The azimuthal anisotropy of charged particles produced in sNN=8.16\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s_{\mathrm {NN}}}=8.16$$\end{document} TeV p+Pb collisions is measured with the ATLAS detector at the LHC. The data correspond to an integrated luminosity of 165 nb-1\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm {nb}^{-1}$$\end{document} that was collected in 2016. Azimuthal anisotropy coefficients, elliptic v2\documentclass[12pt]{minimal}
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\begin{document}$$v_2$$\end{document} and triangular v3\documentclass[12pt]{minimal}
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\begin{document}$$v_3$$\end{document}, extracted using two-particle correlations with a non-flow template fit procedure, are presented as a function of particle transverse momentum (pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document}) between 0.5 and 50 GeV. The v2\documentclass[12pt]{minimal}
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\begin{document}$$v_2$$\end{document} results are also reported as a function of centrality in three different particle pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document} intervals. The results are reported from minimum-bias events and jet-triggered events, where two jet pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document} thresholds are used. The anisotropies for particles with pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document} less than about 2 GeV are consistent with hydrodynamic flow expectations, while the significant non-zero anisotropies for pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document} in the range 9–50 GeV are not explained within current theoretical frameworks. In the pT\documentclass[12pt]{minimal}
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\begin{document}$$p_\mathrm {T}$$\end{document} range 2–9 GeV, the anisotropies are larger in minimum-bias than in jet-triggered events. Possible origins of these effects, such as the changing admixture of particles from hard scattering and the underlying event, are discussed.
publisher-imprint-nameSpringervolume-issue-count12issue-article-count73issue-toc-levels0issue-pricelist-year2020issue-copyright-holderEDP Sciences, Societa Italiana di Fisica (SIF) and Springer-Verlag GmbH, DEissue-copyright-year2020article-contains-esmNoarticle-numbering-styleContentOnlyarticle-registration-date-year2020article-registration-date-month1article-registration-date-day7article-toc-levels0toc-levels0volume-typeRegularjournal-productNonStandardArchiveJournalnumbering-styleContentOnlyarticle-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessonline-firstfalsepdf-file-referenceBodyRef/PDF/10052_2020_Article_7624.pdfpdf-typeTypesettarget-typeOnlinePDFissue-online-date-year2020issue-online-date-month3issue-online-date-day3issue-typeRegulararticle-typeOriginalPaperjournal-subject-primaryPhysicsjournal-subject-secondaryElementary Particles, Quantum Field Theoryjournal-subject-secondaryNuclear Physics, Heavy Ions, Hadronsjournal-subject-secondaryQuantum Field Theories, String Theoryjournal-subject-secondaryMeasurement Science and Instrumentationjournal-subject-secondaryAstronomy, Astrophysics and Cosmologyjournal-subject-secondaryNuclear Energyjournal-subject-collectionPhysics and Astronomyopen-accesstrueIntroduction
The collisions of heavy nuclei at relativistic speeds generate hot and dense droplets of matter composed of deconfined quarks and gluons known as the quark–gluon plasma (QGP) [1, 2]. Studies of the QGP at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have yielded a wealth of surprising results that reveal a complex set of QGP-related phenomena. Bulk hadron production, occurring mainly at low transverse momentum (pT≲3\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} \lesssim 3$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}), exhibits significant azimuthal anisotropies that are well described in terms of nearly inviscid hydrodynamic flow of the QGP [1]. The final hadron momentum anisotropies arise from inhomogeneities in the initial spatial distribution of the QGP translated to momentum space via strong differential pressure gradients. These anisotropies are characterised in terms of a Fourier decomposition:Y(ϕ)=G[1+2∑n=1∞vncos(n(ϕ-Ψn))],\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} Y(\phi ) = G\Big [1 + 2\sum ^{\infty }_{n=1} v_{n} \cos (n(\phi -\Psi _{n}))\Big ], \end{aligned}$$\end{document}where vn\documentclass[12pt]{minimal}
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\begin{document}$$v_{n}$$\end{document} are the anisotropy coefficients, Ψn\documentclass[12pt]{minimal}
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\begin{document}$$n^\mathrm {th}$$\end{document}-order orientation of the anisotropy, and the normalization, G, is set by the integral of the distribution. In particular, v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{2}$$\end{document} and v3\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}$$\end{document} are referred to as the elliptic and triangular coefficients, respectively.
In addition, the production of high transverse momentum hadrons (pT≳10\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} \gtrsim 10$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}) is highly suppressed relative to the yields expected from nuclear thickness scaling of proton–proton collision yields [3]. This suppression is understood to result from high momentum transfer parton–parton interactions followed by the outgoing partons losing energy via radiative and collisional processes in the QGP – processes referred to as jet quenching [4–6]. These high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadrons and associated jets are also observed to have a non-zero azimuthal anisotropy [7–9], despite being well outside the nominal domain where the anisotropies are interpreted in terms of hydrodynamic flow. Instead, these anisotropies are understood to also arise from inhomogeneities in the initial spatial distribution of the QGP, but in this case, where the jet quenching effect is stronger for partons traversing longer paths through the QGP and weaker for partons traversing shorter paths [10]. In this way, low- and high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadrons have a common orientation of their azimuthal anisotropy in a given event, because both are correlated with the orientation of the initial geometry of the colliding nucleons. It is notable that, for more than a decade, an outstanding and challenging theoretical puzzle has been how to quantitatively describe both high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadron suppression and azimuthal anisotropy in Pb+Pb collisions [11]. There are a number of proposed explanations for resolving this puzzle in heavy-ion collisions – see Refs. [12–17] for examples.
Measurements in smaller collision systems, pp\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb collisions at the LHC [18–23] and p\documentclass[12pt]{minimal}
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\begin{document}$${}^{3}$$\end{document}He+Au at RHIC [24], indicate significant azimuthal anisotropies for low-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadrons with patterns quite similar to those observed in the larger heavy-ion collision systems. For a recent review see Ref. [25]. These observations have raised the question of whether smaller and shorter-lived droplets of QGP are formed in these smaller collision systems. Indeed, models employing nearly inviscid hydrodynamics for the QGP provide a quantitative description of this large body of data at low pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} [26].
In contrast, measurements aimed at observing signatures of jet quenching in small collision systems have found no such effect. Measurements of hadron and jet pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} indicate production yields consistent with those in pp\documentclass[12pt]{minimal}
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\begin{document}$$pp$$\end{document} collisions scaled up by the expected nuclear thickness in p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb [27–29] and d+Au collisions [30], and that the pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}-balance between dijets or hadron–jet pairs is unmodified in p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb collisions within uncertainties [31, 32]. The ATLAS experiment has also published results for the hadron azimuthal anisotropy up to pT≈12\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} that hint at a non-zero anisotropy extending into the region beyond the usual hydrodynamic interpretation and into the regime of jet quenching [33]. However, it is unlikely that there can be differential jet quenching as a function of orientation relative to the QGP geometry if there is no jet quenching in p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb collisions as observed in the spectra. Thus, there are two related outstanding puzzles, one being the lack of jet quenching observed in the spectra, if indeed small droplets of QGP are formed, and the other being what mechanism can lead to high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadron anisotropies other than differential jet quenching.
This paper presents a measurement of the azimuthal anisotropy of unidentified hadrons as a function of pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} and centrality in sNN=8.16\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb collisions with the ATLAS detector. The measurement is made using two-particle correlations, measured separately for minimum-bias triggered (MBT) events and events requiring a jet with pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} greater than either 75 Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} or 100 Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. There are contributions to the azimuthal correlations from particle decays, jets, dijets, and global momentum conservation, which have traditionally been referred to as ‘non-flow’ [34]. Using this nomenclature, a standard template fitting procedure is applied to subtract non-flow contributions [19, 20]. To decrease the residual influence of the non-flow correlation in the jet events, a novel procedure is used to restrict the acceptance of particles according to the location of jets in the event. Assuming that the two-particle anisotropy coefficients are the products of the corresponding single-particle coefficients (factorisation), the elliptic and triangular anisotropy coefficients, v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}$$\end{document}, are reported as a function of pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}. Additionally, v2\documentclass[12pt]{minimal}
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ATLAS detector
The ATLAS experiment [35] at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and nearly 4π\documentclass[12pt]{minimal}
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In this analysis, a two-level trigger system was used to select events, with a first-level (L1) trigger implemented in hardware followed by a software-based high-level trigger (HLT) which reconstructs the event in a manner similar to the final offline reconstruction. Events used for the measurements presented in this paper were selected using several triggers. MBT events were selected by a trigger that requires a signal in at least one minimum-bias trigger scintillator counter at L1 [38] followed by the requirement of at least one reconstructed track at the HLT stage. Events with a high-pT\documentclass[12pt]{minimal}
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\begin{document}$$\left| \eta \right| < 3.2$$\end{document}). These events were first required to have energy deposits at L1 that are compatible with the presence of a jet and then to pass various thresholds for the jet transverse energy at the HLT stage.
Data and event selection
During p+Pb data-taking in 2016, the LHC was configured with a beam composed of protons with an energy of 6.5 Te\documentclass[12pt]{minimal}
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\begin{document}$$\mathrm {nb}^{-1}$$\end{document} of luminosity. In addition, data were selected by the high-level jet triggers with transverse energy thresholds of 75 Ge\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb luminosity, respectively.
Events selected by the triggers described above were reconstructed offline following procedures that were optimised for the Run-2 detector configuration [39]. Events are required to have at least one reconstructed vertex. To reduce the contribution from events with multiple in-time p\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} > 0.4$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. That is, events are only allowed to have one vertex with seven or more associated tracks. Two classes of jet events were defined by requiring an offline jet with pT>75\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} respectively, and were drawn from the jet-triggered event samples with the analogous online thresholds. The trigger efficiency, given this offline selection, was greater than 97% for both jet samples.
Events were further characterised by the sum of the transverse energy in the FCal module in the direction of the Pb beam, ΣETPb\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma E_{\text {T}}^\mathrm{{Pb}}$$\end{document}. The event centrality is defined as the ΣETPb\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma E_{\text {T}}^\mathrm{{Pb}}$$\end{document} percentile of the events in minimum-bias collisions, after accounting for the inefficiency introduced by the trigger and event selection criteria, and was determined in a way similar to previous analyses of Run-1 p+Pb data at sNN=5.02Te\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s_{_\text {NN}}} = 5.02~\text {Te}\text {V}$$\end{document} [27, 40]. Events within the 0–90% centrality range were used in this analysis, with low (high) values corresponding to high-ΣETPb\documentclass[12pt]{minimal}
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\begin{document}$$\Sigma E_{\text {T}}^\mathrm{{Pb}}$$\end{document}) events with large (small) overall particle multiplicity. Since the acceptance of the FCal is separate from that of the ID, this centrality definition has the benefit of reducing event-selection-induced biases in the measured quantities [41].
Track and jet reconstruction
The reconstruction, selection, and calibration of charged-particle tracks and calorimetric jets, and their performance as determined using Monte Carlo (MC) simulations, are described below.
Charged-particle tracks and collision vertices are reconstructed in the ID using the algorithms described in Ref. [39]. Inner detector tracks with pT>0.4\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |<2.5$$\end{document} were required to satisfy a set of quality criteria similar to those described in Ref. [19]. The total number of reconstructed ID tracks satisfying these selection criteria in a given event is called the multiplicity or Nchrec\documentclass[12pt]{minimal}
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\begin{document}$$N_{\mathrm {ch}}^{\mathrm {rec}}$$\end{document}. The reconstruction and selection efficiency for primary [42] charged hadrons to meet these criteria was determined using a sample of 3 million minimum-bias p+Pb events simulated by the Hijing generator [43]. Events were generated with both beam configurations. The ATLAS detector response to the generated events was determined through a full Geant 4 simulation [44, 45], and the simulated events were reconstructed in the same way as the data. Over the measured kinematic range, the efficiency varies from approximately 50%\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} at mid-rapidity.
Jets are reconstructed using energy deposits in the calorimeter system, η<4.9\documentclass[12pt]{minimal}
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\begin{document}$$\left| \eta \right| < 4.9$$\end{document}, in a range partially overlapping with both the ID and the FCal used to determine centrality. The reconstruction closely follows the procedure used in other measurements for Pb+Pb and pp collisions [46, 47]. Jets are measured by applying the anti-kt\documentclass[12pt]{minimal}
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\begin{document}$$R=0.4$$\end{document} to energy deposits in the calorimeter. No jets with pT<15\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} are considered. An iterative procedure is used to obtain an event-by-event estimate of the η\documentclass[12pt]{minimal}
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\begin{document}$$\eta $$\end{document}-dependent underlying-event energy density, while excluding jets from that estimate. The jet kinematics are corrected for this background and for the detector response using an η\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} $$\end{document}-dependent calibration derived from fully simulated and reconstructed Pythia 8 [50] hard-scattering events configured with the NNPDF23LO parton distribution function set [51] and the A14 set of tuned parameters [52] to model non-perturbative effects. An additional, small correction, based on in situ studies of jets recoiling against photons, Z bosons, and jets in other regions of the calorimeter, is applied [53, 54]. Simulation studies show that for jets with pT>75\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} resolution below 10% after the calibration procedure.
Analysis procedure
This analysis is based on previous ATLAS two-particle correlation studies [19, 20]. To construct the two-particle correlation functions, the selected inner-detector tracks with pT>0.4\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} are divided into two sets, referred to as A- and B-particles in this paper, although they are sometimes referred to as trigger and associated particles in the literature. To reduce the contribution of non-flow correlations from decays and jets, two restrictions are placed on A–B particle pairs drawn from the two sets. First, as was done in previous analyses [19, 20], the particles are required to be separated in pseudorapidity with |ΔηAB|=|ηB-ηA|>2\documentclass[12pt]{minimal}
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\begin{document}$$|\Delta \eta ^\mathrm {AB}| = |\eta ^\mathrm {B}-\eta ^\mathrm {A}| > 2$$\end{document}. This requirement removes the short-range decay and jet fragmentation structure, while emphasising global, early-time correlations. Due to the enhanced contribution from jet correlations in the jet-triggered events, an additional constraint was developed for this analysis. Namely, B-particles are required to be separated in pseudorapidity by one unit from all reconstructed jets with pTjet>15\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} ^{\mathrm {jet}}>15$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}, i.e. |ΔηjB|=|ηB-ηjet|>1\documentclass[12pt]{minimal}
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\begin{document}$$|\Delta \eta ^{\mathrm {jB}}| = |\eta ^\mathrm {B}-\eta ^{\mathrm {jet}}| > 1$$\end{document}. This latter requirement is only applied to the jet-triggered events, and in this way, the jets act as a source of high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} A-particles but contribute few B-particles.
The correlation functions, S(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$S(\Delta \phi )$$\end{document}, are defined as the yields of particle pairs passing the above event and pair selection, binned in Δϕ=ϕA-ϕB\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \phi =\phi ^\mathrm {A}-\phi ^\mathrm {B}$$\end{document}, and normalised by the total number of A-particles. Corrections for the imperfect trigger and tracking efficiencies are applied as weights to the entries of the correlation functions. A mixed-event correction, M(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$M(\Delta \phi )$$\end{document}, is generated by correlating A-particles from one event with B-particles from a different event with a vertex z-position differing by less than 10 mm and a number of reconstructed charged particles (Nchrec\documentclass[12pt]{minimal}
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\begin{document}$$N_{\mathrm {ch}}^{\mathrm {rec}}<100$$\end{document} and less than 20 for Nchrec>100\documentclass[12pt]{minimal}
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\begin{document}$$N_{\mathrm {ch}}^{\mathrm {rec}}> 100$$\end{document}. Thus, the mixed events contain only trivial detector acceptance effects and no physical correlations. To reduce the statistical uncertainty introduced by the correction, each event is mixed with five others meeting the above vertex z and Nchrec\documentclass[12pt]{minimal}
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\begin{document}$$N_{\mathrm {ch}}^{\mathrm {rec}}$$\end{document} conditions. The corrected correlation is, then, Y(Δϕ)=S(Δϕ)/M(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$Y(\Delta \phi )=S(\Delta \phi )/M(\Delta \phi )$$\end{document}, where M(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$S(\Delta \phi )$$\end{document}. Jet events are mixed with other jet events, and the |ΔηjB|\documentclass[12pt]{minimal}
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\begin{document}$$|\Delta \eta ^{\mathrm {jB}}|$$\end{document} condition is applied with respect to the jets in the A-particle event only. Thus, the B-particle acceptance is consistent between the same- and and mixed-event correlations.
To extract the anisotropy coefficients while accounting for residual non-flow, the ATLAS template fitting procedure, as used for previous results [19, 20], is applied to Y(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$Y(\Delta \phi )$$\end{document}. In this procedure, Y(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$Y(\Delta \phi )$$\end{document} is found for two different selections of event activity quantified by centrality: a central selection, Ycent(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$Y^{\mathrm {cent}}(\Delta \phi )$$\end{document}, and a peripheral selection, Yperi(Δϕ)\documentclass[12pt]{minimal}
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\begin{document}$$Y^{\mathrm {cent}}(\Delta \phi )$$\end{document} is expressed asYcent(Δϕ)=FYperi(Δϕ)+G[1+2∑n=24vn,ncos(nΔϕ)],\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} Y^\mathrm {cent}(\Delta \phi ) = FY^\mathrm {peri}(\Delta \phi ) + G\Big [1 + 2\sum ^{4}_{n=2} v_{n,n} \cos (n\Delta \phi ) \Big ]\,, \end{aligned}$$\end{document}where F and each vn,n\documentclass[12pt]{minimal}
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\begin{document}$$\chi ^2$$\end{document} minimiser [55], accounting for correlations between parameters.
Figure 1 shows an example of two template fits using jet-triggered events with jet pT>100\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \phi \approx \pi $$\end{document}. Removing much of the jet correlation in this way reduces the overall sensitivity to the template method assumption that the shape of the non-flow contribution is the same for the central and peripheral selections. However, violation of this assumption will introduce distortions that could potentially bias the harmonic coefficients. This is explicitly tested by varying the centrality selection of the peripheral template, as discussed further in Section 6. Two additional examples of template fits from the jet-triggered events with jet pT>100\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} and with the B-particle jet rejection are plotted in Figure 2. These show the behaviour of the template fits for high A-particle pT\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. Both require 3.5<pTA<4.0Ge\documentclass[12pt]{minimal}
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\begin{document}$$3.5<p_{\text {T}} ^\mathrm {A}<4.0~\text {Ge}\text {V}$$\end{document} and are made with 60–90% peripheral selection and 0–5% central selection. The left plot is made with no selection on the B-particles and the right plot is made requiring the B-particles to have |ΔηjB|>1\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} ^\mathrm {jet} > 15~\text {Ge}\text {V}$$\end{document} in the event. In the upper panels, the open circles show the scaled and shifted peripheral template with uncertainties omitted, the closed circles show the central data, and the red line shows the fit (template and harmonic functions). The blue dashed line shows the second-order harmonic component, Y2ridge\documentclass[12pt]{minimal}
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\begin{document}$$n=3$$\end{document} contributions to the sum in Eq. 1, respectively). The lower panels show the difference between the central data and the peripheral template along with the second and third harmonic functions. The resulting v2,2\documentclass[12pt]{minimal}
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\begin{document}$$16<p_{\text {T}} ^\mathrm {A}<100~\text {Ge}\text {V}$$\end{document}. In the upper panels, the open circles show the scaled and shifted peripheral template with uncertainties omitted, the closed circles show the central data, and the red line shows the fit (template and harmonic functions). The blue dashed line shows the second-order harmonic component, Y2ridge\documentclass[12pt]{minimal}
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If the particle momentum correlations originate from a global field, as is the case for collective expansion, the vn,n\documentclass[12pt]{minimal}
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\begin{document}$$v_{n,n}$$\end{document} will factorise such that vn,n(pTA,pTB)=vn(pTA)·vn(pTB)\documentclass[12pt]{minimal}
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\begin{document}$$v_{n,n}(p_{\text {T}} ^\mathrm {A},p_{\text {T}} ^\mathrm {B}) = v_n(p_{\text {T}} ^\mathrm {A})\cdot v_n(p_{\text {T}} ^\mathrm {B})$$\end{document}. By assuming this relation and making specific pT\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} v_n(p_{\text {T}} ^\mathrm {A})=v_{n,n}(p_{\text {T}} ^\mathrm {A},p_{\text {T}} ^\mathrm {B})/ \sqrt{v_{n,n}(p_{\text {T}} ^\mathrm {B},p_{\text {T}} ^\mathrm {B})}, \end{aligned}$$\end{document}where vn,n(pTA,pTB)\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}, although the dependence of the extracted anisotropy on this choice is explored in Section 7.
The relative yield of particle pairs entering the correlation functions is estimated assuming a simple, two-component model of particle production. Particles are assumed to be produced either by hard scattering (HS) processes, such as jet production, or by soft underlying event (UE) processes. With this assumption, the correlation functions are constructed from pairs pulled from a mixture of the two sources. Particle pairs can be formed in the following four A–B combinations: UE–UE, UE–HS, HS–UE, and HS–HS. The event-by-event yields of the UE and HS processes are estimated by classifying the charged particles according to their azimuthal orientation relative to the leading jet or, in the case of MBT events that contain no jets with pT>15\documentclass[12pt]{minimal}
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\begin{document}$$|\eta |<4.9$$\end{document}, relative to the leading hadron. The following regions are defined relative to this leading vector:
Then, assuming that HS particles are completely contained in the towards region and the UE particles are distributed uniformly in azimuth, the following relations are inferred:NUE=2Ntrans,NHS=Ntoward-Ntrans,\documentclass[12pt]{minimal}
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\begin{document}$$N_\mathrm {toward}$$\end{document} and are, thus, insensitive to event-by-event fluctuations. However, it is not possible to classify individual particles. It should be noted that the assumptions used in this derivation are likely not perfect; for example, the UE is not uniformly distributed in ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}, event by event, due to the presence of azimuthal anisotropy. The leading object may be more likely to be oriented with the anisotropy, in which case the UE yield would be underestimated and the HS yield overestimated. However, the analysis proceeds with the assumptions as given and includes no additional uncertainty for this potential effect.
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\begin{document}$$\Delta \eta ^\mathrm {jB}$$\end{document} rejections produce a geometric correlation between the yields of A- and B-particles and, thus, the number of pairs is not the simple product of the two individual yields. Accounting for the dependencies, the total yield of particle pairs can be expressed in the following wayYX--Z=∫-2.52.5dNXA(ηA)dηA[∫25d2NZB(ηA,|ΔηAB|)dηAd|ΔηAB|d|ΔηAB|]dηA,\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} Y_\text {X--Z}=\int _{-2.5}^{2.5} \frac{\mathrm {d}N^\mathrm {A}_\mathrm {X}(\eta ^\mathrm {A})}{\mathrm {d}\eta ^\mathrm {A}} \Bigg [ \int _2^5 \frac{\mathrm {d}^2N^\mathrm {B}_\mathrm {Z}(\eta ^\mathrm {A},|\Delta \eta ^\mathrm {AB}|)}{\mathrm {d}\eta ^\mathrm {A} \mathrm {d}|\Delta \eta ^\mathrm {AB}|} \mathrm {d}|\Delta \eta ^\mathrm {AB}| \Bigg ] \mathrm {d}\eta ^\mathrm {A} \, , \end{aligned}$$\end{document}where X–Z could be any pairwise combination of UE and HS. In the case of jet events, the ΔηjB\documentclass[12pt]{minimal}
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\begin{document}$$\Delta \eta ^\mathrm {AB}$$\end{document} distributions so it’s effects are taken into account.
Systematic uncertainties
The systematic uncertainties fall into two categories: those associated with both the MBT and jet events and those associated with only the jet events. The uncertainties are determined by assessing the difference between the nominal value of v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}$$\end{document} and the value after a given variation. Unless otherwise stated, the uncertainties are defined as asymmetric one-standard-deviation errors. The final uncertainty is the quadrature sum of the uncertainty from each individual source. The relative downward and upward systematic uncertainties from different sources and all sources combined are shown for v2\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}.
For both the MBT and jet events, the sensitivity to the trigger and tracking efficiency corrections was assessed by removing each. This variation (‘Track/trig Eff.’ in Table 1) yields a 0–2% (2–4%) difference for MBT (jet) events, depending on track pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}, and is subdominant. In the construction of the correlation functions, the uncertainty in the mixed-event correction was again found by removing it from the analysis. This variation results in an uncertainty that vanishes at low pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} but grows to 20% (10%) at high pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} for MBT (jet) events, but remains subdominant to statistical uncertainties over the whole pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} range. Regarding the template fitting procedure, the centrality range for the peripheral reference selection was varied from the nominal 60–90% to 50–70% and 70–90%. This variation (‘Peri. reference’) results in an uncertainty of about 2% at low pT\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} depending on the event trigger. This last uncertainty is dominant in this category for most of the pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}, the sensitivity of the measurements in MBT events to the mixed event correction and reference selection is significantly higher than in jet events; this is particularly noticeable for the v3\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} are 5–10 times larger than in the jet-triggered events.
The following set of uncertainties is associated with jet events only. To assess the sensitivity to the uncertainty in the jet energy scale and the impact of imperfect trigger efficiency, the jet pT\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}, respectively. This variation (‘Trig jet pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} ’) results in a symmetric uncertainty that is smaller than 1% at low particle pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} and that increases to about 10% with increasing pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}. It is subdominant to other sources in this category. The jets used in the B-particle jet rejection were varied to include only jets with pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} are incorporated as a symmetric uncertainty that is subdominant to other sources in this category. The ΔηjB\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}, where it is the dominant positive uncertainty. Finally, an uncertainty is assigned to account for the potential of the UE to bias the event selection. The azimuthal modulation of the UE increases the reconstructed pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} threshold will bias the events to have more jets correlated with the flow plane. The impact of this effect on the measured results was assessed in simulation by mixing jet events with a realistic UE containing azimuthal anisotropy. The resulting uncertainty only affects v2\documentclass[12pt]{minimal}
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Results
Figure 3 shows the extracted second- (v2\documentclass[12pt]{minimal}
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\begin{document}$$4<p_{\text {T}} ^\mathrm {A}<9$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} in pTjet>100\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} events, where it is within about 30–40%. Although the large uncertainties prevent strong conclusions from being drawn, there is a hint of a difference in behaviour at high pTA\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} ^\mathrm {A}$$\end{document} where the factorisation breaking is greater for MBT events than for jet events. This result could be due to the B-particle jet rejection scheme used for the jet events. Correlations resulting from hard-process, e.g. from back-to-back jets, specifically violate the factorisation assumption, and the B-particle jet rejection dramatically limits the contribution from these processes from entering the correlation functions in jet events. However, the correlations from MBT events have no such rejection, and could, therefore, be more susceptible to hard-process correlations at high pTA\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} ^\mathrm {A}$$\end{document}.
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\begin{document}$$v_{2}$$\end{document} plotted as a function of centrality for MBT events (black squares), events with jet pT>75\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document} (bottom). Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
Figure 5 shows v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{2}$$\end{document} plotted as a function of centrality for MBT events and both classes of jet events. The results are divided into three regions in A-particle pT\documentclass[12pt]{minimal}
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\begin{document}$$v_{2}$$\end{document} as the collisions become more peripheral.
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\begin{document}$$\text {Ge}\text {V}$$\end{document} compared with theoretical calculations from Ref. [14]. This theoretical calculation, within the jet quenching paradigm, invokes a stronger parton coupling to the QGP near the transition temperature, which helps to reduce the tension in simultaneously matching the nucleus–nucleus high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadron spectrum suppression and the azimuthal anisotropy v2\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb geometries referred to as ‘size a’ and ‘size b’, where the latter has a smaller initial QGP volume. The predictions are slightly lower than the data for both v2\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} hadrons, as expressed by the quantity RpPb=d2NpPb/dpTdy/(TpPb×d2σpp/dpTdy)\documentclass[12pt]{minimal}
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\begin{document}$$R_{p\mathrm {Pb}} = \mathrm {d}^{2}N_{p\mathrm {Pb}}/\mathrm {d}p_{\text {T}} \mathrm {d}y / (T_{p\mathrm {Pb}} \times \mathrm {d}^{2}\sigma _{pp}/\mathrm {d}p_{\text {T}} \mathrm {d}y)$$\end{document} where TpPb\documentclass[12pt]{minimal}
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\begin{document}$$T_{p\mathrm {Pb}}$$\end{document} represents the nuclear thickness of the Pb nucleus, as determined via a Monte Carlo Glauber calculation [56]. Shown in comparison are published experimental results from ATLAS and ALICE for RpPb\documentclass[12pt]{minimal}
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\begin{document}$$R_{p\mathrm {Pb}} = 1$$\end{document} [41, 57]. The ALICE experiment uses the notation QpPb\documentclass[12pt]{minimal}
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\begin{document}$$Q_{p\mathrm {Pb}}$$\end{document} for the same quantity to describe a bias that may exist due to the centrality categorisation. There are uncertainties in the experimental measurements related to the centrality or multiplicity selection in p\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} azimuthal anisotropy and the lack of yield suppression.
Coefficients v2\documentclass[12pt]{minimal}
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\begin{document}$$Q_{p\mathrm {Pb}}$$\end{document} data from ALICE [41]. Theoretical calculations (red/orange lines) from Ref. [14] are also shown in this panel; the dotted line gives the results of the ‘size a’ configuration and the dash-dotted line gives the results of the ‘size b’ configuration
Figure 7 shows the MBT v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}$$\end{document} substantially below the experimental results for pT=\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. It should be noted that calculations presented in Ref. [26] are performed, consistently between the hydrodynamic and eremitic components, only for massless partons and with an ideal equation of state. Thus, one does not expect quantitative agreement and is looking for rather qualitative trends. More sophisticated treatments in the hydrodynamic regime result in better quantitative agreement with the anisotropy coefficients at low pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} [58, 59]. It is worth highlighting that traditional parton energy-loss calculations connect the high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} particles. The same is true with this eremitic calculation, and thus, it should also be in contradistinction to p\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb high-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} experimental data indicating almost no suppression, i.e. jet quenching.
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\begin{document}$$p$$\end{document}+Pb collisions from the MBT event sample. Theoretical calculations relevant to the low-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} regime from an ‘eremitic’ framework from Romatschke [26] are also shown. The lines are Padé-type fits connecting the two regimes, where the red dotted line is for v2\documentclass[12pt]{minimal}
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\begin{document}$$v_{2}$$\end{document} and the blue dash-dotted line is for v3\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}$$\end{document}. Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
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\begin{document}$$p_{\text {T}}$$\end{document} anisotropies could lie in an initial-state effect, potentially encoded in a model such as Pythia 8. Shown in Figure 8 is a Pythia 8 calculation with hard2pp\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb events generated in the default Angantyr framework [60]. It is emphasised that this version of Pythia does not include the recently developed string–string, or so-called string shoving, implementation [61]. The generator-level charged particles are then processed with the entire analysis procedure, including the non-flow template fit. The result is a negative v2,2\documentclass[12pt]{minimal}
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\begin{document}$$v_{2,2}$$\end{document} for all momenta, in contradistinction to the experimental data. Further investigation reveals that Pythia 8 run in ‘hard’ scattering mode has correlations with large pseudorapidity separation between particle pairs as a result of the specific implementation of initial-state radiation. This correlation is reduced in high-multiplicity events because of the large number of uncorrelated UE particles, and thus results in a negative v2,2\documentclass[12pt]{minimal}
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\begin{document}$$v_{2,2}$$\end{document} after subtracting the non-flow contribution.
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\begin{document}$$p_{\text {T}} {} > 100$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. The two top plots show example correlation functions, with template fits, from a low particle-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} selection (top right). In the upper panels of the two top plots, the open circles show the scaled and shifted peripheral template with uncertainties omitted, the closed circles show the central data, and the red histogram shows the fit (template and harmonic functions). The blue dashed line shows the second-order harmonic component, Y2ridge\documentclass[12pt]{minimal}
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\begin{document}$$n=3$$\end{document} contributions to the sum in Eq. 1, respectively). The lower panels show the difference between the central data and the peripheral template along with the second and third harmonic functions. The resulting v2,2\documentclass[12pt]{minimal}
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Figure 9 shows the published Pb+Pb results for v2\documentclass[12pt]{minimal}
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\begin{document}$$\text {Te}\text {V}$$\end{document} [62]. Results from MBT and jet pT>100\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb events are plotted as black squares and orange diamonds, respectively, and those from Pb+Pb are plotted as green circles. Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
Returning to the issue of the difference in the intermediate pT\documentclass[12pt]{minimal}
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\begin{document}$$p$$\end{document}+Pb MBT and jet event results, the source of hadrons in this region should be considered. As detailed previously, in a highly simplified picture one can classify hadrons as originating from hard scatterings (HS) or from the underlying event (UE). Thus, pairs of particles of A and B types can come from the combinations HS–HS, HS–UE, UE–HS, and UE–UE. Figure 10 presents the measured pair fractions for both MBT and jet, 0–5% central events plotted as a function of the A-particle pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} in each case, and HS–UE combinations dominate at high pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}. Combinations with HS B-particles are sub-dominant, because there are fewer jet particles than UE particles in central events; for the jet selected events, these combinations are further suppressed by the B-particle jet rejection condition. Figure 11 shows the dominant contributions from the MBT and jet events overlaid. Although the same qualitative behaviour is found in each case, the point at which the HS–UE pairs become dominant over the other combinations is at a lower pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} for jet events than for MBT events.
This behaviour can also be seen in Figure 12, in which the pair fractions are plotted as a function of centrality, and again, the values for MBT and jet events are overlaid. The centrality-dependent results are plotted for low, medium, and high A-particle pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} ranges in the same way as in Figure 5. At low pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} transition region, MBT events have a larger UE–UE contribution and smaller HS–UE contribution compared to jet events. At high pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}, central events show a difference between UE–UE and HS–UE that is reduced in more-peripheral events and absent for more peripheral than 25% centrality. The overall trend of the pair fractions with centrality is quite similar to that of v2\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}, and significant centrality dependence in addition to MBT–jet event ordering in the mid-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} transition region.
Particle pair yield composition fractions for MBT events (top), events with jet pT>75\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}. Green and blue open circles represent HS–HS and UE–HS pairs, respectively, and red and violet closed circles represent UE–UE and HS–UE pairs, respectively. Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
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\begin{document}$$p_{\text {T}}$$\end{document}. Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
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\begin{document}$$\text {Ge}\text {V}$$\end{document} (bottom). Statistical uncertainties are shown as narrow vertical lines on each point, and systematic uncertainties are presented as coloured boxes behind the points
Thus, a potential explanation for the lower v2\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} region is simply that, in that region, the HS particles have lower anisotropy coefficients than UE particles, and MBT events have a larger fraction of UE–UE pairs than jet-triggered events. In the low and high pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} regions, the same types of pairs dominate in both the MBT and jet-triggered events, namely UE–UE and HS–UE respectively, and hence the anisotropy coefficients agree between the event samples. If this explanation is correct, it also aids in understanding Figure 9 in which there is a significant difference between the p\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} region, because the relative pair fractions are potentially significantly different.
This particle mixing picture is attractive in that it naturally explains the general shape of the v2(pT)\documentclass[12pt]{minimal}
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\begin{document}$$v_{3}{}{}(p_{\text {T}})$$\end{document} distributions as well as the ordering of the different event samples. However, it is noted that the correspondence between the differences in the flow coefficients and pair fractions is not quantitative; the differences in the flow coefficients are fractionally much larger than the differences in the pair fractions. Thus, there are either additional sources of correlation or our assumptions are violated in some way (e.g. the two assumed HS and UE sources are too simplistic or the measured pair fractions do not accurately represent the sources, as is discussed in Section 5). That said, for particle pT>20\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document}) particles, irrespective of the pair fractions.
Conclusion
This paper presents Fourier coefficients of the azimuthal distribution of unidentified charged particles from 165 nb-1\documentclass[12pt]{minimal}
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\begin{document}$$v_{2}$$\end{document}, monotonically decreasing from central to peripheral events. This behaviour can be qualitatively explained within a simplified two-component model of particle production, in which the magnitude of the correlation in this region is determined by the admixture of charged particles originating from soft and hard processes in the given event selection. The measured particle pair yields support this qualitative argument.
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\begin{document}$$v_n$$\end{document} results are again consistent between MBT and jet events. Although the uncertainties in the v3\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}. This result cannot be explained in the theoretical context of jet quenching or eremitic expansion calculations while simultaneously describing the observed lack of suppression of high-pT\documentclass[12pt]{minimal}
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Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.
We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, UK; DOE and NSF, USA. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and Compute Canada, Canada; COST, ERC, ERDF, Horizon 2020, and Marie Skłodowska-Curie Actions, European Union; Investissements d’ Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain; The Royal Society and Leverhulme Trust, UK.
The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [64].
Data Availability Statement
This manuscript has no associated data or the data will not be deposited.[Authors' comment: All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/).This information is taken from the ATLAS Data Access Policy, which is a public document that can be downloaded from http://opendata.cern.ch/record/413 [opendata.cern.ch].]
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\begin{document}$$\sqrt{s}= 5.02$$\end{document} TeV, Phys. Lett. B 774, 351 (2017), arXiv: 1701.07145 [nucl-th]BierlichCGustafsonGLönnbladLShahHThe Angantyr model for Heavy-Ion Collisions in PYTHIA8JHEP2018101342018JHEP...10..134B10.1007/JHEP10(2018)134C. Bierlich, Microscopic collectivity: The ridge and strangeness enhancement from string-string interactions, Nucl. Phys. A 982, 499 (2019), The 27th International Conference on Ultrarelativistic Nucleus-Nucleus Collisions: Quark Matter 2018ATLAS Collaboration, Measurement of the azimuthal anisotropy of charged particles produced in sNN=5.02\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{s_{NN}} = 5.02$$\end{document} TeV Pb+Pb collisions with the ATLAS detector, Eur. Phys. J. C 78, 997 (2018). arXiv: 1808.03951 [hep-ex]LoizidesCKaminJd’EnterriaDImproved Monte Carlo Glauber predictions at present and future nuclear collidersPhys. Rev. C2018970549102018PhRvC..97e4910L10.1103/PhysRevC.97.054910ATLAS Collaboration, ATLAS Computing Acknowledgements, ATL-GEN-PUB-2016-002, https://cds.cern.ch/record/2202407
ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r,ϕ)\documentclass[12pt]{minimal}
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\begin{document}$$(r, \phi )$$\end{document} are used in the transverse plane, ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document} being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ\documentclass[12pt]{minimal}
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\begin{document}$$\theta $$\end{document} as η=-lntan(θ/2)\documentclass[12pt]{minimal}
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\begin{document}$$\eta = -\ln \tan (\theta /2)$$\end{document}. Transverse momentum and transverse energy are defined as pT=psinθ\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} = p \sin \theta $$\end{document} and ET=Esinθ\documentclass[12pt]{minimal}
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\begin{document}$$E_{\text {T}} = E \sin \theta $$\end{document}, respectively. Angular distance ΔR\documentclass[12pt]{minimal}
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\begin{document}$$\Delta {R}$$\end{document} is defined as (Δη)2+(Δϕ)2\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{ (\Delta \eta )^2 + (\Delta \phi )^2 }$$\end{document}.
The term ‘hard’ refers to Pythia 8 run with the following settings: HardQCD:all=on, PartonLevel:MPI=off, and containing a jet with pT>100\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} > 100$$\end{document}Ge\documentclass[12pt]{minimal}
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\begin{document}$$\text {Ge}\text {V}$$\end{document}.