IV. CONCLUSIONS
We have shown that ATLAS results on ρ n **in** Pb+Pb
**collisions** can be explained by hydrodynamics. The mech- anism driving the **correlation** **between** the **mean** trans- verse **momentum** **and** **anisotropic** **flow** **in** Pb+Pb colli- sions can be traced back to the initial density profile, i.e., to the early stages of the collision. This implies **in** turn that this observable has limited sensitivity to the details of the hydrodynamic expansion **in** general, **and** to the transport coefficients of the fluid **in** particular, as nicely confirmed by the hydrodynamic results (Fig. 9) of Ref. [42]. We have found that hp t i fluctuations are driven

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associated ridge particles was detected, also consistent with triangular **flow**.
VI. SUMMARY
We have introduced the concepts of participant triangularity **and** triangular **flow**, which quantify the triangular anisotropy **in** the initial **and** final states of **heavy**-**ion** **collisions**. It has been shown that inclusive **and** triggered two-particle azimuthal correlations at large η **in** **heavy**-**ion** **collisions** are well described by the first three Fourier components. It has been demonstrated that event-by-event fluctuations lead to a finite triangularity value **in** Glauber Monte Carlo events **and** that this triangular anisotropy **in** the initial geometry leads to a triangular anisotropy **in** particle production **in** the AMPT model. The third Fourier coefficient of azimuthal correlations at large pseudorapidity separations have been found to be dominated by triangular **flow** **in** the model. We have studied the ratio of the third **and** second Fourier coefficients of azimuthal correlations **in** experimental data **and** the AMPT model as a function of centrality, pseudorapidity range **and** trigger particle **momentum**. A qualitative agreement **between** data **and** model has been observed. This suggests that the ridge **and** broad away-side features observed **in** two-particle **correlation** measurements **in** Au + Au **collisions** contain a significant, **and** perhaps dominant, contribution from triangular **flow**. Our findings support previous evidence from

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After the inspection of the centrality dependence of Fig. 2, we show **in** Fig. 3 the rapidity dependence of RZ for the most central **collisions**. For this purpose we use the proton yield (A) whose relatively high cross sec- tions permit a fine subdivision of the rapidity bins. **In**- verting projectile **and** target changes, as expected, the sign of the RZ-values; besides that, both results agree within errors. The dashed-dotted line (±0.393 y (0) ) describes an average of both measurements (being the same except for the sign) **and** can be used to deconvo- lute the overall measured rapidity distribution dN/dy (0) (Fig. 3b) for Ru+Ru into separated rapidity distribu- tions for the projectile- **and** for the target-nucleons. For each rapidity bin, the number of projectile (target) nu- cleons was obtained as Npr = 0.5 (1 + 0.393 y (0) ) N (Ntr = 0.5 (1 − 0.393 y (0) ) N ). The overall dN/dy (0) distribution was obtained by extrapolating the measured **transverse** **momentum** spectra, within the backward de- tector acceptance, according to the procedure described **in** [5]. After deconvolution a shift **between** the two de- duced rapidity distributions emerges, demonstrating that a memory of the initial target/projectile translatory mo- tion survives throughout a central collision.

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respectively, **and** Ψ n is the n-th harmonic symmetry plane angle. For a smooth matter distribution **in** the
colliding nuclei, the symmetry planes of all harmonics coincide with the reaction plane defined by the beam direction **and** the impact parameter, the vector connecting the centers of the two colliding nuclei at closest approach. **In** this case, for particles produced at midrapidity, all odd Fourier coefficients are zero by symmetry. Due to event-by-event fluctuations of the positions of the participating nucleons inside the nuclei, the shape of the initial energy density of the **heavy**-**ion** collision **in** general is not symmetric with respect to the reaction plane, **and** the Ψ n may deviate from the reaction plane. This gives rise to

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3 Institut de physique th´ eorique, Universit´ e Paris Saclay, CNRS, CEA, F-91191 Gif-sur-Yvette, France
(Dated: July 13, 2015)
Viscous hydrodynamics is commonly used to model the evolution of the matter created **in** an ultra-relativistic **heavy**-**ion** collision. It provides a good description of **transverse** **momentum** spectra **and** **anisotropic** **flow**. These observables, however, cannot be consistently derived using viscous hydrodynamics alone, because they depend on the microscopic interactions at freeze-out. We derive the ideal hydrodynamic limit **and** the first-order viscous correction to **anisotropic** **flow** (v 2 , v 3 **and** v 4 )

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sions above 35% centrality [11]. This has been recently shown to result from a slight upward curvature of the relation **between** v 2 **and** ε 2 [12].
**In** Sec. II, we show that these deviations can be quan- tified by adding a cubic response term to the usual linear response. We study the variation of the response coeffi- cients as a function of centrality **in** hydrodynamics. **In** Sec. III, we study the effect of the cubic response on elliptic **flow** fluctuations **in** relation with LHC data. **In** Sec. IV, we study the deviations **between** **anisotropic** **flow** **and** the predictor.

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The measured R AA is compared with various model predictions such as TAMU [56] **and** SCET [57] (Fig. 2, left), **and** MC@sHQ+EPOS2 [58, 59] (Fig. 2, right). **In** the TAMU model, the interactions are described by elastic **collisions** only. The SCET model implements medium-induced gluon radiation via modified splitting functions with finite quark masses. These SCET calculations depend on the coupling constant g which describes the coupling strength **between** hard partons **and** the QGP medium. Its value is g = 1.9–2. **In** the MC@sHQ+EPOS2 model, two different options are considered, including either energy loss from medium-induced gluon radiation **and** collisional (elastic) processes or only collisional energy loss. **In** the scenario with pure collisional energy loss, the scattering rates are scaled by a global factor K larger than unity (K = 1.5) **in** order to reproduce the R AA **and** elliptic **flow** of open **heavy**- flavour hadrons measured at midrapidity at the LHC [58]. With a combination of collisional **and** radiative energy loss, the scaling factor is K = 0.8. All these models also consider a nuclear modification of the PDF (EPS09) [17]. Note that **in** the MC@sHQ+EPOS2 model shadowing is not considered for beauty- quark production. **In** addition to independent fragmentation, a contribution of hadronisation via quark recombination is included **in** all models with the exception of SCET. The SCET calculations provide a fair description of the data **in** central **collisions** but deviate from the data **in** peripheral **collisions**. The TAMU calculations underestimate the suppression at p T > 6 GeV/c **in** central **and** semi-central **collisions**, **in** particular. Both versions of the MC@sHQ+EPOS2 model, without **and** with radiative energy loss, describe the measurement within uncertainties for all centrality classes over the entire p T interval. The results obtained at forward rapidity for muons from **heavy**-flavour hadron decays at √ s NN = 5.02 TeV complement those obtained at midrapidity for the electrons from **heavy**-flavour hadron decays [24] by the ALICE collaboration as well as the prompt D-meson [25, 26] **and** beauty measurements via B ± mesons [31], non-prompt D 0 [31] **and** J/ψ [30] by the ALICE **and** CMS collaborations. The measured R AA of muons from **heavy**-flavour hadron decays for p T > 8 GeV/c is compatible with that obtained for beauty (D 0 **and** J/ψ from beauty hadrons, B ± ) for p hadron T > 10 GeV/c [30, 31] within uncertainties, although **in** a different kinematic region (different p T **and** y intervals).

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w = N −1/4 σ, (B17)
so that both conditions (B16) are satisfied **in** the limit N 1.
We generate a large number of Monte Carlo events. For each event, we sample the positions of N sources, where N is the same for all events, according to the dis- tribution (B8). The initial entropy density **in** the event is then defined by Eqs. (B1) **and** (B15). We then compute the corresponding energy density, (x), using the equa- tion of state, Eq. (B9). Since the equation of state is scale invariant, the final results are independent of the normal- ization constant **in** Eq. (B15). We carry out two sets of calculations, using two different values of the speed of sound: c 2

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Neglected **in** these analyses is the first Fourier harmonic V 1 . The observed V 1 is smaller than V 2 **and** V 3 [ 3 , 10 ], **and** receives a sizable contribution from global **momentum** conservation [ 14 , 15 ], which makes its interpretation less straightforward. Fluctuations are expected to create a di- pole asymmetry **in** the system [ 16 ], resulting **in** a specific directed **flow** pattern, with high **transverse** **momentum** particles flowing **in** the direction of the steepest gradient **and** low p T particles flowing **in** the opposite direction. Hints of this directed **flow** have been extracted from pub- lished V 1 data at the Relativistic **Heavy**-**Ion** Collider (RHIC) by two of the authors [ 17 ], **and** its magnitude **and** p T -dependence were shown to be **in** agreement with ideal hydrodynamic calculations [ 18 ]. Note that this quan- tity is distinct from the directed **flow** observable that has been obtained **in** the past from measurements employing a rapidity-odd projection [ 19 ]. That rapidity-odd v 1 gives a negligible contribution to V 1 near midrapidity **and** repre- sents different physics [ 20 ].

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(Dated: August 7, 2019)
We show that experimental data on cumulants of **anisotropic** **flow** **in** **heavy**-**ion** **collisions** probe the non-Gaussian statistics of the energy density field created right after the collision. We carry out a perturbative expansion of the initial anisotropies of the system **in** terms of its density fluctuations. We argue that the **correlation** **between** the magnitudes of elliptic **flow** **and** triangular **flow**, dubbed sc(3, 2), is generically of the same sign **and** order of magnitude as the kurtosis of triangular **flow** **in** a hydrodynamic picture. The experimental observation that these quantities are negative implies that the distribution of energy around a given point has positive skew.

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from the d/p ratio vs. v z (where v z is the particle centre of mass velocity component
along the QP axis) **and** from < N > /Z vs. v z for Z=1,3,4. Concerning the isospin
diﬀusion process [15-17], driven by the isospin gradient **between** target **and** projectile, exploiting the excellent isotopic resolution of FAZIA we observed a systematic isospin enrichment for the QP for the reaction on 48 Ca (Fig.3 of [12]), conﬁrming other direct

The offline event selection for p+p events are carried out for events with MinBias trigger, and, since the TO counters cannot be used for p+p triggering due to i[r]

ple, studies of measured correlated adjacent detector hit probabilities **in** the Plastic Wall showed a worst case (Au+Au at 1.5A GeV) double hit probability of 8%, lowering the ap- parent total multiplicity, which was nearly compensated by a cross-talk **between** detector units of 6%, raising the apparent multiplicity. This cross talk was mainly due to imperfect alignment of the beam axis with the apparatus. The rationale for dropping further going detailed efficiency considerations within the filtered acceptances was that the charge bal- ances, after 4π reconstruction, were found to be accurate to typically 5% (see the tables **in** the appendix) for all the 25 system-energies studied, i.e. for a statistically significant sampling encompassing a large variation **in** energy **and** multiplicity. **In** our analysis the Plastic Wall **and** the CDC are treated as ’master’ detectors required for the registration of an ejectile. The Helitron efficiency was taken care of by matching its signals for H isotopes to Z=1 hits **in** the Plastic Wall after subtracting from the Plastic Wall hits the estimated pion contributions known from our earlier study [38]. At incident energies beyond 1A GeV, where the Plastic Wall showed a large background for Z ≥ 2, a matching of Z with the Helitron was required (**in** addition to track matching) using the energy loss signals **and** assuming for the Helitron the same efficiency as for Z=1. Other assumptions were found to be **in** conflict with the global charge balances. The Barrel, as a slave detector to the CDC, was used to improve isotope identification (for H **and** He) whenever its signal matched the CDC tracking. The mixing of adjacent particles is estimated to be less or equal to 10%, except for tritons **and** 3 He **in** the low energy run where it could be up to 20%.

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DOI: 10.1103/PhysRevLett.119.011601
Introduction. —Relativistic **collisions** of **heavy** ions at RHIC **and** LHC result **in** the formation of a strongly interacting state of matter known as the quark-gluon plasma (QGP). While these experiments provide an invaluable window into properties of quantum chromodynamics (QCD), our theoretical understanding of QGP **in** QCD remains far from complete. **In** recent years, gauge-gravity duality (holography) has enabled theoretical studies of certain, usually supersymmetric, classes of large-N field theories, which are most readily performed at infinitely strong ( ’t Hooft) coupling λ. As a result of those advances, many properties of QGP previously conceived as impen- etrably complex, such as its collective far-from-equilibrium behavior, can now be analyzed using numerical general relativity techniques. At infinite coupling, **heavy** **ion** **collisions** have been successfully modeled by (dual) colli- sions of gravitational shock waves **in** Einstein bulk theory with an extra dimension **and** a negative cosmological constant [1 –5] (see [6 –8] for reviews.).

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forward **and** backward rapidities over ∆φ = 360 ◦ .
The data were recorded using a minimum bias trig- ger that requires at least one hit **in** each of the beam- beam counters (BBC) at forward **and** backward rapidity, 3.0 < |η| < 3.9. Di-electron events must pass an addi- tional trigger that consisted of an OR **between** the level-1 electron **and** photon triggers. The electron trigger re- quires matching hits **between** the EMCal **and** RICH **in** a small angular area with a minimum energy deposition of 0.4 GeV **in** any 2 ×2 patch of EMCal towers. The photon trigger requires a minimum energy deposition of 1.4 GeV **in** any 4×4 set of overlapping EMCal towers. A J/ψ trig- ger efficiency of 96% was achieved within the vertex range |z vtx | < 30 cm. Di-muon triggered events were selected

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Over the last decades, the Equation of State (EoS) of nuclear matter has been widely studied **in** nuclear re- actions **in** order to put constraints on theoretical mod- els. These latter aim to describe both nuclear proper- ties at microscopic scale **and** astrophysical phenomena at macroscopic scale. **In** the first case, the EoS allows to understand some aspects of the collision via the underly- ing mechanisms like deep inelastic scattering, fusion re- actions, collective motions to mention a few examples [1]. **In** the second one, the EoS allows to describe the **heavy** compact astrophysical objects, as for instance Core Col- lapse SuperNovae **and** the formation of neutron stars [2]. Transport properties of the nuclear medium, **in** partic-

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material. He considered a heterogeneous continuum composed of two constituents. The strength homogenisation was evaluated at both mesoscopic **and** macroscopic scales. The proposed model is very simple **and** makes use of the mixture law: at the macroscopic scale the strength is the average of the strengths of each constitutive phase, weighted by the corresponding material volume fraction. **In** [31] De Buhan **and** Taliercio addressed the same problem by extending the theoretical model proposed **in** [30] **and** by considering among the constitutive phases the presence of the fibre-matrix interface. The strength domain is assumed to vary point-wise **and** it is approximated by an equivalent homogenised strength field composed of two parts: the isotropic part, that does not depends upon the volume fraction, **and** the **anisotropic** one depending on the volume fraction of each phase. **In** [9] the most common phenomenological failure criteria (i.e. the Hill [22], Hoff- man [23], Tsai-Wu [24] **and** the Zhang-Evans [33] criteria) have been formulated **in** the mathematical framework of the polar method. This unified formulation through inva- tiants has been utilised to formulate **and** solve the problem of maximising the strength of a generic orthotropic sheet **in** terms of its material orientation. **In** [19] the unified formulation presented **in** [9] was generalised **in** order to formulate a homogenised failure criterion at the laminate level. The Tsai-Hill criterion was formulated (at the laminate level) **in** terms of the laminate strength invariants **and** the problem of maximising the strength of a laminated plate subject to **in**-plane loads was addressed.

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L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

With the full E802/E866 data available, we have been able to determine and compare shapes and magnitudes of the rapidity distributions for reactions of varying numbe[r]

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DOI: 10.1103/PhysRevC.93.034914
I. INTRODUCTION
Prompt photons are an important probe for the study of the hot, dense matter formed **in** the high-energy collision of **heavy** ions. Being colorless, they are transparent to the subsequent evolution of the matter **and** probe the very initial stages of the collision. Their production rates are therefore expected to be directly sensitive to the overall thickness of the colliding nuclear matter. The rates are also expected to be sensitive to modifications of the partonic structure of nucleons bound **in** a nucleus, which are implemented as nuclear modifications [ 1 – 3 ] to the parton distribution functions (PDFs) measured **in** deep-inelastic lepton-proton **and** proton-proton (pp) scattering experiments. These effects include nuclear shadowing (the depletion of the parton densities at low Bjorken x), antishadowing (an enhancement at moderate x), **and** the EMC effect [ 4 ]. Photon rates are also sensitive to final-state interactions **in** the hot **and** dense medium, via the conversion of high-energy quarks **and** gluons into photons through rescattering. This is predicted to lead to an increased photon production rate relative to standard expectations [ 5 , 6 ]. Prompt photons have two primary sources. The first is direct emission, which proceeds at leading order via quark-gluon Compton scattering qg → qγ or quark-antiquark annihilation

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