whosespace-time dynamics is well described by relativistic viscous hydrodynamic models [1, 2]. During itsexpansion, the large pressure gradients of theQGPconvert the spatial anisotropies in the initial-state geometryintomomentum anisotropies of the final-state particles. Suchmomentum anisotropies are often characterizedby a Fourier expansion of particle density in azimuthal angle φ, dN/dφ ∝ 1 + 2

∑∞n=1 vn cos n(φ − Φn),

where vn and Φn are the magnitude and phase of the nth-order anisotropy. Extensive studies of vn and theirevent-by-event fluctuations in the last decade [3–13] have provided strong constraints on the properties ofthe QGP and the initial-state geometry [14–19]. Most of these studies, however, assume that the initialcondition and dynamic evolution of the QGP are boost-invariant in the longitudinal direction. Recently,LHC experiments made the first observation [20, 21] of "flow decorrelations" in Pb+Pb collisions, whichshow that, even in a given event, vn and Φn can fluctuate along the longitudinal direction. Hydrodynamicmodel calculations [22–27] show that such flow decorrelations are driven mostly by primordial longitudinalstructure in the initial-state geometry. Testing how flow decorrelations vary with beam energy and the sizeof the collision systems can improve our knowledge about the early-time dynamics of the QGP.

This letter investigates the system-size dependence of longitudinal decorrelations of v2, v3, v4 by performingmeasurements in 129Xe+129Xe collisions and comparing them with 208Pb+208Pb collisions. Recentmeasurements [28–30] show that the vn has modest difference (< 10-20%) between these two systems asa function of centrality, except in the most central collisions where the difference for v2 is significantlylarger. Model calculations [31, 32] suggest that these differences are compatible with the expected orderingof the initial eccentricities and roles of viscous effects in the two systems. It is of great interest to studywhether the decorrelation of vn follows similar ordering as the vn between the two systems, which shouldprovide insight on the nature of the initial sources that initiates both the transverse harmonic flow and theirlongitudinal fluctuations.

The measurement is performed using the ATLAS inner detector (ID) and forward calorimeters (FCal) alongwith the trigger and data acquisition system [33, 34]. The ID measures charged particles over pseudorapidityrange |η | < 2.5 1 using a combination of silicon pixel detectors, silicon micro-strip detectors (SCT), anda straw-tube transition radiation tracker, all immersed in a 2 T axial magnetic field [35, 36]. The FCalmeasures the sum of the transverse energy

∑ET over 3.2 < |η | < 4.9 for centrality determination, and

uses tungsten and copper absorbers with liquid argon as the active medium. The FCal towers consist ofcalorimeter cells grouped into regions in ∆η × ∆φ of 0.1 × 0.1. The ATLAS trigger system [34] consists ofa level-1 (L1) trigger implemented using a combination of dedicated electronics and programmable logic,and a software based high-level trigger.

This analysis uses 3µb−1 of √sNN =5.44 TeV Xe+Xe data collected in 2017. The events are selected byrequiring total transverse energy deposited in the calorimeters over |η | < 4.9 as estimated in the L1 triggersystem to be larger than 4 GeV. In the offline analysis, the z-position of the primary vertex of each event isrequired to be within 100 mm of the nominal IP. Events containing more than one inelastic interaction(pile-up) are suppressed by exploiting the correlation between the transverse energy

∑ET measured in

the FCal and the number of tracks associated with a primary vertex. The fraction of pile-up after eventselection is estimated to be less than 0.2%. The event centrality [37] is based on the

∑ET in the FCal. A

Glauber model [38, 39] is used to determine the mapping between∑

ET and the centrality percentiles, aswell as to provide an estimate of the average number of participating nucleons, Npart, for each centrality

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detectorand the z-axis along the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y-axis pointsupward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. Thepseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2).

2

interval. This analysis is restricted to the 0–70% centrality percentiles where the L1 trigger is estimated tobe fully efficient.

Charged-particle tracks are reconstructed from hits in the ID using a reconstruction procedure developed fortracking in dense environments in proton-proton (pp) collisions, and optimized for heavy-ion collisions [40].Tracks used in this analysis are required to have 0.5 < pT < 3 GeV and |η | < 2.4, at least two pixel hits, ahit in the first pixel layer when one is expected, at least eight SCT hits, and no missing hit in the SCT. Inaddition, the point of closest approach of the track is required to be within 1 mm of the primary vertexin both the transverse and longitudinal directions. More details on the track selections can be found inRef. [30]. The pT range is chosen to be same as for the Pb+Pb results [21].

The efficiency ε(pT, η) of the track reconstruction and track selection requirements is evaluated usingminimum-bias Xe+Xe Monte Carlo (MC) events produced with the HIJING [41] event generator withthe effect of flow added using the procedure described in Ref. [42]. The response of the detector wassimulated using Geant4 [43], and the resulting events are reconstructed with the same algorithms asapplied to the data. For |η | < 1, the efficiency is 60% at low pT and increases to 73% at higher pT. For|η | > 1, the efficiency ranges between 40% and 60% depending on the pT. The efficiency depends weaklyon the centrality. The change of about 3% over the whole centrality range is observed only for low pTparticles. The uncertainties of ε(pT, η), arising mainly from the uncertainty in the detector material budget,are between 1–4% depending on pT and η. The rate of falsely reconstructed tracks f (pT, η) is found tobe significant only for pT < 0.8 GeV in the central collisions where it ranges from 2% at η ≈ 0 to 6% at|η | > 2. The fake rate decreases rapidly for higher pT values.

The method and analysis procedure follows closely those established in Ref. [21], described briefly below.The nth-order azimuthal anisotropy in an event is estimated using the observed flow vectors:

qn ≡ Σjwjeinφ j /(Σjwj) (1)

in either the ID or the FCal, where the sum runs over charged particles for the ID or towers for the FCal,in a η interval, and φ j and wj are the azimuthal angle and the weight assigned to each track or tower,respectively. The weight for the FCal is the ET of each tower, and the weight for the ID is calculatedas d(η, φ)(1 − f (pT, η))/ε(pT, η) [44] to correct for tracking performance. The additional factor d(η, φ),derived from the data, corrects for azimuthal non-uniformity of the detector performance in each η interval.The flow vectors qn are further corrected by an event-averaged offset: qn − 〈qn〉.

The longitudinal flow decorrelations are studied using product of flow vectors in the ID qn(η) and in theFCal qn(ηref) [20], averaged over events in a given centrality interval,

rn |n(η) =〈qn(−η)q

∗n(ηref)〉

〈qn(η)q∗n(ηref)〉

=〈vn(−η)vn(ηref) cos n[Φn(−η) − Φn(ηref)]〉

〈vn(η)vn(ηref) cos n[Φn(η) − Φn(ηref)]〉, (2)

where ηref is a reference pseudorapidity range in the FCal, common to both the numerator and thedenominator. The rn |n correlator defined this way quantifies the decorrelation between η and −η [20, 45].Three reference η ranges, 3.2 < |ηref | < 4.0, 4.0 < |ηref | < 4.9 and 3.2 < |ηref | < 4.9 are used. Since⟨qn(−η)q

∗n(ηref)

⟩=

⟨qn(η)q

∗n(−ηref)

⟩for a symmetric system, the correlator is further symmetrized to

enhance the statistics,

rn |n(η) =

⟨qn(−η)q

∗n(ηref) + qn(η)q

∗n(−ηref)

⟩〈qn(η)q

∗n(ηref) + qn(−η)q

∗n(−ηref)〉

. (3)

3

The symmetrization procedure also allows further cancellation of any differences between η and −η in thedetector performance.

If flow harmonics for two-particle correlation from two different η factorize into single-particle harmonics,i.e. 〈vn(η1)vn(η2)〉

2 =⟨vn(η1)

2⟩ ⟨vn(η2)

2⟩, then it is expected that rn |n(η) = 1. Therefore, a value ofrn |n(η) different from unity implies a factorization-breaking effect due to longitudinal flow decorrelations.The deviation of rn |n from unity can be parameterized with a linear function, rn |n(η) = 1 − 2Fnη. Theslope parameter Fn is obtained via a simple linear-regression [21],

Fn =

∑i(1 − rn |n(ηi))ηi

2∑

i η2i

, (4)

where the sum runs over all rn |n data points as a function of η. If rn |n is a linear function in η, thelinear-regression is equivalent to a linear fit, but it is well defined even if rn |n has nonlinear behavior.

The systematic uncertainties on rn |n and slope parameter Fn arise from the uncertainties in the trackselection and reconstruction efficiency, the acceptance reweighting procedure and centrality definition.Most of them enter the analysis through the particle weights in Eq. (1). The systematic uncertainties areestimated by varying different aspects of the analysis, recalculating rn |n and Fn and comparing with thenominal results. The systematic uncertainty associated with the fake tracks is estimated by looseningthe requirements on transverse and longitudinal impact parameter [30], the resulting changes are 1–2%for F2, 1–4% for F3, and 1–9% for F4. The uncertainty associated with ε(η, pT) is evaluated by varyingthe tracking efficiency up and down within its uncertainties, the influence is less than 1% for Fn. Theeffect of reweighting to account for non-uniformity in the detector azimuthal acceptance is studied bysetting d(η, φ) = 1 and repeating the analysis. The change is found to be 0.6–2% for F2 and F3, and 2–7%for F4. The uncertainty due to centrality definition is estimated by varying the mapping between

∑ET

and centrality percentiles, and the influence is 0.5–4% for F2 and F3, and 0.5–8% for F4. In most of thecases, the total systematic uncertainties are smaller than the corresponding statistical uncertainties. Finally,HIJING events with azimuthal anisotropy imposed according to measured vn but without decorrelationsare used to cross check the detector performance: the qn is calculated using both the generated andreconstructed tracks, and the resulting correlators are compared and found to be consistent within theirstatistical uncertainties.

Figure 1 shows the results of rn |n(η) for n = 2, 3 and 4 in six centrality intervals, quantifying the flowdecorrelation between η and −η according to Eq. 2. The rn |n shows an approximately linear decrease withη, implying stronger flow decorrelation at large η. The magnitudes of decorrelation for r3 |3 and r4 |4 aresignificantly larger than that for r2 |2. The choice of |ηref | of 4.0 < |ηref | < 4.9 for r2 |2 is different from3.2 < |ηref | < 4.9 chosen for r3 |3 and r4 |4, in order to reduce sensitivity to non-flow correlation as detailedbelow.

From the rn |n, the slope parameter Fn is calculated via Eq.(4) and summarized in Fig. 2 as a function ofcentrality percentiles. The left panels show the Fn for three |ηref | ranges and right panels show Fn for threepT ranges. Within uncertainties, the F3 and F4 show very weak dependence on centrality. The F2 values,on the other hand, show a strong centrality dependence: they are smallest in the 20-30% centrality intervaland larger towards more central or more peripheral collisions. This strong centrality dependence is relatedto the fact that v2 is dominated by the average elliptic geometry in mid-central collision and therefore isless affected by decorrelations, while it is dominated by fluctuation-driven collision geometry in centraland peripheral collisions [24, 25].

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Figure 1: The η dependence of r2 |2, r3 |3 and r4 |4 in Xe+Xe for six centrality intervals. The |ηref | is chosen to be4.0 < |ηref | < 4.9 for r2 |2, and 3.2 < |ηref | < 4.9 for r3 |3 and r4 |4. The error bars and shaded boxes represent statisticaland systematic uncertainties, respectively.

Figure 2 also shows that F2 has sizable variation between various choices of |ηref | or pT in central andmid-central collisions. The contribution from non-flow correlations associated with back-to-back dijetscould bias the decorrelation signal. Since the gap between η and ηref in the denominator of rn |n is smallerthan the gap between −η and ηref in the numerator, the non-flow contributions from dijets are expectedto increase the denominator more than the numerator and therefore tend to increase the Fn values. Suchnon-flow contributions are expected to be larger for smaller |ηref | or larger pT. However, although thedata show a larger F2 for smaller |ηref | compatible with non-flow, they show a smaller F2 for larger pTopposite to the expectation from non-flow. Within uncertainties, the F3 and F4, as well as the original r3 |3and r4 |4, show no differences between various pT or |ηref | ranges, suggesting that they are not affectedby non-flow. All these trends are qualitatively similar to the previous observation in Pb+Pb collisions at√sNN = 5.02 TeV [21]. Based on results in Fig. 2, 4.0 < |ηref | < 4.9 is chosen for F2, but a wider range3.2 < |ηref | < 4.9 is chosen for F3 and F4 for better precision.

To gain insights on the system-size dependence of the longitudinal fluctuations, Figure 3 compares the Fn

from the Xe+Xe system with those obtained in the Pb+Pb system at √sNN = 5.02 TeV from Ref. [21] as afunction of centrality percentiles (left column) or Npart (right column). For both systems, the F2 shows astrong dependence on centrality percentile and Npart, while both F3 and F4 show rather weak dependences.In the peripheral collisions, the F2 for the two systems agree only when plotted as a function of Npart forNpart < 80, while uncertainties of F3 in the Xe+Xe data are too large to reveal differences from those ofPb+Pb as a function of either centrality percentiles or Npart. When compared as a function of centralitypercentile, both F2 and F3 agree in the most central collisions, but they do not agree as a function of Npartin the large Npart region. In the mid-central collisions, the F2 is much larger in Xe+Xe than Pb+Pb, whilean opposite trend is observed for F3. The F4 values have rather weak dependences on either centrality

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Figure 2: The centrality dependence of Fn calculated for three |ηref | ranges (left) and three pT ranges (right) for n = 2(top row), n = 3 (middle row) and n = 4 (bottom row). The error bars and shaded boxes represent statistical andsystematic uncertainties, respectively.

percentiles or Npart, and they agree between the two systems. The data are also compared with results froma hydrodynamic model with longitudinal fluctuations included [46, 47]. This model describes quantitativelythe behavior of the F2 and F4 in mid-central collisions, but fails to describe the magnitude of the F3 as wellas the splitting between the two systems.

To further understand the relationship between the transverse harmonic flow and its longitudinal fluctuations,Figure 4 compares the ratios of flow decorrelation FXeXe

n /FPbPbn for 0.5 < pT < 3 GeV with ratios of flow

harmonics vXeXen /vPbPbn for 0.5 < pT < 5 GeV from Ref. [30] as a function of centrality percentiles. Whilethe vn-ratios all decrease with centrality, the Fn-ratios increase with centrality; this opposite trend impliesthat when the ratio of average flow is larger, the ratio of its relative fluctuations in the longitudinal directionare smaller and vice versa. Beyond this overall opposite trend, there are other contrasting features between

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Figure 3: The Fn compared between Xe+Xe and Pb+Pb [21] as a function of centrality percentiles (left) and Npart(right) for n = 2 (top row), n = 3 (middle row) and n = 4 (bottom row). The error bars and shaded boxes on the datarepresent statistical and systematic uncertainties, respectively. The results from a hydrodynamic model [46, 47] areshown as solid lines (Xe+Xe) and dashed lines (Pb+Pb) with the vertical error bars denoting statistical uncertainty ofthe model predictions.

the two types of ratios. The F2-ratio is always above one, while the v2-ratio decreases to below one around10-20% centrality; the F2-ratio is larger than the v2-ratio except in the 0–5% centrality interval where thev2-ratio is enhanced due to the presence of deformation of Xe nucleus [31]. The differences between theF3-ratio and the v3-ratio are smaller, but with different centrality dependences: while the v3-ratio decreasesnearly linearly with centrality, the F3-ratio first decreases and then increases as a function of centrality. TheF4-ratio has larger uncertainties, but also shows opposite and much stronger centrality dependence trendcompared with the v4-ratio. The hydrodynamic model from Ref. [31] describes quantitatively the trend ofthe vn-ratio, the agreement with Fn is worse and in particular the model [46, 47] overestimates the F2- andF3-ratio for centrality percentiles beyond 20–30%. This comparison suggests that the longitudinal structure

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Figure 4: The ratio of FXeXen /FPbPb

n from data [21] (solid symbols) and model [46, 47] (solid lines) and vXeXen /vPbPbn

for data [30] (open symbols) and model [31] (dashed lines) as a function of centrality for n = 2 (left), n = 3 (middlepanel) and n = 4 (right), respectively. The error bars and shaded boxes on the data represent statistical and systematicuncertainties, respectively. The vertical error bars on the theory calculations represent the statistial uncertainties.

of the initial geometry may have a different system-size dependence from its transverse structure describedby eccentricities.

In summary, ATLAS presents the first measurement of longitudinal decorrelations for harmonic flow vnin Xe+Xe collisions at √sNN =5.44 TeV, based on 3 µb−1 data. The results are compared with resultsfrom Pb+Pb collisions at √sNN =5.02 TeV. The decorrelation signal increases approximately linearly as afunction of the η separation between the two particles. The slope of this dependence is nearly independentof centrality percentiles and pT for n = 3 and 4. For n = 2, the effect is the smallest in mid-centralcollisions and increases for more central or more peripheral collisions, and the slope also depends on pT.Furthermore, the slope in most of the centrality range is found to be larger in Xe+Xe than Pb+Pb for n = 2,while an opposite trend is observed for n = 3. This reverse ordering was not observed for the v2 and v3when compared between the two collision systems. Hydrodynamic models are found to describe the ratiosof vn between Xe+Xe and Pb+Pb, but fail to describe most of the magnitudes and trends of the ratios of thevn decorrelations between Xe+Xe and Pb+Pb. This suggests that models tuned to describe the transversedynamics may not necessarily describe the longitudinal structure of the initial-state geometry. System-sizedependence of flow decorrelations provides new insights on the dynamics of vn in the longitudinal direction.The measurement provides an important input for the complete modeling of three-dimensional initialconditions of heavy-ion collisions that is used in hydrodynamic models.

8

Appendix

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eXe

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Figure 5: The ratio of FXeXen /FPbPb

n from data [21] (symbols) and model (solid lines) as a function of centrality forn = 2 (left panel), n = 3 (middle panel) and n = 4 (right panel), respectively. The error bars and shaded boxes on thedata represent statistical and systematic uncertainties, respectively. The vertical error bars on the theory calculationsrepresent the statistial uncertainties.

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Figure 6: The F2 (top row), F3 (middle row) and F4 (bottom row) for 3.2 < |ηref | < 4.0 (left), 4.0 < |ηref | < 4.9(middle), and 3.2 < |ηref | < 4.9 (right) from Xe+Xe collisions for three pT intervals. The error bars and shadedboxes represent statistical and systematic uncertainties, respectively.

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Figure 7: The r2 |2(η) compared between three |ηref | ranges in six centrality intervals, one panel for each centralityinterval. The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 8: The r3 |3(η) compared between three |ηref | ranges in six centrality intervals, one panel for each centralityinterval. The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 9: The r4 |4(η) compared between three |ηref | ranges in six centrality intervals, one panel for each centralityinterval. The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 10: The r2 |2(η) compared between three pT ranges in six centrality intervals, one panel for each centralityinterval. The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 11: The r3 |3(η) compared between three pT ranges in six centrality intervals, one panel for each centralityinterval. The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 12: The r4 |4(η) compared between three pT ranges in six centrality intervals, one panel for each centrality.The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 13: The r2 |2(η) compared between Xe+Xe and Pb+Pb in six centrality intervals, one panel for each centrality.The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 14: The r3 |3(η) compared between Xe+Xe and Pb+Pb in six centrality intervals, one panel for each centrality.The error bars and shaded boxes represent statistical and systematic uncertainties, respectively.

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Figure 15: The r4 |4(η) compared between Xe+Xe and Pb+Pb in six centrality intervals, one panel for each centrality.The error bars and shaded boxes represent statistical and systematic uncertainties, respectively

14

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