Linear and non-linear flow mode in Pb-Pb collisions at $\sqrt{s_{\rm NN}} =$ 2.76 TeV

TL;DR

This paper investigates the linear and non-linear flow modes in Pb-Pb collisions at 2.76 TeV, providing insights into initial conditions and medium properties through anisotropic flow measurements.

Contribution

It presents the first detailed analysis of higher order flow modes ($V_4$, $V_5$, $V_6$) including mode-coupling effects in Pb-Pb collisions at LHC energies.

Findings

Measured higher order flow coefficients for different centralities.

Compared experimental results with theoretical models.

Constrained initial geometry and shear viscosity to entropy density ratio.

Abstract

The second and the third order anisotropic flow, $V_{2}$ and $V_3$, are mostly determined by the corresponding initial spatial anisotropy coefficients, $\varepsilon_{2}$ and $\varepsilon_{3}$, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, $V_n$ ($n > 3$), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow $V_n$ for $n=4$, $5$, $6$ with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range $|\eta| < 0.8$ and the transverse momentum range $0.2 < p_{\rm T} < 5.0$ GeV/$c$ as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.

Figures

Equations

$$\frac{dN}{d\phi }\propto 1+2\sum _{n=1}^{\infty }{v}_n\cos [n(\phi -{\Psi }_n)],$$

$${\epsilon }_n{e}^{in{\Phi }_n}\equiv -\frac{⟨r^n{e}^{in\varphi }⟩}{⟨r^n⟩}(\mathrm{for}n>1),$$

$$V_4$$

$$V_5$$

$$V_6$$

$${\epsilon }_4^{{}^{\prime }}{e}^{i4{\Phi }_4^{{}^{\prime }}}\equiv -\frac{⟨z^4⟩-3{⟨z^2⟩}^2}{⟨r^4⟩}={\epsilon }_4{e}^{i4{\Phi }_4}+\frac{3{⟨r^2⟩}^2}{⟨r^4⟩}{\epsilon }_2^2{e}^{i4{\Phi }_2},$$

$$\frac{⟨V_4(V_2^{\ast }{)}^2{v}_2^2⟩}{⟨V_4(V_2^{\ast }{)}^2⟩⟨v_2^2⟩}=\frac{⟨v_2^6⟩}{⟨v_2^4⟩⟨v_2^2⟩},$$

$$\frac{⟨V_5{V}_3^{\ast }{V}_2^{\ast }{v}_2^2⟩}{⟨V_5{V}_3^{\ast }{V}_2^{\ast }⟩⟨v_2^2⟩}=\frac{⟨v_2^4{v}_3^2⟩}{⟨v_2^2{v}_3^2⟩⟨v_2^2⟩}.$$

$$v_n\{2\}=⟨⟨\cos n({\phi }_1-{\phi }_2)⟩{⟩}^{1/2}={⟨v_n^2⟩}^{1/2}.$$

$$v_n\{2\}=⟨⟨\cos (n{\phi }_1^A-n{\phi }_2^B)⟩{⟩}^{1/2}={⟨v_n^2⟩}^{1/2}.$$

$$\frac{{⟨V_4(V_2^{\ast }{)}^2{v}_2^2⟩}^A}{{⟨V_4(V_2^{\ast }{)}^2⟩}^A⟨v_2^2⟩}=\frac{⟨⟨\cos (4{\phi }_1^A+2{\phi }_2^A-2{\phi }_3^B-2{\phi }_4^B-2{\phi }_5^B)⟩⟩}{⟨⟨\cos (4{\phi }_1^A-2{\phi }_2^B-2{\phi }_3^B)⟩⟩⟨⟨\cos (2{\phi }_1^A-2{\phi }_2^B)⟩⟩},$$

$$\frac{⟨v_2^6⟩}{⟨v_2^4⟩⟨v_2^2⟩}=\frac{⟨⟨\cos (2{\phi }_1^A+2{\phi }_2^A+2{\phi }_3^A-2{\phi }_4^B-2{\phi }_5^B-2{\phi }_6^B)⟩⟩}{⟨⟨\cos (2{\phi }_1^A+2{\phi }_2^A-2{\phi }_3^B-2{\phi }_4^B)⟩⟩⟨⟨\cos (2{\phi }_1^A-2{\phi }_2^B)⟩⟩}.$$

$$\frac{{⟨V_5{V}_3^{\ast }{V}_2^{\ast }{v}_2^2⟩}^A}{{⟨V_5{V}_3^{\ast }{V}_2^{\ast }⟩}^A⟨v_2^2⟩}=\frac{⟨⟨\cos (5{\phi }_1^A+2{\phi }_2^A-3{\phi }_3^B-2{\phi }_4^B-2{\phi }_5^B)⟩⟩}{⟨⟨\cos (5{\phi }_1^A-3{\phi }_2^B-2{\phi }_3^B)⟩⟩⟨⟨\cos (2{\phi }_1^A-2{\phi }_2^B)⟩⟩},$$

$$\frac{⟨v_2^4{v}_3^2⟩}{⟨v_2^2{v}_3^2⟩⟨v_2^2⟩}=\frac{⟨⟨\cos (3{\phi }_1^A+2{\phi }_2^A+2{\phi }_3^A-3{\phi }_4^B-2{\phi }_5^B-2{\phi }_6^B)⟩⟩}{⟨⟨\cos (3{\phi }_1^A+2{\phi }_2^A-3{\phi }_3^B-2{\phi }_4^B)⟩⟩⟨⟨\cos (2{\phi }_1^A-2{\phi }_2^B)⟩⟩}.$$

$$v_{4,22}^A$$

$$v_{5,32}^A$$

$$v_{6,222}^A$$

$$v_{6,33}^A$$

$$v_{4,22}$$

$$v_{5,32}$$

$$v_{6,222}$$

$$v_{6,33}$$

$$v_4^{\mathrm{L}}=\sqrt{v_4^2\{2\}-v_{4,22}^2},$$

$$v_5^{\mathrm{L}}=\sqrt{v_5^2\{2\}-v_{5,32}^2}.$$

$${\rho }_{4,22}$$

$${\rho }_{5,32}$$

$${\rho }_{6,222}$$

$${\rho }_{6,33}$$

$${\chi }_{4,22}$$

$${\chi }_{5,32}$$

$${\chi }_{6,222}$$

$${\chi }_{6,33}$$

Full text

\PHyear2017 \PHnumber103 \PHdate10 May

\ShortTitleLinear and non-linear flow modes in Pb–Pb at 2.76 TeV

\CollaborationALICE Collaboration††thanks: See Appendix A for the list of collaboration members \ShortAuthorALICE Collaboration

The second and the third order anisotropic flow, $V_{2}$ and $V_{3}$, are mostly determined by the corresponding initial spatial anisotropy coefficients, $\varepsilon_{2}$ and $\varepsilon_{3}$, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, $V_{n}$ ($n>3$), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow $V_{n}$ for $n=4$, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range $|\eta|<0.8$ and the transverse momentum range $0.2<p_{\rm T}<5.0$ GeV/$c$ as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.

1 Introduction

The primary goal of the ultra-relativistic heavy-ion collision programme at the Large Hadron Collider (LHC) is to study the properties of the Quark-Gluon Plasma (QGP), a novel state of strongly interacting matter that is proposed to exist at high temperatures and energy densities [1, 2]. Studies of azimuthal correlations of produced particles have contributed significantly to the characterisation of the matter created in heavy-ion collisions [3, 4]. Anisotropic flow, which quantifies the anisotropy of the momentum distribution of final state particles, is sensitive to the event-by-event fluctuating initial geometry of the overlap region, together with the transport properties and equation of state of the system [4, 5, 6, 7]. The successful description of anisotropic flow results by hydrodynamic calculations suggests that the created medium behaves as a nearly perfect fluid [5, 4] with a shear viscosity to entropy density ratio, $\eta/s$, close to a conjectured lower bound $1/4\pi$ [8]. Anisotropic flow is characterised using a Fourier decomposition of the particle azimuthal distribution in the plane transverse to the beam direction [9, 10]:

[TABLE]

where $N$ is the number of produced particles, $\varphi$ is the azimuthal angle of the particle and $\Psi_{n}$ is the $n^{th}$ order flow symmetry plane. The $n^{th}$ order (complex) anisotropic flow $V_{n}$ is defined as: $V_{n}\equiv v_{n}\,e^{in\Psi_{n}}$, where $v_{n}=|V_{n}|$ is the flow coefficient, and $\Psi_{n}$ represents the azimuth of $V_{n}$ in momentum space. For non-central heavy-ion collisions, the dominant flow coefficient is $v_{2}$, referred to as elliptic flow. Non-vanishing values of higher flow coefficients $v_{3}$–$v_{6}$ at the LHC are ascribed primarily to the response of the produced QGP to fluctuations of the initial energy density profile of the colliding nucleons [11, 12, 13, 14, 15].

The standard (moment-defined) initial anisotropy coefficients $\varepsilon_{n}$ together with their corresponding initial symmetry planes (also called participant planes) $\Phi_{n}$ can be calculated from the transverse positions $(r,\phi)$ of the participating nucleons

[TABLE]

where $\left<\,\right>$ denotes the average over the transverse position of all participating nucleons, $\phi$ is azimuthal angle, and $n$ is the order of the coefficient [11, 16]. It has been shown in [17, 18] that $V_{2}$ and $V_{3}$ are mostly determined with the same order initial spatial anisotropy coefficients $\varepsilon_{2}$ and $\varepsilon_{3}$, respectively. Considering that $\eta/s$ reduces the hydrodynamic response of $v_{n}$ to $\varepsilon_{n}$, it was proposed in [19, 18, 20, 21] that $v_{n}/\varepsilon_{n}$ (for $n=2,3$) could be a direct probe to quantitatively constrain the $\eta/s$ of the QGP in hydrodynamic calculations. However, $\varepsilon_{n}$ cannot be determined experimentally. Instead, they are obtained from various theoretical models, resulting in large uncertainties in the estimated $\eta/s$ derived indirectly from $v_{2}$ and $v_{3}$ measurements [19, 17]. On the other hand, higher order anisotropic flow $V_{n}$ with $n>3$ probe smaller spatial scales and thus are more sensitive to $\eta/s$ than $V_{2}$ and $V_{3}$ due to more pronounced viscous corrections [16, 22]. Thus, the study of the full set of flow coefficients is expected to constrain both $\varepsilon_{n}$ and $\eta/s$ simultaneously. However, it was realised later that $V_{n}$ with $n>3$ is not linearly correlated with the corresponding $\varepsilon_{n}$ [16, 23, 22], which makes the extraction of $\eta/s$ from measurements of higher order flow coefficients less straightforward. In addition to the study of flow coefficients, the results of correlations between different order anisotropic flow angles and amplitudes shed light on both the early stage dynamics and the transport properties of the created QGP [24, 25, 26, 27, 28, 29, 30, 31, 32]. In particular, the characteristic pattern of flow symmetry plane correlations (also known as angular correlations of flow-vectors) observed in experiments is reproduced quantitatively by theoretical calculations [29, 30, 31, 33, 32]. However, the correlations between flow coefficients (also known as amplitude correlations of flow-vectors), investigated using symmetric cumulants, provide stricter constraints on initial conditions and $\eta/s$ than the individual $v_{n}$ measurements [24, 25, 31, 26, 27, 28, 32]. It is a challenge for current theoretical models to provide quantitative descriptions of the correlations between different order flow coefficients.

As discussed above, it is known that the lower order anisotropic flow $V_{n}$ ($n=$ 2, 3) is largely determined by a linear response of the system to the corresponding $\varepsilon_{n}$ (except in peripheral collisions). Higher order anisotropic flow $V_{n}$ with $n>$ 3 have contributions not only from the linear response of the system to $\varepsilon_{n}$, but also contributions proportional to the product of $\varepsilon_{2}$ and/or $\varepsilon_{3}$. These contributions are usually called non-linear response [25, 34] in higher order anisotropic flow. For a single event, $V_{n}$ with $n=$ 4, 5 and 6 can be decomposed into the so-called linear and the non-linear contributions, according to

[TABLE]

Here $\chi_{n,mk}$ is a new observable called the non-linear mode coefficient [34] and $V_{n}^{\rm NL}$ represents the non-linear mode which has contributions from modes with lower order anisotropy coefficients. The $V_{n}^{\rm L}$ term represents the linear mode, which was naïvely expected from the linear response of the system to the same order $\varepsilon_{n}$. However, a recent hydrodynamic calculation showed that $V_{n}^{\rm L}$ is not driven by the linear response to the standardly moment-defined $\varepsilon_{n}$ introduced in Eq. (2), but the corresponding cumulant-defined anisotropy coefficient $\varepsilon_{n}^{{}^{\prime}}$ [30, 35]. For example, $V_{4}^{\rm L}$ is expected to be driven by the 4th-order cumulant-defined anisotropy coefficient and its corresponding initial symmetry plane which can be calculated as

[TABLE]

where $z=re^{i\phi}$. The calculations for other order anisotropy coefficients and their corresponding initial symmetry planes can be found in [30, 35]. If the non-linear and linear modes of higher order anisotropic flow, $V_{n}^{\rm NL}$ and $V_{n}^{\rm L}$, are uncorrelated (e.g. $V_{n}^{\rm L}$ is perpendicular to $V_{n}^{\rm NL}$), they can be isolated. One of the proposed approaches to validate the assumption that $V_{n}^{\rm NL}$ and $V_{n}^{\rm L}$ are uncorrelated is testing the following relations [25]:

[TABLE]

If the above relations are valid, one could combine the analyses of higher order anisotropic flow with respect to their corresponding symmetry planes and to the planes of lower order anisotropic flow $V_{2}$ or $V_{3}$ to eliminate the uncertainty from initial state assumptions and extract $\eta/s$ with better precision [34].

In this Letter, the linear and non-linear modes in higher order anisotropic flow generation are studied in Pb–Pb collisions at \mbox{\sqrt{s_{{}_{\rm NN}}}}= 2.76 TeV with the ALICE detector. The main observables are introduced in Section 2 and the experimental setup is described in Section 3. Section 4 presents the study of the systematic uncertainties of the above mentioned observables. The results and their discussion are provided in Section 5. Section 6 contains the summary and conclusions.

2 Observables and analysis methods

Ideally, the flow coefficient $v_{n}$ can be measured via the azimuthal correlations of emitted particles with respect to the symmetry plane $\Psi_{n}$ as $v_{n}=\left<\cos n(\varphi-\Psi_{n})\right>$. Since $\Psi_{n}$ is unknown experimentally, the simplest approach to obtain $v_{n}$ is using 2-particle correlations:

[TABLE]

Here $\langle\langle\,\rangle\rangle$ denotes the average over all particles in a single event and then an average over all events, $\left<\right>$ indicates the event average of over all events, and $\varphi_{i}$ represents the azimuthal angle of the $i$-th particle. The analysed events are divided into two sub-events A and B, separated by a pseudorapidity gap, to suppress non-flow effects. The latter are the azimuthal correlations not associated to the common symmetry plane $\Psi_{n}$, such as jets and resonance decays. Thus, we modify Eq. (9) to

[TABLE]

Here $\varphi_{1}^{A}$ and $\varphi_{2}^{B}$ are selected from subevent A and B, respectively.

Before introducing observables related to the linear and non-linear modes in higher order anisotropic flow, it is crucial to verify whether Eqs. (7-8) are applicable. The left and right hand sides of Eq. (7) are obtained by constructing suitable multi-particle correlations [34]:

[TABLE]

Similarly, we can validate Eq. (8) by calculating both sides with [34]:

[TABLE]

The magnitude of $V_{n}^{\rm NL}$ was denoted as $v_{n}\{\Psi_{m}\}$ (here $\Psi_{m}$ is the lower order flow symmetry plane and $m=2,3$) in [34]. The notation $v_{n,mk}$, where $n$ specifies the order of the flow term while $m$ and $k$ etc. denote the contributing lower order flow symmetry planes, is used in this Letter. If the linear and non-linear modes are independent, then the non-linear mode in higher order anisotropic flow can be analysed by correlating $V_{n}$ with $\Psi_{2}$ or/and $\Psi_{3}$ [34]. For sub-event A we can define:

[TABLE]

Similarly, one can obtain $v_{n,mk}^{B}$ for sub-event B. The average of $v_{n,mk}^{A}$ and $v_{n,mk}^{B}$, defined as $v_{n,mk}$, quantifies the magnitude of the non-linear mode in higher order anisotropic flow, which can be written as [36]:

[TABLE]

The approximation is valid if the correlation between lower ($n=2,3$) and higher ($n>3$) flow coefficients is weak.

As can be seen in Eqs. (3-5), the calculation for $V_{6}$ is more complicated than $V_{4}$ and $V_{5}$, and the exact expression for $v_{6}^{\rm L}$ is currently not available. Therefore, we only focus on the two non-linear modes of $V_{6}$ without discussing $v_{6}^{\rm L}$. According to Eqs. (3) to (4), the magnitudes of the linear mode in higher order anisotropic flow can be calculated as:

[TABLE]

The ratio of $v_{n,mk}$ to $v_{n}\{2\}$, denoted as $\rho_{n,mk}$, can be calculated as:

[TABLE]

These observables measure the correlations between different order flow symmetry planes if the correlations between different order flow coefficients are weak. They are very similar to the so-called weighted event-plane correlations measured by the ATLAS Collaboration [33]. The differences are as follows: $\langle v_{2}^{2}\,v_{3}^{2}\rangle$ is used in Eq. (20) and (26), while $\langle v_{2}^{2}\rangle\langle v_{3}^{2}\rangle$ was used in [33], which did not consider the anti-correlations between $v_{2}$ and $v_{3}$ found in [27]. In addition, multi-particle correlations are used for $v_{2}$ and $v_{3}$ in the denominator of the observables, while two-particle correlations are used in the event-plane correlations which might be biased from fluctuations of $v_{2}$ and $v_{3}$.

The non-linear mode coefficients $\chi_{n,mk}$ in Eqs. (3) to (5) are defined as:

[TABLE]

These quantify the contributions of the non-linear mode and are expected to be independent of $v_{2}$ or $v_{3}$.

All of the observables above are based on 2- and multi-particle correlations, which can be obtained using the generic framework for anisotropic flow analyses introduced in Ref. [24].

3 Experimental setup and data analysis

The data samples analysed in this Letter were recorded by ALICE during the Pb–Pb runs of the LHC at a centre-of-mass energy of \mbox{\sqrt{s_{{}_{\rm NN}}}}=2.76 TeV in 2010. Minimum bias Pb–Pb collision events were triggered by the coincidence of signals in the V0 detector [37, 38], with an efficiency of 98.4% of the hadronic cross section [39]. The V0 detector is composed of two arrays of scintillator counters, V0-A and V0-C, which cover the pseudorapidity ranges $2.8<\eta<5.1$ and $-3.7<\eta<-1.7$, respectively. Beam background events were rejected using the timing information from the V0 and the Zero Degree Calorimeter (ZDC) [37] detectors and by correlating reconstructed clusters and tracklets with the Silicon Pixel Detectors (SPD). The fraction of pile-up events in the data sample is found to be negligible after applying dedicated pile-up removal criteria [40]. Only events with a reconstructed primary vertex within $\pm 10$ cm from the nominal interaction point along the beam direction were used in this analysis. The primary vertex was estimated using tracks reconstructed by the Inner Tracking System (ITS) [37, 41] and Time Projection Chamber (TPC) [37, 42]. The collision centrality was determined from the measured V0 amplitude and centrality intervals were defined following the procedure described in [39]. About 13 million Pb–Pb events passed all of the event selection criteria.

Tracks reconstructed using the combined information from the TPC and ITS are used in this analysis. This combination ensures a high detection efficiency, optimum momentum resolution, and a minimum contribution from photon conversions and secondary charged particles produced either in the detector material or from weak decays. To reduce the contributions from secondaries, charged tracks were required to have a distance of closest approach to the primary vertex in the longitudinal ($z$) direction and transverse ($xy$) plane smaller than 3.2 cm and 2.4 cm, respectively. Additionally, tracks were required to have at least 70 TPC space points out of the maximum 159. The average $\chi^{2}$ per degree of freedom of the track fit to the TPC space points was required to be below 2. In this study, tracks were selected in the pseudorapidity range $|\eta|<0.8$ and the transverse momentum range 0.2 $<p_{\rm{T}}<$ 5.0 GeV/$c$.

4 Systematic uncertainties

Numerous sources of systematic uncertainty were investigated by varying the event and track selection as well as the uncertainty associated with the possible remaining non-flow effects in the analysis. The variation of the results with the collision centrality is calculated by alternatively using the TPC or SPD to estimate the event multiplicity and is found to be less than 3% for all observables. Results with opposite polarities of the magnetic field within the ALICE detector and with narrowing the nominal $\pm$10 cm range of the reconstructed vertex along the beam direction from the centre of the ALICE detector to 9, 8 and 7 cm do not show a difference of more than 2% compared to the default selection criteria for various measurements. The contributions from pileup events to the final systematic uncertainty are found to be negligible. The sensitivity to the track selection criteria was explored by varying the number of TPC space points and by using tracks reconstructed in the TPC alone. Varying the number of TPC space points from 70 to 80, 90 and 100 out of a possible 158, results in a 1–3% variation of the results for $v_{n}$, within 1.5% for $\rho_{n,mk}$ and $\chi_{n,mk}$. Using TPC-only tracks leads to a difference of less than 14%, 17% and 8% for $v_{n}$, $\rho_{n,mk}$ and $\chi_{n,mk}$, respectively. Both effects were included in the evaluation of the systematic uncertainty. Several different approaches have been applied to estimate the effects of non-flow. These include the investigation of multi-particle correlations with various $|\Delta\eta|$ gaps, the application of the like-sign technique which correlates two particles with either all positive or negative charges and suppress such non-flow as due to resonance decays, as well as the calculations using HIJING Monte Carlo simulations [43], which do not include anisotropic flow. It was found that the possible remaining non-flow effects are less than 10.5%, 11% and 7% for $v_{n}$, $\rho_{n,mk}$ and $\chi_{n,mk}$, respectively. They are taken into account in the final systematic uncertainty. The systematic uncertainties evaluated for each source mentioned above were added in quadrature to obtain the total systematic uncertainty of the measurements.

5 Results and discussion

As discussed in Sec. 2, one can validate the assumption that linear and non-linear modes in higher order anisotropic flow are uncorrelated via Eqs. (7) and (8). These have been tested in A Multi-Phase Transport (AMPT) model [25] as well as in the hydrodynamic calculations [44]. Good agreement between left- and right-hand sides of Eqs. (7) and (8) is found for all centrality classes, independent of the initial conditions and the ideal or viscous fluid dynamics used in the calculations. Thus, it is crucial to check these equalities in data, to further confirm the assumption that the two components are uncorrelated and can be isolated independently. Figure 1 confirms that the agreement observed in theoretical calculations is also present in the data despite small deviations found in central collisions when testing Eqs. (8). Their centrality dependency are similar as the previous theoretical predictions [25, 44]. The measurements support the assumption that higher order anisotropic flow $V_{n}$ ($n>3$) can be modeled as the sum of independent linear and non-linear modes.

The magnitudes of linear and non-linear modes in higher order anisotropic flow are reported as a function of collision centrality in Fig. 2. In this Letter, sub-events A and B are built in the pseudorapidity ranges $-0.8<\eta<-0.4$ and $0.4<\eta<0.8$, respectively, which results in a pseudorapidity gap of $|\Delta\eta|>0.8$ for all presented measurements. It can be seen that the linear mode $v_{4}^{\rm L}$ depends weakly on centrality and is the larger contribution to $v_{4}\{2\}$ for the centrality range 0–30%. The non-linear mode, $v_{4,22}$, increases monotonically as the centrality decreases and saturates around centrality percentile 50%, becoming the dominant source for centrality intervals above 40%. Similar trends of centrality dependence have been observed for $V_{5}$, although $v_{5,32}$ becomes the dominant contribution in centrality percentile above 30%. Only two non-linear components $v_{6,222}$ and $v_{6,33}$ are discussed for $V_{6}$. It is shown in Fig. 2 (right) that $v_{6,222}$ increases monotonically as the centrality decreases to centrality 50%, while $v_{6,33}$ has a weaker centrality dependence compared to $v_{6,222}$.

The linear and non-linear modes in higher order anisotropic flow were investigated by the ATLAS Collaboration [26] using a different approach based on “Event Shape Engineering” [45]. With this method one can utilise large fluctuations in the initial geometry of the system to select events corresponding to a specific initial shape. The conclusion is qualitatively consistent with what is reported here, although a direct comparison is not possible due to the different kinematic cuts (especially the integrated $p_{\rm{T}}$ range) used in the two measurements. The higher order anisotropic flow induced by lower order anisotropic flow were also measured using the event-plane method at the LHC [46, 14]. However, the measurements of the non-linear mode presented in this Letter are based on the multi-particle correlations method with a $|\Delta\eta|$ gap. This method makes it easier to measure an observable like $v_{5,32}$, which is less straightforward to define using the event plane method [46, 14]. In addition, as pointed out in [47, 34, 25], this new multi-particle correlations method should strongly suppress short-range (in pseudorapidity) non-flow effects and provides a robust measurement without any dependence on the experimental acceptance. The measurements are compared to recent hydrodynamic calculations from a hybrid ${\tt IP}$-${\tt Glasma+MUSIC+UrQMD}$ model [48], in which realistic event-by-event initial conditions are used and the hydrodynamic evolution takes into account both shear and bulk viscosity. It is shown that this hydrodynamic calculation could describe quantitatively the total magnitudes of $V_{4}$ and $V_{6}$, as well as the magnitudes of their linear and non-linear modes, while it slightly overestimates the results for $V_{5}$.

The centrality dependence of $\rho_{n,mk}$, which quantifies the angular correlations between different order flow symmetry planes, is presented in Fig. 3. It is observed that $\rho_{4,22}$ increases from central to peripheral collisions, which suggests that the correlations between $\Psi_{2}$ and $\Psi_{4}$ are stronger in peripheral than in central collisions. It implies that $V_{4}^{\rm NL}$ tends to align with $V_{4}$ in more peripheral collisions. The results of $\rho_{6,33}$, which measures the correlation of $\Psi_{3}$ and $\Psi_{6}$, do not exhibit a strong centrality dependence within the statistical uncertainties. As mentioned above, $\rho_{4,22}$ and $\rho_{6,33}$ are similar to the previous “event-plane correlation” measurements $\left<\cos(4\Phi_{4}-4\Phi_{2})\right>_{w}$ and $\left<\cos(6\Phi_{6}-6\Phi_{3})\right>_{w}$ in [33]. The comparisons between measurements of these observables are also presented in Fig. 3. The results are compatible with each other, despite the different kinematic ranges used by ATLAS and this analysis. It should be also noted that the measurements of $\rho_{n,mk}$ presented in this Letter show the symmetry plane correlations at mid-pseudorapidity $|\eta|<0.8$ while ATLAS measured the symmetry plane correlations using $-4.8<\eta<-0.5$ and $0.5<\eta<4.8$ for two-plane correlations, and using $-2.7<\eta<-0.5$, $0.5<\eta<2.7$ and $3.3<|\eta|<4.8$ for 3-plane correlations [33]. Previous investigations suggest that there might be $\eta$-dependent fluctuations of the flow symmetry plane and the flow magnitude [49, 50]. As a consequence, one might expect a difference when measuring the correlations of flow symmetry planes from different pseudorapidity regions. However, Fig. 3 shows good agreement between the ALICE and ATLAS measurements. Therefore, no obvious indication that the flow symmetry plane varies with $\eta$ can be deduced from this comparison. It is noticeable in Fig. 3 that the $\rho_{5,32}$ measurement seems slightly higher than the $\left<\cos(5\Phi_{5}-3\Phi_{3}-2\Phi_{2})\right>_{w}$ measurement. This is mainly due to a small difference between the definitions of the observable as introduced in Sec. 2: the term $\left<v_{2}^{2}\,v_{3}^{2}\right>^{1/2}$ is used in $\rho_{5,32}$, whereas $\left<v_{2}^{2}\right>^{1/2}\left<v_{3}^{2}\right>^{1/2}$ is used in the “event-plane correlations” [33]. Considering the known anti-correlations between $v_{2}$ and $v_{3}$ [26, 27], $\left<v_{2}^{2}\,v_{3}^{2}\right>^{1/2}$ could be up to 10% lower than $\left<v_{2}^{2}\right>^{1/2}\left<v_{3}^{2}\right>^{1/2}$ depending on the centrality class [27], leading to a slightly larger $\rho_{5,32}$ than $\left<\cos(5\Phi_{5}-3\Phi_{3}-2\Phi_{2})\right>_{w}$ from ATLAS.

It has been observed in hydrodynamic and transport model calculations that the symmetry plane correlations, e.g. correlations of second and fourth order symmetry planes, change sign during the system evolution [29, 30, 32]. The measured flow symmetry plane correlations could be nicely explained by the combination of contributions from linear and non-linear modes in higher order anisotropic flow [30]. This indicates that the flow symmetry plane correlation $\rho_{n,mk}$ carries important information about the dynamic evolution of the created system. In addition, the model calculations suggest that stronger initial symmetry plane correlations are reflected in stronger correlations between the flow symmetry planes in the final state [29, 32]. And a larger value of $\eta/s$ of the QGP leads to weaker flow symmetry plane correlations in the final state. As pointed out in [29], the hydrodynamic calculations from ${\tt VISH2+1}$ using Monte Carlo Glauber (MC-Glb) or Monte Carlo Kharzeev-Levin-Nardi (MC-KLN) initial conditions can only describe qualitatively the trends of the centrality dependence of the event-plane correlation measurements by ATLAS. It is therefore expected that these hydrodynamic calculations cannot describe the presented ALICE measurements, which are compatible with the ATLAS event-plane correlation measurements. Figure 3 shows that the hydrodynamic calculations from ${\tt IP}$-${\tt Glasma+MUSIC+UrQMD}$ [48] reproduce nicely the measurements of symmetry plane correlations $\rho_{n,mk}$. The measurements of $\rho_{n,mk}$ presented in this Letter, together with the comparison to hydrodynamic calculations, should place constraints on the initial conditions and $\eta/s$ of the QGP in hydrodynamic calculations.

Figure 4 presents the measurements of the non-linear mode coefficients as a function of collision centrality. It is observed that $\chi_{4,22}$ and $\chi_{6,222}$ decrease modestly from central to mid-central collisions, and stay almost constant from mid-central to more peripheral collisions. For $\chi_{5,32}$ and $\chi_{6,33}$ strong centrality dependence is not observed either. Thus, the dramatic increase of $v_{n,mk}$ shown in Fig. 2 appears to be mainly due to the increase of $v_{2}$ and/or $v_{3}$ from central to peripheral collisions and not the increase of the non-linear mode coefficient. It is also noteworthy that the relationship of $\chi_{4,22}\sim\chi_{6,33}\approx\frac{\chi_{5,32}}{2}$ is approximately valid, as predicted by hydrodynamic calculations [34]. The comparisons to event-by-event viscous hydrodynamic calculations from ${\tt VISH2+1}$ [44] and from ${\tt IP}$-${\tt Glasma+MUSIC+UrQMD}$ [48] are also presented in Fig. 4. ${\tt VISH2+1}$ shows that $\chi_{4,22}$ calculations with MC-Glb initial conditions are larger than those with MC-KLN initial conditions, i.e. $\chi_{4,22}$ depends on the initial conditions. At the same time, the curves with different $\eta/s$ values for ${\tt VISH2+1}$ are very similar, indicating that $\chi_{4,22}$ is insensitive to $\eta/s$. The measurements favor IP-Glasma and MC-KLN over MC-Glb initial conditions regardless of $\eta/s$. This suggests that the $\chi_{4,22}$ measurement can be used to constrain the initial conditions, with less concern of the setting of $\eta/s(T)$ in hydrodynamic calculations than previous flow observables.

It was predicted that $\chi_{6,222}<\chi_{6,33}$ based on the ideal hydrodynamic calculation using smooth initial Gaussian density profiles [34], whereas an opposite prediction was obtained in the ideal hydrodynamic calculation evolving genuinely bumpy initial conditions obtained from a Monte Carlo sampling of the initial nucleon positions in the colliding nuclei [44]. It is seen in Fig. 4 that $\chi_{6,222}\sim\chi_{6,33}$ within the current uncertainties. The data are not able to discriminate the different predictions in [34] and [44]. Hydrodynamic calculations using MC-KLN and IP-Glasma initial conditions give better descriptions of $\chi_{6,222}$, compared to the ones using MC-Glb initial conditions. For $\chi_{5,32}$ none of the combinations of initial conditions and $\eta/s$ in the hydrodynamic calculations agree quantitatively with data. This might be due to the current difficulty of describing the anti-correlations between $v_{2}$ and $v_{3}$ in hydrodynamic calculations [27, 51], which are involved in the calculation of $\chi_{5,32}$. Furthermore, ${\tt VISH2+1}$ calculations show that $\chi_{5,32}$ and $\chi_{6,33}$ are very weakly sensitive to the initial conditions, but decrease as $\eta/s$ increases. The investigation with the ${\tt VISH2+1}$ hydrodynamic framework shows that the sensitivity of $\chi_{5,32}$ and $\chi_{6,33}$ to $\eta/s$ is not due to sensitivity to shear viscous effects during the buildup of hydrodynamic flow. Instead, as found in [44], it is due to the $\eta/s$ at freeze-out. The measurements of $\chi_{5,32}$ and $\chi_{6,33}$ do not further constrain the $\eta/s$ during system evolution, however, they provide unique information on $\eta/s$ at freeze-out which was poorly known and cannot be obtained from other anisotropic flow related observables. Further improvement of model calculations on correlations between different order flow coefficients are necessary to better understand the comparison of $\chi_{5,32}$ obtained from data and hydrodynamic calculations. The $\chi_{6,33}$ results are consistent with hydrodynamic calculations from ${\tt VISH2+1}$ with MC-KLN initial conditions using $\eta/s=0.08$ and ${\tt IP}$-${\tt Glasma+MUSIC+UrQMD}$ with a $\eta/s=0.095$. It is shown that $\chi_{5,32}$ and $\chi_{6,33}$ have a weak centrality dependence if a smaller $\eta/s$ is used in the hydrodynamic calculations. Such a weak centrality dependence of $\chi_{5,32}$ and $\chi_{6,33}$ is observed in data as well. The measurements presented here suggest a small $\eta/s$ value at freeze-out, which can be useful to constrain the temperature dependence of the shear viscosity over entropy density ratio, $\eta/s(\rm T)$, in the development of hydrodynamic frameworks. These results suggest that future tuning of the parameterisations of $\eta/s(\rm T)$ in hydrodynamic frameworks using the presented measurements is necessary.

6 Summary

The linear and non-linear modes in higher order anisotropic flow generation were studied with 2- and multi-particle correlations in Pb–Pb collisions at $\sqrt{s_{{}_{\rm NN}}}=$ 2.76 TeV. The results presented in this Letter show that higher order anisotropic flow can be isolated into two independent contributions: the component that arises from a non-linear response of the system to the lower order initial anisotropy coefficients $\varepsilon_{2}$ and/or $\varepsilon_{3}$, and a linear mode which is driven by linear response of the system to the same order cumulant-defined anisotropy coefficient. A weak centrality dependence is observed for the contributions from linear mode whereas the contributions from non-linear mode increase dramatically as the collision centrality decreases, and it becomes the dominant source in higher order anisotropic flow in mid-central to peripheral collisions. It is shown that this is mainly due to the increase of lower order flow coefficients $v_{2}$ and $v_{3}$. The correlations between different flow symmetry planes are measured. The results are compatible with the previous “event-plane correlation” measurements, and can be quantitatively described by calculations using the ${\tt IP}$-${\tt Glasma+MUSIC+UrQMD}$ framework. Furthermore, non-linear mode coefficients, which have different sensitivities to the shear viscosity over entropy density ratio $\eta/s$ and the initial conditions, are presented in this Letter. Comparisons to hydrodynamic calculations suggest that the data is described better by hydrodynamic calculations with smaller $\eta/s$. In addition, the MC-Glb initial condition is disfavoured by the presented results.

Measurements of linear and non-linear modes in higher order anisotropic flow and their comparison to hydrodynamic calculations provide more precise constraints on the initial conditions and temperature dependence of $\eta/s$. These results could also offer new insights into the geometry of the fluctuating initial state and into the dynamical evolution of the strongly interacting medium produced in relativistic heavy-ion collisions at the LHC.

Acknowledgements

The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS), Armenia; Austrian Academy of Sciences and Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC) , China; Ministry of Science, Education and Sport and Croatian Science Foundation, Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research — Natural Sciences, the Carlsberg Foundation and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE) and Council of Scientific and Industrial Research (CSIR), New Delhi, India; Indonesian Institute of Science, Indonesia; Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education and National Science Centre, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation and National Research Centre Kurchatov Institute, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba, Ministerio de Ciencia e Innovacion and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.

Appendix A The ALICE Collaboration

S. Acharya${}^{\textrm{\scriptsize 139}}$, D. Adamová${}^{\textrm{\scriptsize 96}}$, J. Adolfsson${}^{\textrm{\scriptsize 34}}$, M.M. Aggarwal${}^{\textrm{\scriptsize 101}}$, G. Aglieri Rinella${}^{\textrm{\scriptsize 35}}$, M. Agnello${}^{\textrm{\scriptsize 31}}$, N. Agrawal${}^{\textrm{\scriptsize 48}}$, Z. Ahammed${}^{\textrm{\scriptsize 139}}$, N. Ahmad${}^{\textrm{\scriptsize 17}}$, S.U. Ahn${}^{\textrm{\scriptsize 80}}$, S. Aiola${}^{\textrm{\scriptsize 143}}$, A. Akindinov${}^{\textrm{\scriptsize 65}}$, S.N. Alam${}^{\textrm{\scriptsize 139}}$, J.L.B. Alba${}^{\textrm{\scriptsize 114}}$, D.S.D. Albuquerque${}^{\textrm{\scriptsize 125}}$, D. Aleksandrov${}^{\textrm{\scriptsize 92}}$, B. Alessandro${}^{\textrm{\scriptsize 59}}$, R. Alfaro Molina${}^{\textrm{\scriptsize 75}}$, A. Alici${}^{\textrm{\scriptsize 54}}$,${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, A. Alkin${}^{\textrm{\scriptsize 3}}$, J. Alme${}^{\textrm{\scriptsize 22}}$, T. Alt${}^{\textrm{\scriptsize 71}}$, L. Altenkamper${}^{\textrm{\scriptsize 22}}$, I. Altsybeev${}^{\textrm{\scriptsize 138}}$, C. Alves Garcia Prado${}^{\textrm{\scriptsize 124}}$, M. An${}^{\textrm{\scriptsize 7}}$, C. Andrei${}^{\textrm{\scriptsize 89}}$, D. Andreou${}^{\textrm{\scriptsize 35}}$, H.A. Andrews${}^{\textrm{\scriptsize 113}}$, A. Andronic${}^{\textrm{\scriptsize 109}}$, V. Anguelov${}^{\textrm{\scriptsize 106}}$, C. Anson${}^{\textrm{\scriptsize 99}}$, T. Antičić${}^{\textrm{\scriptsize 110}}$, F. Antinori${}^{\textrm{\scriptsize 57}}$, P. Antonioli${}^{\textrm{\scriptsize 54}}$, R. Anwar${}^{\textrm{\scriptsize 127}}$, L. Aphecetche${}^{\textrm{\scriptsize 117}}$, H. Appelshäuser${}^{\textrm{\scriptsize 71}}$, S. Arcelli${}^{\textrm{\scriptsize 27}}$, R. Arnaldi${}^{\textrm{\scriptsize 59}}$, O.W. Arnold${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, I.C. Arsene${}^{\textrm{\scriptsize 21}}$, M. Arslandok${}^{\textrm{\scriptsize 106}}$, B. Audurier${}^{\textrm{\scriptsize 117}}$, A. Augustinus${}^{\textrm{\scriptsize 35}}$, R. Averbeck${}^{\textrm{\scriptsize 109}}$, M.D. Azmi${}^{\textrm{\scriptsize 17}}$, A. Badalà${}^{\textrm{\scriptsize 56}}$, Y.W. Baek${}^{\textrm{\scriptsize 61}}$,${}^{\textrm{\scriptsize 79}}$, S. Bagnasco${}^{\textrm{\scriptsize 59}}$, R. Bailhache${}^{\textrm{\scriptsize 71}}$, R. Bala${}^{\textrm{\scriptsize 103}}$, A. Baldisseri${}^{\textrm{\scriptsize 76}}$, M. Ball${}^{\textrm{\scriptsize 45}}$, R.C. Baral${}^{\textrm{\scriptsize 68}}$, A.M. Barbano${}^{\textrm{\scriptsize 26}}$, R. Barbera${}^{\textrm{\scriptsize 28}}$, F. Barile${}^{\textrm{\scriptsize 33}}$,${}^{\textrm{\scriptsize 53}}$, L. Barioglio${}^{\textrm{\scriptsize 26}}$, G.G. Barnaföldi${}^{\textrm{\scriptsize 142}}$, L.S. Barnby${}^{\textrm{\scriptsize 95}}$,${}^{\textrm{\scriptsize 113}}$, V. Barret${}^{\textrm{\scriptsize 82}}$, P. Bartalini${}^{\textrm{\scriptsize 7}}$, K. Barth${}^{\textrm{\scriptsize 35}}$, E. Bartsch${}^{\textrm{\scriptsize 71}}$, M. Basile${}^{\textrm{\scriptsize 27}}$, N. Bastid${}^{\textrm{\scriptsize 82}}$, S. Basu${}^{\textrm{\scriptsize 141}}$,${}^{\textrm{\scriptsize 139}}$, B. Bathen${}^{\textrm{\scriptsize 72}}$, G. Batigne${}^{\textrm{\scriptsize 117}}$, A. Batista Camejo${}^{\textrm{\scriptsize 82}}$, B. Batyunya${}^{\textrm{\scriptsize 78}}$, P.C. Batzing${}^{\textrm{\scriptsize 21}}$, I.G. Bearden${}^{\textrm{\scriptsize 93}}$, H. Beck${}^{\textrm{\scriptsize 106}}$, C. Bedda${}^{\textrm{\scriptsize 64}}$, N.K. Behera${}^{\textrm{\scriptsize 61}}$, I. Belikov${}^{\textrm{\scriptsize 135}}$, F. Bellini${}^{\textrm{\scriptsize 27}}$, H. Bello Martinez${}^{\textrm{\scriptsize 2}}$, R. Bellwied${}^{\textrm{\scriptsize 127}}$, L.G.E. Beltran${}^{\textrm{\scriptsize 123}}$, V. Belyaev${}^{\textrm{\scriptsize 85}}$, G. Bencedi${}^{\textrm{\scriptsize 142}}$, S. Beole${}^{\textrm{\scriptsize 26}}$, A. Bercuci${}^{\textrm{\scriptsize 89}}$, Y. Berdnikov${}^{\textrm{\scriptsize 98}}$, D. Berenyi${}^{\textrm{\scriptsize 142}}$, R.A. Bertens${}^{\textrm{\scriptsize 130}}$, D. Berzano${}^{\textrm{\scriptsize 35}}$, L. Betev${}^{\textrm{\scriptsize 35}}$, A. Bhasin${}^{\textrm{\scriptsize 103}}$, I.R. Bhat${}^{\textrm{\scriptsize 103}}$, A.K. Bhati${}^{\textrm{\scriptsize 101}}$, B. Bhattacharjee${}^{\textrm{\scriptsize 44}}$, J. Bhom${}^{\textrm{\scriptsize 121}}$, L. Bianchi${}^{\textrm{\scriptsize 127}}$, N. Bianchi${}^{\textrm{\scriptsize 51}}$, C. Bianchin${}^{\textrm{\scriptsize 141}}$, J. Bielčík${}^{\textrm{\scriptsize 39}}$, J. Bielčíková${}^{\textrm{\scriptsize 96}}$, A. Bilandzic${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, G. Biro${}^{\textrm{\scriptsize 142}}$, R. Biswas${}^{\textrm{\scriptsize 4}}$, S. Biswas${}^{\textrm{\scriptsize 4}}$, J.T. Blair${}^{\textrm{\scriptsize 122}}$, D. Blau${}^{\textrm{\scriptsize 92}}$, C. Blume${}^{\textrm{\scriptsize 71}}$, G. Boca${}^{\textrm{\scriptsize 136}}$, F. Bock${}^{\textrm{\scriptsize 106}}$,${}^{\textrm{\scriptsize 84}}$,${}^{\textrm{\scriptsize 35}}$, A. Bogdanov${}^{\textrm{\scriptsize 85}}$, L. Boldizsár${}^{\textrm{\scriptsize 142}}$, M. Bombara${}^{\textrm{\scriptsize 40}}$, G. Bonomi${}^{\textrm{\scriptsize 137}}$, M. Bonora${}^{\textrm{\scriptsize 35}}$, J. Book${}^{\textrm{\scriptsize 71}}$, H. Borel${}^{\textrm{\scriptsize 76}}$, A. Borissov${}^{\textrm{\scriptsize 19}}$, M. Borri${}^{\textrm{\scriptsize 129}}$, E. Botta${}^{\textrm{\scriptsize 26}}$, C. Bourjau${}^{\textrm{\scriptsize 93}}$, P. Braun-Munzinger${}^{\textrm{\scriptsize 109}}$, M. Bregant${}^{\textrm{\scriptsize 124}}$, T.A. Broker${}^{\textrm{\scriptsize 71}}$, T.A. Browning${}^{\textrm{\scriptsize 108}}$, M. Broz${}^{\textrm{\scriptsize 39}}$, E.J. Brucken${}^{\textrm{\scriptsize 46}}$, E. Bruna${}^{\textrm{\scriptsize 59}}$, G.E. Bruno${}^{\textrm{\scriptsize 33}}$, D. Budnikov${}^{\textrm{\scriptsize 111}}$, H. Buesching${}^{\textrm{\scriptsize 71}}$, S. Bufalino${}^{\textrm{\scriptsize 31}}$, P. Buhler${}^{\textrm{\scriptsize 116}}$, P. Buncic${}^{\textrm{\scriptsize 35}}$, O. Busch${}^{\textrm{\scriptsize 133}}$, Z. Buthelezi${}^{\textrm{\scriptsize 77}}$, J.B. Butt${}^{\textrm{\scriptsize 15}}$, J.T. Buxton${}^{\textrm{\scriptsize 18}}$, J. Cabala${}^{\textrm{\scriptsize 119}}$, D. Caffarri${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 94}}$, H. Caines${}^{\textrm{\scriptsize 143}}$, A. Caliva${}^{\textrm{\scriptsize 64}}$, E. Calvo Villar${}^{\textrm{\scriptsize 114}}$, P. Camerini${}^{\textrm{\scriptsize 25}}$, A.A. Capon${}^{\textrm{\scriptsize 116}}$, F. Carena${}^{\textrm{\scriptsize 35}}$, W. Carena${}^{\textrm{\scriptsize 35}}$, F. Carnesecchi${}^{\textrm{\scriptsize 27}}$,${}^{\textrm{\scriptsize 12}}$, J. Castillo Castellanos${}^{\textrm{\scriptsize 76}}$, A.J. Castro${}^{\textrm{\scriptsize 130}}$, E.A.R. Casula${}^{\textrm{\scriptsize 24}}$,${}^{\textrm{\scriptsize 55}}$, C. Ceballos Sanchez${}^{\textrm{\scriptsize 9}}$, P. Cerello${}^{\textrm{\scriptsize 59}}$, S. Chandra${}^{\textrm{\scriptsize 139}}$, B. Chang${}^{\textrm{\scriptsize 128}}$, S. Chapeland${}^{\textrm{\scriptsize 35}}$, M. Chartier${}^{\textrm{\scriptsize 129}}$, J.L. Charvet${}^{\textrm{\scriptsize 76}}$, S. Chattopadhyay${}^{\textrm{\scriptsize 139}}$, S. Chattopadhyay${}^{\textrm{\scriptsize 112}}$, A. Chauvin${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, M. Cherney${}^{\textrm{\scriptsize 99}}$, C. Cheshkov${}^{\textrm{\scriptsize 134}}$, B. Cheynis${}^{\textrm{\scriptsize 134}}$, V. Chibante Barroso${}^{\textrm{\scriptsize 35}}$, D.D. Chinellato${}^{\textrm{\scriptsize 125}}$, S. Cho${}^{\textrm{\scriptsize 61}}$, P. Chochula${}^{\textrm{\scriptsize 35}}$, K. Choi${}^{\textrm{\scriptsize 19}}$, M. Chojnacki${}^{\textrm{\scriptsize 93}}$, S. Choudhury${}^{\textrm{\scriptsize 139}}$, T. Chowdhury${}^{\textrm{\scriptsize 82}}$, P. Christakoglou${}^{\textrm{\scriptsize 94}}$, C.H. Christensen${}^{\textrm{\scriptsize 93}}$, P. Christiansen${}^{\textrm{\scriptsize 34}}$, T. Chujo${}^{\textrm{\scriptsize 133}}$, S.U. Chung${}^{\textrm{\scriptsize 19}}$, C. Cicalo${}^{\textrm{\scriptsize 55}}$, L. Cifarelli${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, F. Cindolo${}^{\textrm{\scriptsize 54}}$, J. Cleymans${}^{\textrm{\scriptsize 102}}$, F. Colamaria${}^{\textrm{\scriptsize 33}}$, D. Colella${}^{\textrm{\scriptsize 66}}$,${}^{\textrm{\scriptsize 35}}$, A. Collu${}^{\textrm{\scriptsize 84}}$, M. Colocci${}^{\textrm{\scriptsize 27}}$, M. Concas${}^{\textrm{\scriptsize 59}}$\Arefidp1804176, G. Conesa Balbastre${}^{\textrm{\scriptsize 83}}$, Z. Conesa del Valle${}^{\textrm{\scriptsize 62}}$, M.E. Connors${}^{\textrm{\scriptsize 143}}$\Arefidp1823568, J.G. Contreras${}^{\textrm{\scriptsize 39}}$, T.M. Cormier${}^{\textrm{\scriptsize 97}}$, Y. Corrales Morales${}^{\textrm{\scriptsize 59}}$, I. Cortés Maldonado${}^{\textrm{\scriptsize 2}}$, P. Cortese${}^{\textrm{\scriptsize 32}}$, M.R. Cosentino${}^{\textrm{\scriptsize 126}}$, F. Costa${}^{\textrm{\scriptsize 35}}$, S. Costanza${}^{\textrm{\scriptsize 136}}$, J. Crkovská${}^{\textrm{\scriptsize 62}}$, P. Crochet${}^{\textrm{\scriptsize 82}}$, E. Cuautle${}^{\textrm{\scriptsize 73}}$, L. Cunqueiro${}^{\textrm{\scriptsize 72}}$, T. Dahms${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, A. Dainese${}^{\textrm{\scriptsize 57}}$, M.C. Danisch${}^{\textrm{\scriptsize 106}}$, A. Danu${}^{\textrm{\scriptsize 69}}$, D. Das${}^{\textrm{\scriptsize 112}}$, I. Das${}^{\textrm{\scriptsize 112}}$, S. Das${}^{\textrm{\scriptsize 4}}$, A. Dash${}^{\textrm{\scriptsize 90}}$, S. Dash${}^{\textrm{\scriptsize 48}}$, S. De${}^{\textrm{\scriptsize 124}}$,${}^{\textrm{\scriptsize 49}}$, A. De Caro${}^{\textrm{\scriptsize 30}}$, G. de Cataldo${}^{\textrm{\scriptsize 53}}$, C. de Conti${}^{\textrm{\scriptsize 124}}$, J. de Cuveland${}^{\textrm{\scriptsize 42}}$, A. De Falco${}^{\textrm{\scriptsize 24}}$, D. De Gruttola${}^{\textrm{\scriptsize 30}}$,${}^{\textrm{\scriptsize 12}}$, N. De Marco${}^{\textrm{\scriptsize 59}}$, S. De Pasquale${}^{\textrm{\scriptsize 30}}$, R.D. De Souza${}^{\textrm{\scriptsize 125}}$, H.F. Degenhardt${}^{\textrm{\scriptsize 124}}$, A. Deisting${}^{\textrm{\scriptsize 109}}$,${}^{\textrm{\scriptsize 106}}$, A. Deloff${}^{\textrm{\scriptsize 88}}$, C. Deplano${}^{\textrm{\scriptsize 94}}$, P. Dhankher${}^{\textrm{\scriptsize 48}}$, D. Di Bari${}^{\textrm{\scriptsize 33}}$, A. Di Mauro${}^{\textrm{\scriptsize 35}}$, P. Di Nezza${}^{\textrm{\scriptsize 51}}$, B. Di Ruzza${}^{\textrm{\scriptsize 57}}$, M.A. Diaz Corchero${}^{\textrm{\scriptsize 10}}$, T. Dietel${}^{\textrm{\scriptsize 102}}$, P. Dillenseger${}^{\textrm{\scriptsize 71}}$, R. Divià${}^{\textrm{\scriptsize 35}}$, Ø. Djuvsland${}^{\textrm{\scriptsize 22}}$, A. Dobrin${}^{\textrm{\scriptsize 35}}$, D. Domenicis Gimenez${}^{\textrm{\scriptsize 124}}$, B. Dönigus${}^{\textrm{\scriptsize 71}}$, O. Dordic${}^{\textrm{\scriptsize 21}}$, L.V.V. Doremalen${}^{\textrm{\scriptsize 64}}$, T. Drozhzhova${}^{\textrm{\scriptsize 71}}$, A.K. Dubey${}^{\textrm{\scriptsize 139}}$, A. Dubla${}^{\textrm{\scriptsize 109}}$, L. Ducroux${}^{\textrm{\scriptsize 134}}$, A.K. Duggal${}^{\textrm{\scriptsize 101}}$, P. Dupieux${}^{\textrm{\scriptsize 82}}$, R.J. Ehlers${}^{\textrm{\scriptsize 143}}$, D. Elia${}^{\textrm{\scriptsize 53}}$, E. Endress${}^{\textrm{\scriptsize 114}}$, H. Engel${}^{\textrm{\scriptsize 70}}$, E. Epple${}^{\textrm{\scriptsize 143}}$, B. Erazmus${}^{\textrm{\scriptsize 117}}$, F. Erhardt${}^{\textrm{\scriptsize 100}}$, B. Espagnon${}^{\textrm{\scriptsize 62}}$, S. Esumi${}^{\textrm{\scriptsize 133}}$, G. Eulisse${}^{\textrm{\scriptsize 35}}$, J. Eum${}^{\textrm{\scriptsize 19}}$, D. Evans${}^{\textrm{\scriptsize 113}}$, S. Evdokimov${}^{\textrm{\scriptsize 115}}$, L. Fabbietti${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, J. Faivre${}^{\textrm{\scriptsize 83}}$, A. Fantoni${}^{\textrm{\scriptsize 51}}$, M. Fasel${}^{\textrm{\scriptsize 84}}$,${}^{\textrm{\scriptsize 97}}$, L. Feldkamp${}^{\textrm{\scriptsize 72}}$, A. Feliciello${}^{\textrm{\scriptsize 59}}$, G. Feofilov${}^{\textrm{\scriptsize 138}}$, J. Ferencei${}^{\textrm{\scriptsize 96}}$, A. Fernández Téllez${}^{\textrm{\scriptsize 2}}$, E.G. Ferreiro${}^{\textrm{\scriptsize 16}}$, A. Ferretti${}^{\textrm{\scriptsize 26}}$, A. Festanti${}^{\textrm{\scriptsize 29}}$, V.J.G. Feuillard${}^{\textrm{\scriptsize 82}}$,${}^{\textrm{\scriptsize 76}}$, J. Figiel${}^{\textrm{\scriptsize 121}}$, M.A.S. Figueredo${}^{\textrm{\scriptsize 124}}$, S. Filchagin${}^{\textrm{\scriptsize 111}}$, D. Finogeev${}^{\textrm{\scriptsize 63}}$, F.M. Fionda${}^{\textrm{\scriptsize 24}}$, E.M. Fiore${}^{\textrm{\scriptsize 33}}$, M. Floris${}^{\textrm{\scriptsize 35}}$, S. Foertsch${}^{\textrm{\scriptsize 77}}$, P. Foka${}^{\textrm{\scriptsize 109}}$, S. Fokin${}^{\textrm{\scriptsize 92}}$, E. Fragiacomo${}^{\textrm{\scriptsize 60}}$, A. Francescon${}^{\textrm{\scriptsize 35}}$, A. Francisco${}^{\textrm{\scriptsize 117}}$, U. Frankenfeld${}^{\textrm{\scriptsize 109}}$, G.G. Fronze${}^{\textrm{\scriptsize 26}}$, U. Fuchs${}^{\textrm{\scriptsize 35}}$, C. Furget${}^{\textrm{\scriptsize 83}}$, A. Furs${}^{\textrm{\scriptsize 63}}$, M. Fusco Girard${}^{\textrm{\scriptsize 30}}$, J.J. Gaardhøje${}^{\textrm{\scriptsize 93}}$, M. Gagliardi${}^{\textrm{\scriptsize 26}}$, A.M. Gago${}^{\textrm{\scriptsize 114}}$, K. Gajdosova${}^{\textrm{\scriptsize 93}}$, M. Gallio${}^{\textrm{\scriptsize 26}}$, C.D. Galvan${}^{\textrm{\scriptsize 123}}$, P. Ganoti${}^{\textrm{\scriptsize 87}}$, C. Gao${}^{\textrm{\scriptsize 7}}$, C. Garabatos${}^{\textrm{\scriptsize 109}}$, E. Garcia-Solis${}^{\textrm{\scriptsize 13}}$, K. Garg${}^{\textrm{\scriptsize 28}}$, P. Garg${}^{\textrm{\scriptsize 49}}$, C. Gargiulo${}^{\textrm{\scriptsize 35}}$, 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A. Rustamov${}^{\textrm{\scriptsize 91}}$, E. Ryabinkin${}^{\textrm{\scriptsize 92}}$, Y. Ryabov${}^{\textrm{\scriptsize 98}}$, A. Rybicki${}^{\textrm{\scriptsize 121}}$, S. Saarinen${}^{\textrm{\scriptsize 46}}$, S. Sadhu${}^{\textrm{\scriptsize 139}}$, S. Sadovsky${}^{\textrm{\scriptsize 115}}$, K. Šafařík${}^{\textrm{\scriptsize 35}}$, S.K. Saha${}^{\textrm{\scriptsize 139}}$, B. Sahlmuller${}^{\textrm{\scriptsize 71}}$, B. Sahoo${}^{\textrm{\scriptsize 48}}$, P. Sahoo${}^{\textrm{\scriptsize 49}}$, R. Sahoo${}^{\textrm{\scriptsize 49}}$, S. Sahoo${}^{\textrm{\scriptsize 68}}$, P.K. Sahu${}^{\textrm{\scriptsize 68}}$, J. Saini${}^{\textrm{\scriptsize 139}}$, S. Sakai${}^{\textrm{\scriptsize 51}}$,${}^{\textrm{\scriptsize 133}}$, M.A. Saleh${}^{\textrm{\scriptsize 141}}$, J. Salzwedel${}^{\textrm{\scriptsize 18}}$, S. Sambyal${}^{\textrm{\scriptsize 103}}$, V. Samsonov${}^{\textrm{\scriptsize 85}}$,${}^{\textrm{\scriptsize 98}}$, A. Sandoval${}^{\textrm{\scriptsize 75}}$, D. Sarkar${}^{\textrm{\scriptsize 139}}$, N. Sarkar${}^{\textrm{\scriptsize 139}}$, P. Sarma${}^{\textrm{\scriptsize 44}}$, M.H.P. Sas${}^{\textrm{\scriptsize 64}}$, E. Scapparone${}^{\textrm{\scriptsize 54}}$, F. Scarlassara${}^{\textrm{\scriptsize 29}}$, R.P. Scharenberg${}^{\textrm{\scriptsize 108}}$, H.S. Scheid${}^{\textrm{\scriptsize 71}}$, C. Schiaua${}^{\textrm{\scriptsize 89}}$, R. Schicker${}^{\textrm{\scriptsize 106}}$, C. Schmidt${}^{\textrm{\scriptsize 109}}$, H.R. Schmidt${}^{\textrm{\scriptsize 105}}$, M.O. Schmidt${}^{\textrm{\scriptsize 106}}$, M. Schmidt${}^{\textrm{\scriptsize 105}}$, S. Schuchmann${}^{\textrm{\scriptsize 106}}$, J. Schukraft${}^{\textrm{\scriptsize 35}}$, Y. Schutz${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 135}}$,${}^{\textrm{\scriptsize 117}}$, K. Schwarz${}^{\textrm{\scriptsize 109}}$, K. Schweda${}^{\textrm{\scriptsize 109}}$, G. Scioli${}^{\textrm{\scriptsize 27}}$, E. Scomparin${}^{\textrm{\scriptsize 59}}$, R. Scott${}^{\textrm{\scriptsize 130}}$, M. Šefčík${}^{\textrm{\scriptsize 40}}$, J.E. Seger${}^{\textrm{\scriptsize 99}}$, Y. Sekiguchi${}^{\textrm{\scriptsize 132}}$, D. Sekihata${}^{\textrm{\scriptsize 47}}$, I. Selyuzhenkov${}^{\textrm{\scriptsize 109}}$,${}^{\textrm{\scriptsize 85}}$, K. Senosi${}^{\textrm{\scriptsize 77}}$, S. Senyukov${}^{\textrm{\scriptsize 3}}$,${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 135}}$, E. Serradilla${}^{\textrm{\scriptsize 75}}$,${}^{\textrm{\scriptsize 10}}$, P. Sett${}^{\textrm{\scriptsize 48}}$, A. Sevcenco${}^{\textrm{\scriptsize 69}}$, A. Shabanov${}^{\textrm{\scriptsize 63}}$, A. Shabetai${}^{\textrm{\scriptsize 117}}$, R. Shahoyan${}^{\textrm{\scriptsize 35}}$, W. Shaikh${}^{\textrm{\scriptsize 112}}$, A. Shangaraev${}^{\textrm{\scriptsize 115}}$, A. Sharma${}^{\textrm{\scriptsize 101}}$, A. Sharma${}^{\textrm{\scriptsize 103}}$, M. Sharma${}^{\textrm{\scriptsize 103}}$, M. Sharma${}^{\textrm{\scriptsize 103}}$, N. Sharma${}^{\textrm{\scriptsize 130}}$,${}^{\textrm{\scriptsize 101}}$, A.I. Sheikh${}^{\textrm{\scriptsize 139}}$, K. Shigaki${}^{\textrm{\scriptsize 47}}$, Q. Shou${}^{\textrm{\scriptsize 7}}$, K. Shtejer${}^{\textrm{\scriptsize 26}}$,${}^{\textrm{\scriptsize 9}}$, Y. Sibiriak${}^{\textrm{\scriptsize 92}}$, S. Siddhanta${}^{\textrm{\scriptsize 55}}$, K.M. Sielewicz${}^{\textrm{\scriptsize 35}}$, T. Siemiarczuk${}^{\textrm{\scriptsize 88}}$, D. Silvermyr${}^{\textrm{\scriptsize 34}}$, C. Silvestre${}^{\textrm{\scriptsize 83}}$, G. Simatovic${}^{\textrm{\scriptsize 100}}$, G. Simonetti${}^{\textrm{\scriptsize 35}}$, R. Singaraju${}^{\textrm{\scriptsize 139}}$, R. Singh${}^{\textrm{\scriptsize 90}}$, V. Singhal${}^{\textrm{\scriptsize 139}}$, T. Sinha${}^{\textrm{\scriptsize 112}}$, B. Sitar${}^{\textrm{\scriptsize 38}}$, M. Sitta${}^{\textrm{\scriptsize 32}}$, T.B. Skaali${}^{\textrm{\scriptsize 21}}$, M. Slupecki${}^{\textrm{\scriptsize 128}}$, N. Smirnov${}^{\textrm{\scriptsize 143}}$, R.J.M. Snellings${}^{\textrm{\scriptsize 64}}$, T.W. Snellman${}^{\textrm{\scriptsize 128}}$, J. Song${}^{\textrm{\scriptsize 19}}$, M. Song${}^{\textrm{\scriptsize 144}}$, F. Soramel${}^{\textrm{\scriptsize 29}}$, S. Sorensen${}^{\textrm{\scriptsize 130}}$, F. Sozzi${}^{\textrm{\scriptsize 109}}$, E. Spiriti${}^{\textrm{\scriptsize 51}}$, I. Sputowska${}^{\textrm{\scriptsize 121}}$, B.K. Srivastava${}^{\textrm{\scriptsize 108}}$, J. Stachel${}^{\textrm{\scriptsize 106}}$, I. Stan${}^{\textrm{\scriptsize 69}}$, P. Stankus${}^{\textrm{\scriptsize 97}}$, E. Stenlund${}^{\textrm{\scriptsize 34}}$, D. Stocco${}^{\textrm{\scriptsize 117}}$, P. Strmen${}^{\textrm{\scriptsize 38}}$, A.A.P. Suaide${}^{\textrm{\scriptsize 124}}$, T. Sugitate${}^{\textrm{\scriptsize 47}}$, C. Suire${}^{\textrm{\scriptsize 62}}$, M. Suleymanov${}^{\textrm{\scriptsize 15}}$, M. Suljic${}^{\textrm{\scriptsize 25}}$, R. Sultanov${}^{\textrm{\scriptsize 65}}$, M. Šumbera${}^{\textrm{\scriptsize 96}}$, S. Sumowidagdo${}^{\textrm{\scriptsize 50}}$, K. Suzuki${}^{\textrm{\scriptsize 116}}$, S. Swain${}^{\textrm{\scriptsize 68}}$, A. Szabo${}^{\textrm{\scriptsize 38}}$, I. Szarka${}^{\textrm{\scriptsize 38}}$, A. Szczepankiewicz${}^{\textrm{\scriptsize 140}}$, U. Tabassam${}^{\textrm{\scriptsize 15}}$, J. Takahashi${}^{\textrm{\scriptsize 125}}$, G.J. Tambave${}^{\textrm{\scriptsize 22}}$, N. Tanaka${}^{\textrm{\scriptsize 133}}$, M. Tarhini${}^{\textrm{\scriptsize 62}}$, M. Tariq${}^{\textrm{\scriptsize 17}}$, M.G. Tarzila${}^{\textrm{\scriptsize 89}}$, A. Tauro${}^{\textrm{\scriptsize 35}}$, G. Tejeda Muñoz${}^{\textrm{\scriptsize 2}}$, A. Telesca${}^{\textrm{\scriptsize 35}}$, K. Terasaki${}^{\textrm{\scriptsize 132}}$, C. Terrevoli${}^{\textrm{\scriptsize 29}}$, B. Teyssier${}^{\textrm{\scriptsize 134}}$, D. Thakur${}^{\textrm{\scriptsize 49}}$, S. Thakur${}^{\textrm{\scriptsize 139}}$, D. Thomas${}^{\textrm{\scriptsize 122}}$, R. Tieulent${}^{\textrm{\scriptsize 134}}$, A. Tikhonov${}^{\textrm{\scriptsize 63}}$, A.R. Timmins${}^{\textrm{\scriptsize 127}}$, A. Toia${}^{\textrm{\scriptsize 71}}$, S. Tripathy${}^{\textrm{\scriptsize 49}}$, S. Trogolo${}^{\textrm{\scriptsize 26}}$, G. Trombetta${}^{\textrm{\scriptsize 33}}$, L. Tropp${}^{\textrm{\scriptsize 40}}$, V. Trubnikov${}^{\textrm{\scriptsize 3}}$, W.H. Trzaska${}^{\textrm{\scriptsize 128}}$, B.A. Trzeciak${}^{\textrm{\scriptsize 64}}$, T. Tsuji${}^{\textrm{\scriptsize 132}}$, A. Tumkin${}^{\textrm{\scriptsize 111}}$, R. Turrisi${}^{\textrm{\scriptsize 57}}$, T.S. Tveter${}^{\textrm{\scriptsize 21}}$, K. Ullaland${}^{\textrm{\scriptsize 22}}$, E.N. Umaka${}^{\textrm{\scriptsize 127}}$, A. Uras${}^{\textrm{\scriptsize 134}}$, G.L. Usai${}^{\textrm{\scriptsize 24}}$, A. Utrobicic${}^{\textrm{\scriptsize 100}}$, M. Vala${}^{\textrm{\scriptsize 66}}$,${}^{\textrm{\scriptsize 119}}$, J. Van Der Maarel${}^{\textrm{\scriptsize 64}}$, J.W. Van Hoorne${}^{\textrm{\scriptsize 35}}$, M. van Leeuwen${}^{\textrm{\scriptsize 64}}$, T. Vanat${}^{\textrm{\scriptsize 96}}$, P. Vande Vyvre${}^{\textrm{\scriptsize 35}}$, D. Varga${}^{\textrm{\scriptsize 142}}$, A. Vargas${}^{\textrm{\scriptsize 2}}$, M. Vargyas${}^{\textrm{\scriptsize 128}}$, R. Varma${}^{\textrm{\scriptsize 48}}$, M. Vasileiou${}^{\textrm{\scriptsize 87}}$, A. Vasiliev${}^{\textrm{\scriptsize 92}}$, A. Vauthier${}^{\textrm{\scriptsize 83}}$, O. Vázquez Doce${}^{\textrm{\scriptsize 107}}$,${}^{\textrm{\scriptsize 36}}$, V. Vechernin${}^{\textrm{\scriptsize 138}}$, A.M. Veen${}^{\textrm{\scriptsize 64}}$, A. Velure${}^{\textrm{\scriptsize 22}}$, E. Vercellin${}^{\textrm{\scriptsize 26}}$, S. Vergara Limón${}^{\textrm{\scriptsize 2}}$, R. Vernet${}^{\textrm{\scriptsize 8}}$, R. Vértesi${}^{\textrm{\scriptsize 142}}$, L. Vickovic${}^{\textrm{\scriptsize 120}}$, S. Vigolo${}^{\textrm{\scriptsize 64}}$, J. Viinikainen${}^{\textrm{\scriptsize 128}}$, Z. Vilakazi${}^{\textrm{\scriptsize 131}}$, O. Villalobos Baillie${}^{\textrm{\scriptsize 113}}$, A. Villatoro Tello${}^{\textrm{\scriptsize 2}}$, A. Vinogradov${}^{\textrm{\scriptsize 92}}$, L. Vinogradov${}^{\textrm{\scriptsize 138}}$, T. Virgili${}^{\textrm{\scriptsize 30}}$, V. Vislavicius${}^{\textrm{\scriptsize 34}}$, A. Vodopyanov${}^{\textrm{\scriptsize 78}}$, M.A. Völkl${}^{\textrm{\scriptsize 106}}$,${}^{\textrm{\scriptsize 105}}$, K. Voloshin${}^{\textrm{\scriptsize 65}}$, S.A. Voloshin${}^{\textrm{\scriptsize 141}}$, G. Volpe${}^{\textrm{\scriptsize 33}}$, B. von Haller${}^{\textrm{\scriptsize 35}}$, I. Vorobyev${}^{\textrm{\scriptsize 36}}$,${}^{\textrm{\scriptsize 107}}$, D. Voscek${}^{\textrm{\scriptsize 119}}$, D. Vranic${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 109}}$, J. Vrláková${}^{\textrm{\scriptsize 40}}$, B. Wagner${}^{\textrm{\scriptsize 22}}$, J. Wagner${}^{\textrm{\scriptsize 109}}$, H. Wang${}^{\textrm{\scriptsize 64}}$, M. Wang${}^{\textrm{\scriptsize 7}}$, D. Watanabe${}^{\textrm{\scriptsize 133}}$, Y. Watanabe${}^{\textrm{\scriptsize 132}}$, M. Weber${}^{\textrm{\scriptsize 116}}$, S.G. Weber${}^{\textrm{\scriptsize 109}}$, D.F. Weiser${}^{\textrm{\scriptsize 106}}$, S.C. Wenzel${}^{\textrm{\scriptsize 35}}$, J.P. Wessels${}^{\textrm{\scriptsize 72}}$, U. Westerhoff${}^{\textrm{\scriptsize 72}}$, A.M. Whitehead${}^{\textrm{\scriptsize 102}}$, J. Wiechula${}^{\textrm{\scriptsize 71}}$, J. Wikne${}^{\textrm{\scriptsize 21}}$, G. Wilk${}^{\textrm{\scriptsize 88}}$, J. Wilkinson${}^{\textrm{\scriptsize 106}}$, G.A. Willems${}^{\textrm{\scriptsize 72}}$, M.C.S. Williams${}^{\textrm{\scriptsize 54}}$, E. Willsher${}^{\textrm{\scriptsize 113}}$, B. Windelband${}^{\textrm{\scriptsize 106}}$, W.E. Witt${}^{\textrm{\scriptsize 130}}$, S. Yalcin${}^{\textrm{\scriptsize 81}}$, K. Yamakawa${}^{\textrm{\scriptsize 47}}$, P. Yang${}^{\textrm{\scriptsize 7}}$, S. Yano${}^{\textrm{\scriptsize 47}}$, Z. Yin${}^{\textrm{\scriptsize 7}}$, H. Yokoyama${}^{\textrm{\scriptsize 133}}$,${}^{\textrm{\scriptsize 83}}$, I.-K. Yoo${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 19}}$, J.H. Yoon${}^{\textrm{\scriptsize 61}}$, V. Yurchenko${}^{\textrm{\scriptsize 3}}$, V. Zaccolo${}^{\textrm{\scriptsize 59}}$,${}^{\textrm{\scriptsize 93}}$, A. Zaman${}^{\textrm{\scriptsize 15}}$, C. Zampolli${}^{\textrm{\scriptsize 35}}$, H.J.C. Zanoli${}^{\textrm{\scriptsize 124}}$, N. Zardoshti${}^{\textrm{\scriptsize 113}}$, A. Zarochentsev${}^{\textrm{\scriptsize 138}}$, P. Závada${}^{\textrm{\scriptsize 67}}$, N. Zaviyalov${}^{\textrm{\scriptsize 111}}$, H. Zbroszczyk${}^{\textrm{\scriptsize 140}}$, M. Zhalov${}^{\textrm{\scriptsize 98}}$, H. Zhang${}^{\textrm{\scriptsize 22}}$,${}^{\textrm{\scriptsize 7}}$, X. Zhang${}^{\textrm{\scriptsize 7}}$, Y. Zhang${}^{\textrm{\scriptsize 7}}$, C. Zhang${}^{\textrm{\scriptsize 64}}$, Z. Zhang${}^{\textrm{\scriptsize 7}}$,${}^{\textrm{\scriptsize 82}}$, C. Zhao${}^{\textrm{\scriptsize 21}}$, N. Zhigareva${}^{\textrm{\scriptsize 65}}$, D. Zhou${}^{\textrm{\scriptsize 7}}$, Y. Zhou${}^{\textrm{\scriptsize 93}}$, Z. Zhou${}^{\textrm{\scriptsize 22}}$, H. Zhu${}^{\textrm{\scriptsize 22}}$, J. Zhu${}^{\textrm{\scriptsize 117}}$,${}^{\textrm{\scriptsize 7}}$, X. Zhu${}^{\textrm{\scriptsize 7}}$, A. Zichichi${}^{\textrm{\scriptsize 12}}$,${}^{\textrm{\scriptsize 27}}$, A. Zimmermann${}^{\textrm{\scriptsize 106}}$, M.B. Zimmermann${}^{\textrm{\scriptsize 35}}$,${}^{\textrm{\scriptsize 72}}$, G. Zinovjev${}^{\textrm{\scriptsize 3}}$, J. Zmeskal${}^{\textrm{\scriptsize 116}}$, S. Zou${}^{\textrm{\scriptsize 7}}$

Affiliation notes

{Authlist}

\Adef

0Deceased

\Adef

idp1804176Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy

\Adef

idp1823568Also at: Georgia State University, Atlanta, Georgia, United States

\Adef

idp4113296Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia

\Adef

idp4471792Also at: Department of Applied Physics, Aligarh Muslim University, Aligarh, India

\Adef

idp5449104Also at: Institute of Theoretical Physics, University of Wroclaw, Poland

Collaboration Institutes

1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia

2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico

3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine

4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India

5Budker Institute for Nuclear Physics, Novosibirsk, Russia

6California Polytechnic State University, San Luis Obispo, California, United States

7Central China Normal University, Wuhan, China

8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France

9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba

10Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain

11Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico

12Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi’, Rome, Italy

13Chicago State University, Chicago, Illinois, United States

14China Institute of Atomic Energy, Beijing, China

15COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan

16Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain

17Department of Physics, Aligarh Muslim University, Aligarh, India

18Department of Physics, Ohio State University, Columbus, Ohio, United States

19Department of Physics, Pusan National University, Pusan, South Korea

20Department of Physics, Sejong University, Seoul, South Korea

21Department of Physics, University of Oslo, Oslo, Norway

22Department of Physics and Technology, University of Bergen, Bergen, Norway

23Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy

24Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy

25Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy

26Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy

27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy

28Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy

29Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy

30Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy

31Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy

32Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy

33Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy

34Division of Experimental High Energy Physics, University of Lund, Lund, Sweden

35European Organization for Nuclear Research (CERN), Geneva, Switzerland

36Excellence Cluster Universe, Technische Universität München, Munich, Germany

37Faculty of Engineering, Bergen University College, Bergen, Norway

38Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia

39Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic

40Faculty of Science, P.J. Šafárik University, Košice, Slovakia

41Faculty of Technology, Buskerud and Vestfold University College, Tonsberg, Norway

42Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

43Gangneung-Wonju National University, Gangneung, South Korea

44Gauhati University, Department of Physics, Guwahati, India

45Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany

46Helsinki Institute of Physics (HIP), Helsinki, Finland

47Hiroshima University, Hiroshima, Japan

48Indian Institute of Technology Bombay (IIT), Mumbai, India

49Indian Institute of Technology Indore, Indore, India

50Indonesian Institute of Sciences, Jakarta, Indonesia

51INFN, Laboratori Nazionali di Frascati, Frascati, Italy

52INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy

53INFN, Sezione di Bari, Bari, Italy

54INFN, Sezione di Bologna, Bologna, Italy

55INFN, Sezione di Cagliari, Cagliari, Italy

56INFN, Sezione di Catania, Catania, Italy

57INFN, Sezione di Padova, Padova, Italy

58INFN, Sezione di Roma, Rome, Italy

59INFN, Sezione di Torino, Turin, Italy

60INFN, Sezione di Trieste, Trieste, Italy

61Inha University, Incheon, South Korea

62Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-IN2P3, Orsay, France

63Institute for Nuclear Research, Academy of Sciences, Moscow, Russia

64Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands

65Institute for Theoretical and Experimental Physics, Moscow, Russia

66Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia

67Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic

68Institute of Physics, Bhubaneswar, India

69Institute of Space Science (ISS), Bucharest, Romania

70Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

71Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany

72Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster, Germany

73Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico

74Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil

75Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

76IRFU, CEA, Université Paris-Saclay, Saclay, France

77iThemba LABS, National Research Foundation, Somerset West, South Africa

78Joint Institute for Nuclear Research (JINR), Dubna, Russia

79Konkuk University, Seoul, South Korea

80Korea Institute of Science and Technology Information, Daejeon, South Korea

81KTO Karatay University, Konya, Turkey

82Laboratoire de Physique Corpusculaire (LPC), Clermont Université, Université Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France

83Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France

84Lawrence Berkeley National Laboratory, Berkeley, California, United States

85Moscow Engineering Physics Institute, Moscow, Russia

86Nagasaki Institute of Applied Science, Nagasaki, Japan

87National and Kapodistrian University of Athens, Physics Department, Athens, Greece, Athens, Greece

88National Centre for Nuclear Studies, Warsaw, Poland

89National Institute for Physics and Nuclear Engineering, Bucharest, Romania

90National Institute of Science Education and Research, Bhubaneswar, India

91National Nuclear Research Center, Baku, Azerbaijan

92National Research Centre Kurchatov Institute, Moscow, Russia

93Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

94Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands

95Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom

96Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Řež u Prahy, Czech Republic

97Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States

98Petersburg Nuclear Physics Institute, Gatchina, Russia

99Physics Department, Creighton University, Omaha, Nebraska, United States

100Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia

101Physics Department, Panjab University, Chandigarh, India

102Physics Department, University of Cape Town, Cape Town, South Africa

103Physics Department, University of Jammu, Jammu, India

104Physics Department, University of Rajasthan, Jaipur, India

105Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen, Germany

106Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

107Physik Department, Technische Universität München, Munich, Germany

108Purdue University, West Lafayette, Indiana, United States

109Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany

110Rudjer Bošković Institute, Zagreb, Croatia

111Russian Federal Nuclear Center (VNIIEF), Sarov, Russia

112Saha Institute of Nuclear Physics, Kolkata, India

113School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom

114Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru

115SSC IHEP of NRC Kurchatov institute, Protvino, Russia

116Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria

117SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France

118Suranaree University of Technology, Nakhon Ratchasima, Thailand

119Technical University of Košice, Košice, Slovakia

120Technical University of Split FESB, Split, Croatia

121The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland

122The University of Texas at Austin, Physics Department, Austin, Texas, United States

123Universidad Autónoma de Sinaloa, Culiacán, Mexico

124Universidade de São Paulo (USP), São Paulo, Brazil

125Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil

126Universidade Federal do ABC, Santo Andre, Brazil

127University of Houston, Houston, Texas, United States

128University of Jyväskylä, Jyväskylä, Finland

129University of Liverpool, Liverpool, United Kingdom

130University of Tennessee, Knoxville, Tennessee, United States

131University of the Witwatersrand, Johannesburg, South Africa

132University of Tokyo, Tokyo, Japan

133University of Tsukuba, Tsukuba, Japan

134Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France

135Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France

136Università degli Studi di Pavia, Pavia, Italy

137Università di Brescia, Brescia, Italy

138V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia

139Variable Energy Cyclotron Centre, Kolkata, India

140Warsaw University of Technology, Warsaw, Poland

141Wayne State University, Detroit, Michigan, United States

142Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary

143Yale University, New Haven, Connecticut, United States

144Yonsei University, Seoul, South Korea

145Zentrum für Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany