Measurement of the impact-parameter dependent azimuthal anisotropy in coherent ρ0 photoproduction in Pb−Pb collisions at √sNN= 5.02 TeV

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Measurement of the impact-parameter dependent azimuthal anisotropy in coherent ρ0 photoproduction in Pb−Pb collisions at √sNN= 5.02 TeV © 2024 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. Funded by SCOAP³ Published version ALICE Collaboration ALICE Collaboration. (2024). Measurement of the impact-parameter dependent azimuthal anisotropy in coherent ρ0 photoproduction in Pb−Pb collisions at √sNN= 5.02 TeV. Physics Letters B, 858, Article 139017. https://doi.org/10.1016/j.physletb.2024.139017 2024 Phys. Lett. B 858 (2024) 139017 Available online 12 September 2024 0370-2693/© 2024 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Contents lists available at ScienceDirect Physics Letters B journal homepage: www.elsevier.com/locate/physletb Letter Measurement of the impact-parameter dependent azimuthal anisotropy in coherent 𝜌0photoproduction in Pb–Pb collisions at √𝑠NN =5.02 TeV .ALICE Collaboration⋆ A R T I C L E I N F O A B S T R A C T Editor: M. Doser Dataset link: https:// www .hepdata .net /record /ins2789555 This Letter presents the first measurement of the impact-parameter dependent angular anisotropy in the decay of coherently photoproduced 𝜌0mesons. The 𝜌0mesons are reconstructed through their decay into pion pairs. The measured anisotropy corresponds to the amplitude of the cos(2𝜙)modulation, where 𝜙is the angle between the two vectors formed by the sum and the difference of the transverse momenta of the pions, respectively. The measurement was performed by the ALICE Collaboration at the LHC using data from ultraperipheral Pb–Pb collisions at a center-of-mass energy of √𝑠NN =5.02 TeV per nucleon pair. Different impact-parameter regions are selected by classifying the events in nuclear-breakup classes. The amplitude of the cos(2𝜙)modulation is found to increase by about one order of magnitude from large to small impact parameters. Theoretical calculations describe the measured cos(2𝜙)anisotropy and its impact-parameter dependence as the result of a quantum interference effect at the femtometer scale, arising from the ambiguity regarding which of the nuclei is the photon source in the interaction. 1. Introduction The heavy ions circulating at the Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC) accelerators are accompanied by a strong, Lorentz contracted, electromagnetic field that can be described as a flux of quasi-real photons. This flux makes it possible to study photoproduction interactions at these facilities [1–4]. Most experimental work uses ultraperipheral collisions (UPCs), where the colliding ions cross paths at impact parameters larger than the sum of their radii. Given the short range of the strong force, UPCs allow one to separate photon-induced processes from hadronic interactions. One of the processes that has received great interest is the photonuclear production of a vector meson, where the incoming photon fluctuates into a quark–antiquark color dipole that scatters off the nucleus traveling in the opposite direction (denoted as the target), and appears as a real vector meson. This process can be either coherent, if the photon couples to the nucleus as a whole, or incoherent, if it interacts with a single nucleon. The two processes result in a different transverse momentum (𝑝T) spectrum; the mean 𝑝Tof the vector meson is related to the size of the target in the impact-parameter plane and it is around 60 (500) MeV/𝑐in the coherent (incoherent) case. In the coherent scenario, it is not known which of the two colliding nuclei emits the photon and which acts as the target, opening up the possibility to study, at femtometer scales, the fundamental quantum mechanical interference between the amplitudes. This idea was first proposed in Ref. [5], where it was ⋆E-mail address: alice -publications @cern .ch. noted that interference effects should be stronger: (𝑖) around midrapidity, where the magnitude of both amplitudes is similar, and (𝑖𝑖) at small impact parameters 𝑏, where 𝑏acts analogously to the distance between slits, in a two-slit interferometer. Coherent vector meson photoproduction accompanied by electromagnetic dissociation (EMD) offers the opportunity to select different impact parameter regions in UPCs [6]. The electromagnetic field of the heavy ions is so intense that there is a non-negligible probability that the two nuclei, besides interacting to produce the 𝜌0, also exchange photons in an independent EMD interaction, where the excited nuclei emit neutrons at beam rapidities. Experimentally, the emitted neutrons can be detected using two zero-degree calorimeters (ZDCs) each of them covering the direction of one of the incoming colliding nuclei. This allows for classifying UPCs as: (i) XnXn, where at least one neutron is detected in each ZDC, (ii) Xn0n + 0nXn, where at least one neutron is detected in only one of the ZDCs, and (iii) 0n0n, where no neutron is detected in the ZDCs; for brevity, the class Xn0n + 0nXn will be denoted as Xn0n in the following text. Since the intensity of the electromagnetic field grows with decreasing impact parameter, the XnXn configuration, where at least three photons are exchanged, selects a region of relatively small impact parameters. The 0nXn and Xn0n configurations select a broader impact-parameter range than XnXn, while 0n0n events encompass all possible impact parameters. EMD is modeled in the RELDIS [7,8] and n𝐎 𝐎n[9]models, while the coherent production of vector mesons accompanied by electromagnetic dissociation is studied with n𝐎 𝐎nand https://doi.org/10.1016/j.physletb.2024.139017 Received 16 June 2024; Received in revised form 27 August 2024; Accepted 9 September 2024 Physics Letters B 858 (2024) 139017 2 ALICE Collaboration STARlight [10]. According to n𝐎 𝐎n, the median impact parameter of coherent 𝜌0photoproduction at the LHC energy changes from about 49 fm in 0n0n to about 19 fm in XnXn. Ref. [5] proposes the suppression of coherent 𝜌0production at small transverse momentum in UPCs as an observable to study interference effects. This effect was measured by the STAR Collaboration in coherent 𝜌0photoproduction at a center-of-mass energy per nucleon pair of √𝑠NN = 200 GeV [11]. The measurement was carried out using two samples, one corresponding to XnXn and the other without any requirement on the detection of neutrons at beam rapidities. As expected, it was observed that the destructive interference was more pronounced in the XnXn sample. Recently, it has been pointed out that interference can also give rise to azimuthal anisotropy, since the incoming photons are linearly polarized. It was suggested to look for this effect in the process 𝛾+𝛾→ 𝑙++𝑙−where 𝛾and 𝑙±denote photons and leptons, respectively [12]. The dependence of this phenomenon on the impact parameter was studied in Ref. [13]. Shortly thereafter, this effect was measured for the XnXn event class by the STAR Collaboration in Au–Au UPCs at √𝑠NN = 200 GeV [14]. These studies were later extended to the photoproduction of a 𝜌0 vector meson, where the 𝜌0inherits the linear polarization of the photon, giving rise to a cos(2𝜙)asymmetry [15,16]. Here, 𝜙is the angle between the two vectors formed by the sum and by the difference of the transverse momenta of the pions produced in the decay 𝜌0→𝜋+𝜋−. More recently, it was proposed to look for cos(𝜙), cos(3𝜙)[17], and cos(4𝜙)[18] modulations. The first two patterns could be produced by the interference of the production of 𝜌0with QED processes, and the last by the interference of resonant and open production of pion pairs. It was also proposed to search for asymmetries in the photoproduction of a J∕𝜓vector meson [19]. The predicted cos(2𝜙)modulation was measured by the STAR Collaboration, for 𝜌0coherent production in XnXn events, in Au–Au and U–U UPCs at √𝑠NN = 200 GeV and √𝑠NN = 193 GeV, respectively [20]. This asymmetry was also recently studied by the CMS Collaboration using exclusive diffractive production of jets at the LHC [21]. The ALICE Collaboration has measured the cross section for EMD in Pb–Pb collisions at center-of-mass energies of √𝑠NN =2.76 TeV [22] and √𝑠NN =5.02 TeV [23], where a good agreement with the predictions from RELDIS and n𝐎 𝐎nwas found. The ALICE Collaboration has also measured coherent 𝜌0photoproduction in Pb–Pb UPCs at √𝑠NN =2.76 TeV [24]and √𝑠NN =5.02 TeV [25], as well as in Xe–Xe UPCs at √𝑠NN =5.44 TeV [26]. The results were compared to predictions from the STARlight and GDL [27]models in Ref. [24], and from STARlight and n𝐎 𝐎nin Refs. [25,26]; in general, the tested models describe well the relative 𝜌0yields in the 0n0n, Xn0n, and XnXn classes. These measurements demonstrate that coherent 𝜌0photoproduction accompanied by EMD is well understood at the LHC and that neutron emission in EMD can be used to select different event classes which are dominated by different impact parameter ranges. In this Letter, the impact-parameter dependence of the cos(2𝜙)asymmetry is studied in Pb–Pb UPCs at √𝑠NN =5.02 TeV using the coherent photoproduction of a 𝜌0meson decaying into a pion pair. The measurements are performed at midrapidity in the range |𝑦| <0.8and in three different EMD classes: 0n0n, Xn0n, and XnXn. 2. Experimental set-up A full description of the ALICE apparatus and its performance is given in Refs. [28,29]. A brief description of the sub-detectors involved in this analysis is given hereafter. The 𝜌0meson is detected through its decay into a pion pair at midrapidity, using the Inner Tracking System (ITS) [30]and the Time Projection Chamber (TPC) [31]to reconstruct the pion tracks. The V0 [32]and ALICE Diffractive (AD) [33] detectors, located at forward rapidities, provide a veto, suppressing hadronic interactions. As mentioned in Sec. 1, three different impact-parameter ranges are selected by means of neutrons emitted at forward rapidities, measured by the ZDCs [22]. The ITS comprises six cylindrical layers coaxial with the beam line. Three different technologies are used, starting from the inner layer: pixel, drift, and strip sensors. Each technology is used in two consecutive layers. All six layers are used for tracking, while the two innermost layers, the Silicon Pixel Detector (SPD), are also used for triggering. The TPC is a large cylindrical gaseous detector that surrounds the ITS. It has a central cathode at high voltage and two readout planes at the end caps, composed of multiwire proportional chambers. It is the main tracking detector and provides particle identification (PID) by measuring the specific ionization energy loss. The ITS and the TPC cover a pseudorapidity interval |𝜂| <0.9and the full azimuth; they are located inside a solenoid magnet that provides a magnetic field of 𝐵=0.5T. The V0 is composed of two scintillator arrays, V0A and V0C, installed on both sides of the nominal interaction point (IP). They cover the pseudorapidity ranges 2.8<𝜂<5.1and −3.7<𝜂<−1.7, respectively. The AD consists of two scintillator stations, ADA and ADC, located along the beam line at +16 m and −19 m from the IP and covering the pseudorapidity ranges 4.8<𝜂<6.3and −7.0<𝜂<−4.9, respectively. There are two ZDC detectors for neutrons, ZNA and ZNC, located at ±112.5m from the IP along the beam line. They detect neutrons with |𝜂| >8.8, with an energy resolution good enough to be sensitive to the emission of a single neutron. Neutron signals are discriminated with a threshold corresponding to an energy deposition of ∼1TeV, which is about three standard deviations below the expected signal from a 2.51 TeV neutron. The ZNs also determine the arrival time of the particles, allowing for the rejection of beam–gas interactions involving charge circulating outside the nominal LHC bunch positions. The analyzed data were recorded by ALICE in 2015, when the LHC provided Pb–Pb collisions at √𝑠NN =5.02 TeV, using a dedicated UPC trigger. This trigger exploits five different signals: four of them veto any activity on either side of the AD or V0 detector within the time window for nominal beam–beam interactions, to suppress hadronic collisions. The fifth signal is a topological trigger that selects events that have at least two track segments, defined as in Ref. [25], in the SPD, with an opening angle in azimuth greater than 153 degrees. This topology was chosen since the coherently produced 𝜌0has a very small transverse momentum and hence the tracks of the pions are almost back-to-back in azimuth. The integrated luminosity of the sample, determined using the V0 detectors as explained in Ref. [25], is about 485 mb−1. 3. Analysis procedure 3.1. Track and event selection Tracks were required to have a distance of closest approach to the event primary vertex smaller than 0.0182 + 0.0350∕(𝑝trk T)1.01 cm in the transverse plane and smaller than 2cm in the longitudinal direction, where 𝑝trk Tis the transverse momentum, in GeV/𝑐, associated to the track. Tracks were also required to have more than 50 associated hits in the TPC, to be reconstructed in both ITS and TPC, and to match the track segments in the SPD that fired the trigger. The events with good tracks were required to fulfill additional selections: (i)have exactly two tracks of opposite sign, (ii)have no offline reconstructed signal in neither the V0 nor AD detectors, and (iii)fulfill the pion selection n2 𝜎1+n2 𝜎2<52, where n𝜎1(n𝜎2) is the difference, in units of the TPC ionization energy loss resolution, between the measured energy loss for track 1 (track 2) and the expected value for a pion with the same momentum. Kinematic selections were also applied: (i)the pion pair rapidity lies in the range |𝑦| <0.8to avoid acceptance edge effects, (ii)the invariant mass of the pion pair is inside the range 0.6GeV/𝑐2<𝑚 𝜋𝜋 < 0.95 GeV/𝑐2, and (iii)the transverse momentum of the 𝜌0candidate is less than 0.1 GeV/𝑐to select coherent processes with high purity. With Physics Letters B 858 (2024) 139017 3 ALICE Collaboration such a selection, the contamination from incoherent events is found to be lower than 4% [25]. More details about event and track selections can be found in Ref. [25]. The data were divided in three independent classes, based on the detection of neutrons at forward rapidity. Events with neutron emission were selected by requiring a signal in ZNA and/or ZNC. The signal time was required to lie within 2ns from the nominal collision time. As explained in Sec. 1, these classes (0n0n, Xn0n, XnXn) can be used to select different impact-parameter ranges for ultraperipheral collisions. For each neutron class, the data were arranged in seven 𝜙intervals of equal size, with 𝜙defined as in Sec. 3.2. The efficiency correction (Sec. 3.3) and signal extraction (Sec. 3.4) were then performed separately for each neutron class and 𝜙interval. 3.2. Asymmetry angle definition The anisotropy described in Sec. 1is predicted to be strongly visible as a function of a variable called 𝜙, defined using the momenta of the pions (𝜋1,2) into which the 𝜌0decays. The 𝜙angle can be defined in two different ways, which will be referred to as average and charge, respectively. In both cases 𝜙is defined as the angle between the transverse components of 𝑝+and 𝑝−, where 𝑝±=𝜋1±𝜋2. Using the average definition, 𝜋1,2are randomly associated to the positive or to the negative track. Using the charge definition, 𝜋1and 𝜋2are the momenta of the positive and of the negative track, respectively. The average definition is helpful since, by construction, it does not allow for a cos(𝜙) component. The two definitions are equivalent in terms of the predicted cos(2𝜙) component. The average definition was chosen as the default one, while the charge definition was used in the evaluation of the systematic uncertainties. In both cases, the 𝜙angle was initially computed within the range of −𝜋to 𝜋. Then, since cos(𝜙) and cos(2𝜙) are even functions, the resulting values were remapped between 0 and 𝜋by flipping the sign of negative values. This procedure improves the stability of signal extraction when fitting the invariant mass spectra in each 𝜙 interval, by doubling the size of the available sample. 3.3. Corrections The correction for the acceptance and efficiency of the detector for the reconstruction and selection of the pion tracks, Acc × 𝜀, was estimated as a function of the pion pair invariant mass using the STARlight [10] Monte Carlo (MC) generator and a realistic description of the ALICE apparatus. This MC production describes accurately the raw data on the vector meson kinematics, with the exception of the transverse momentum distribution [24]. In order to improve the agreement of the MC with data, a re-weighting procedure, described in the following, was applied to the generated 𝑝2 Tspectrum. The first step of the procedure is to fit the inclusive pion pair 𝑝2 Tdistribution of the generated MC. For sufficiently high transverse momentum, 𝑝2 Tcan be approximated with the Mandelstam variable 𝑡, while for very low 𝑝2 T the contribution from the transverse momentum of the photon plays an important role and hence the approximation is no longer valid. Having this in mind, the MC spectrum was fitted for 𝑝2 T>(0.01)2(GeV/𝑐)2using the function d𝑁 d𝑝2 T =𝑐∣𝐹(∣ 𝑡∣,𝑎 Pb,𝑅 Pb)∣ 2,(1) where 𝑐is a normalization constant and 𝐹(∣ 𝑡 ∣) is the form factor of the lead nucleus, obtained as a numerical approximation of the Fourier transform of a Wood–Saxon function [34,35], with fit parameters 𝑅Pb and 𝑎Pb. The weights were then computed using w(𝑝T)=∣𝐹(∣ 𝑡∣,𝑎 0 Pb,𝑅 X)∣ 2 ∣𝐹(∣ 𝑡∣,𝑎 0 Pb,𝑅 0 Pb)∣ 2,(2) where 𝑎0 Pb and 𝑅0 Pb are the parameters extracted from the fit to the MC spectrum and 𝑅Xis chosen in such a way that, after applying the weights to each event of a given generated 𝑝T, the reconstructed 𝑝2 Tspectrum in the MC best reproduces the one in the data. This is achieved by minimizing the bin-by-bin difference between the 𝑝Tdistributions of data and reconstructed MC as a function of 𝑅X, using a 𝜒2-like variable, in the region 𝑝2 T>(0.01)2(GeV/𝑐)2, where the model used for the reweighting is valid. It was verified that the best-fit values of 𝑅Xcomputed for different 𝜙ranges were all compatible among themselves, hence the weights were obtained utilizing the full data set. The Acc × 𝜀correction was obtained using the re-weighted STARlight MC simulations by computing the ratio of reconstructed to generated number of pion pairs in each invariant mass and 𝜙interval, after applying the weights discussed above at the generation level. The number of pion pairs found in data, for each invariant mass and 𝜙interval, was then divided by Acc × 𝜀, to obtain the corrected mass spectra. This was done for each neutron class and 𝜙range. The integrated Acc × 𝜀was found to slightly increase as a function of the invariant mass, ranging from ∼ 10.5% at 𝑚𝜋𝜋 =0.6 GeV/𝑐2to ∼ 14% at 𝑚𝜋𝜋 =0.95 GeV/𝑐2. 3.4. Signal extraction The corrected invariant mass spectra, in each neutron class and in each 𝜙interval, were fitted with: d𝑁 d𝑚𝜋𝜋 =𝑃(𝑚𝜋𝜋)+𝑛𝜇𝜇 𝑀(𝑚𝜋𝜋),(3) where 𝑚𝜋𝜋 is the pion pair invariant mass, 𝑃(𝑚𝜋𝜋)is the function used to describe the pion pair spectrum, 𝑀(𝑚𝜋𝜋)is the shape, estimated with a dedicated MC based on the STARlight generator, of the background originating from muons produced in the 𝛾𝛾 →𝜇+𝜇−process and misidentified as pions, and 𝑛𝜇𝜇 is a normalization constant for said background. Two different parameterizations were used for the pion spectrum. The first parameterization uses a modified Söding model [36]: 𝑃(𝑚𝜋𝜋)=∣𝐴⋅𝐵𝑊𝜌+𝐵∣2,(4) where 𝐵𝑊𝜌is the relativistic Breit–Wigner shape that describes the 𝜌0, 𝐴is its amplitude, and 𝐵is the amplitude of the continuum pion pair production. The relativistic Breit–Wigner function describing the 𝜌0resonance is: 𝐵𝑊𝜌=√𝑚𝜋𝜋 𝑚𝜌Γ𝜌(𝑚𝜋𝜋) 𝑚2 𝜋𝜋 −𝑚2 𝜌+𝑖𝑚𝜌Γ𝜌(𝑚𝜋𝜋),(5) where 𝑚𝜌is the 𝜌0pole mass and Γ𝜌(𝑚𝜋𝜋)=Γ(𝑚𝜌)𝑚𝜌 𝑚𝜋𝜋 (𝑚2 𝜋𝜋 −4𝑚2 𝜋 𝑚2 𝜌−4𝑚2 𝜋)3∕2 ,(6) where Γ(𝑚𝜌) is the 𝜌0pole width. Since 𝐵𝑊𝜌is complex, an interference term between the 𝜌0and the continuum arises from the square module in Eq. (4). The second parameterization uses the model by Ross and Stodolsky [37]: 𝑃(𝑚𝜋𝜋)=𝑓∣𝐵𝑊𝜌∣2(𝑚𝜌 𝑚𝜋𝜋 )𝑘,(7) with fit parameters 𝑓and 𝑘. The fits were performed by fixing 𝑚𝜌and Γ(𝑚𝜌)to the central values reported for a 𝜌0formed in a photoproduction reaction, namely, 𝑚𝜌= 769.2 MeV/𝑐2and Γ(𝑚𝜌)= 151.5 MeV/𝑐2[38]. As discussed in Ref. [25], it was verified that the extracted 𝜌0yield does not vary significantly when the fit function is modified to include a contribution from 𝜔decays. To assess the stability of the signal extraction, it was carried out for each 𝜙interval using 48 different strategies. These strategies included Physics Letters B 858 (2024) 139017 4 ALICE Collaboration Fig. 1. Invariant-mass distribution of pion pairs, with superimposed Söding (solid line) and Ross-Stodolsky (dotted line) fits, for the range 0 <𝜙 <𝜋∕7 in the 0n0n (left) and XnXn (right) neutron classes. The different components of the pion-pair production amplitude in the Söding model are shown: the Breit–Wigner shape that describes the 𝜌0(finer dotted line), the continuum process (dash-dotted line), and the interference between the 𝜌0and the continuum (dash-dot-dot-dot line). The Breit–Wigner extracted from the Ross-Stodolsky model (finest dotted line) is also shown. In this example, the background contribution from misidentified muons is fixed to zero in the fit. 12 different combinations of bin size and fit range (with the widest tested range being 0.6-0.95 GeV/𝑐2and the narrowest 0.65-0.9 GeV/𝑐2), using the Söding or the Ross-Stodolsky model to describe the pion pair mass spectrum, and using 𝑛𝜇𝜇 as a free fit parameter or fixing it to zero. An example of the mass fits, for a specific 𝜙interval and for the 0n0n and XnXn classes, is shown in Fig. 1. After the fit, the 𝜌0yield is obtained by integrating the signal function, |𝐴 𝐵𝑊𝜌|2for the Söding model and 𝑓|𝐵𝑊𝜌|2for the Ross-Stodolsky model, in the mass range 0.6 <𝑚 𝜋𝜋 (GeV/𝑐2) <0.95. 3.5. Asymmetry extraction The extraction of the amplitude of the modulation is affected by the migration of events between neutron classes, due to ZDC detector efficiency and pile-up effects, as discussed in Ref. [25]. To take this into account, a simultaneous fit to the measured 𝜌0yield as a function of 𝜙in all three experimental classes (0n0n, Xn0n, XnXn) was performed, using the following expression: ⎛⎜⎜⎝ 𝑛𝜌0n0n(𝜙) 𝑛𝜌Xn0n(𝜙) 𝑛𝜌XnXn(𝜙)⎞⎟⎟⎠ =⎛⎜⎜⎝ 1 1 1⎞⎟⎟⎠ +⎛⎜⎜⎝ 𝑤0n0n →0n0n 𝑤Xn0n →0n0n 𝑤XnXn →0n0n 𝑤0n0n →Xn0n 𝑤Xn0n →Xn0n 𝑤XnXn →Xn0n 𝑤0n0n →XnXn 𝑤Xn0n →XnXn 𝑤XnXn →XnXn ⎞⎟⎟⎠ ×⎛⎜⎜⎝ 𝑎20n0n 𝑎2Xn0n 𝑎2XnXn ⎞⎟⎟⎠ cos(2𝜙),(8) where 𝑛𝜌0n0n is the normalized 𝜌0yield in a given 𝜙range for the experimental 0n0n class, and similarly for other classes, and the fitting parameters 𝑎20n0n, 𝑎2Xn0n, and 𝑎2XnXn are the amplitudes of the cos(2𝜙) modulation in the corresponding three physical classes. The coefficients 𝑤Y→Zrepresent the contribution of the physical neutron class Y to the yield in the experimental neutron class Z, computed using the measured cross-section ratios and migration probabilities as determined in Ref. [25]. The constant term is fixed to unity by normalization. An example of this simultaneous fit is shown in Fig. 2. The central value and the statistical uncertainty of the cos(2𝜙) modulation amplitude were determined, for each neutron emission class, by averaging the results obtained with the 48 fit configurations described in Sec. 3.4. 3.6. Systematic uncertainties The systematic uncertainty related to the signal extraction includes the effect on the extracted cos(2𝜙) amplitudes of variations in the strategy for fitting the invariant mass spectra. These include: binning, range, modeling of the 𝜌0signal, and treatment of background. The uncertainty was obtained as the standard deviation of the distribution of the fitted amplitudes over the 48 trials mentioned in Sec. 3.4. This uncertainty is 12% for 0n0n, 9% for Xn0n, and 13% for XnXn. An additional systematic uncertainty, related to the definition of the 𝜙angle, was estimated by testing two variations in the analysis strategy. In the first variation, 𝜙is computed according to the charge definition mentioned in Sec. 3.2. In this case, the yield distribution can have a sizeable cos(𝜙)component [17], which is added to the fit function of Eq. (8), with its amplitude as an additional free parameter. In the second variation, the average definition of 𝜙is used, as in the default strategy, but a cos(𝜙)component is nevertheless added to the fit function. The systematic uncertainty was evaluated in each class as the largest difference between the result obtained with the default setting and that obtained with the two strategies presented in this paragraph. It amounts to 3.6% for 0n0n, 5.6% for Xn0n, and 3.3% for XnXn. As a consistency check for the Acc × 𝜀correction, the analysis was repeated in several rapidity sub-ranges, each containing approximately half the total number of reconstructed 𝜌0candidates. In each neutron emission class, the amplitudes extracted in sub-ranges were all found to be compatible, within one standard deviation, with each other and with the amplitude extracted in the full rapidity range. The uncertainty on the Acc × 𝜀correction arises then mainly from the re-weighting procedure described in Sec. 3.3. It was obtained by using the two values of 𝑅X for which the 𝜒2increases by one unit with respect to the minimum, instead of the 𝑅Xvalue that minimizes the 𝜒2. The systematic uncertainty is estimated in each class as the largest difference between the results obtained with the original and with the modified sets of weights. It amounts to 2.9% for 0n0n, 0.8% for Xn0n, and 0.9% for XnXn. The systematic uncertainties related to the migration of events across neutron classes are evaluated by propagating the uncertainties of the ZN pile-up probability (9%) and efficiency (1%), all taken from Ref [25], to the extraction of the cos(2𝜙) amplitude. The resulting uncertainty from pile-up is 0.1%, 2.3%, and 0.9%, respectively, for the 0n0n, Xn0n, and Physics Letters B 858 (2024) 139017 5 ALICE Collaboration Fig. 2. Example of a simultaneous fit to the 𝜌0yield as a function of 𝜙, used to extract the amplitude of the cos(2𝜙)modulation in all neutron classes. The contribution of each physical class to the yield in all experimental classes is shown. Fig. 3. Amplitudes of the cos(2𝜙)modulation of the 𝜌0yield in Pb–Pb collisions at √𝑠NN =5.02TeV in all neutron classes. The results are compared with the Xing et al. [15]and W. Zhao et al. [40]model predictions and, for the XnXn class, with the STAR results [20]in Au–Au and U–U collisions at RHIC. For all the experimental data points, statistical uncertainties are represented with a bar and systematic uncertainties with a box. Table 1 Summary of the relative systematic uncertainties for the measured amplitude of the cos(2𝜙)modulation. Source Uncertainty (%) 0n0n Xn0n+ 0nXn XnXn Signal extraction 12 9.1 13 𝜙definition 3.6 5.7 3.3 Acc × 𝜀2.9 0.8 0.9 ZN pile-up 0.1 2.3 0.9 ZN efficiency 0.7 0.1 0.1 Total 12.6 11.0 13.3 XnXn classes. The uncertainty from the ZN efficiency is 0.7%, 0.1%, and 0.1%, respectively, for the 0n0n, Xn0n, and XnXn classes. The contributions to the systematic uncertainty in the amplitude of the cos(2𝜙) modulation discussed in the previous paragraphs are listed in Table 1. The total uncertainty is obtained as the quadratic sum of all the contributions. It amounts to 12.6% for 0n0n, 11% for Xn0n, and 13.3% for XnXn, and is dominated by the signal extraction for all event classes. 4. Results Fig. 3shows the extracted amplitude of the cos(2𝜙)modulation as a function of the neutron class; the numerical values are reported in Table 2, along with the n𝐎 𝐎nMC estimates of the median impact parameter of the collision for each neutron class. Similar values for the median impact parameters are found using the analytical model presented in Ref. [39]; the values for the XnXn case are also similar to those reported in Ref. [6]. The table also reports the amplitudes predicted by two models described below. The measured anisotropy shows a clear trend with the impact parameter, with a significant increase, by one order of magnitude, from 0n0n to XnXn. The results are compared with the models by H. Xing et al. [15] and by W. Zhao et al. [40]. In both calculations, the 𝜌0signal is integrated in the same kinematic region as in this analysis. In the Xing et al. model, the quasi-real photon exchanged by the nuclei is treated as a color quark–antiquark dipole, that recombines to produce a 𝜌0after scattering off the color-glass-condensate state [41] inside the nuclei. As discussed in Sec. 1, the cos(2𝜙)anisotropy in the model emerges from the presence of two elements: the first is that the photon is linearly polarized along the impact parameter and this polarization is transferred Physics Letters B 858 (2024) 139017 6 ALICE Collaboration Table 2 Amplitudes of the cos(2𝜙)modulation of the 𝜌0yield as a function of 𝜙in all neutron classes, with statistical and systematic uncertainties. An estimate of the median impact parameter of the collision in each neutron class, obtained with the n𝐎 𝐎nMC, is also reported, as well as the predictions by the H. Xing et al. [15]and W. Zhao et al. [40]models. Neutron class median b(n𝐎 𝐎n) amplitude stat. syst. H. Xing et al. W. Zhao et al. 0n0n 49.0 fm 0.028 0.011 0.003 0.015 – 0.031 0.042 – 0.044 Xn0n 22.5 fm 0.14 0.04 0.016 0.14 – 0.19 0.136 – 0.138 XnXn 18.2 fm 0.25 0.06 0.03 0.26 – 0.29 0.200 – 0.214 to the produced vector meson; the second is that there is an interference between the two amplitudes that contribute to the cross section of the vector meson photoproduction process. The interference effect increases as the impact parameter decreases, producing a larger anisotropy for small impact parameters. The uncertainty of the model mostly comes from the probability of emitting a neutron from the scattered nucleus at a given impact parameter, where the latter has been estimated using three different parametrizations from Refs. [42–44]. The model prediction is compatible with data for all neutron classes. The model of W. Zhao et al. [40]is based on the same formalism as the model by H. Xing et al. [15]with two main differences: (i) the interaction of the quark–antiquark dipole with the target is implemented by computing the corresponding Wilson lines, and (ii) the color-charge density used to obtain the Wilson lines is varied event-by-event to represent the different possible color configurations of the target. The quoted uncertainty in the model originates from the statistical precision related to the finite number of sampled configurations. This model, which predicts a milder variation of the modulation amplitude with the neutron class as compared to Xing et al., also gives a reasonable description of the data, with the possible exception of the 0n0n class. For the XnXn class, the amplitude measured by ALICE is also compared with the ones [20] measured by the STAR Collaboration for Au–Au and U–U collisions at the center-of-mass energies of √𝑠NN = 200 GeV and √𝑠NN = 193 GeV, respectively. It is found to be compatible with both. This is consistent with the models, which, for the XnXn selection, predict the cos(2𝜙) modulation amplitude to vary with the colliding nuclei and the center-of-mass energy by less than the current experimental uncertainties. 5. Summary The first measurement of the impact-parameter dependent angular anisotropy in the pion-pair decay of coherently photoproduced 𝜌0 mesons from Pb–Pb ultraperipheral collisions at a center-of-mass energy of √𝑠NN = 5.02 TeV, performed with the ALICE detector, has been presented. The anisotropy is quantified via the distribution of the azimuthal angle 𝜙, defined in Sec. 3.2. The impact parameter is estimated considering neutron emission at forward rapidity. A significant, impact-parameter dependent cos(2𝜙)modulation is observed, with the amplitude of the modulation increasing by about one order of magnitude from the 0n0n (no neutrons emitted, large impact parameter) to the XnXn (neutrons emitted by both colliding nuclei, relatively small impact parameter) class. This trend is reproduced by the theoretical models [15,40]. The result for the XnXn class is compatible with similar measurements by the STAR Collaboration. The coherent photonuclear production of a vector meson in UPCs can be seen as a double-slit experiment [45], where the interference occurs between the amplitudes for quasi-real photon emission by either of the two colliding nuclei. The unambiguous observation of this interference through the measurement of the cos(2𝜙)anisotropy of the 𝜌0yield is a proof of the validity of quantum mechanics at femtometer scales. This is the first measurement of this effect in terms of the impact-parameter dependence. The larger data samples expected from the LHC Run 3 and Run 4 will enable a detailed characterization of the quantum interference effects. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability This manuscript has associated data in a HEPData repository at: https://www .hepdata .net /record /ins2789555. 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 centers 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, Austrian Science Fund (FWF): [M 2467-N36] 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), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020-2027 (object CERN), Bulgaria; Ministry of Education of China (MOEC), Ministry of Science & Technology of China (MSTC) and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the Villum Fonden and Danish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland; Commissariat à l’Énergie 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 und Forschung (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), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia Physics Letters B 858 (2024) 139017 7 ALICE Collaboration (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Académico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)), Netherlands; The Research Council of Norway, Norway; Pontificia Universidad Católica del Perú, Peru; Ministry of Science and Higher Education, National Science Centre and WUT ID-UB, 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, Ministry of Research and Innovation and Institute of Atomic Physics and Universitatea Nationala de Stiinta si Tehnologie Politehnica Bucuresti, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology (SUT), National Science and Technology Development Agency (NSTDA) and National Science, Research and Innovation Fund (NSRF via PMU-B B05F650021), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), 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. In addition, individual groups or members have received support from: Czech Science Foundation (grant no. 23-07499S), Czech Republic; European Research Council (grant no. 950692), European Union; ICSC -Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, European Union - NextGenerationEU; Academy of Finland (Center of Excellence in Quark Matter) (grant nos. 346327, 346328), Finland. References [1] G. Baur, K. Hencken, D. Trautmann, S. Sadovsky, Y. Kharlov, Coherent 𝛾𝛾 and 𝛾A interactions in very peripheral collisions at relativistic ion colliders, Phys. Rep. 364 (2002) 359–450, arXiv :hep -ph /0112211 [hep -ph]. [2] A.J. Baltz, et al., The physics of ultraperipheral collisions at the LHC, Phys. Rep. 458 (2008) 1–171, arXiv :0706 .3356 [nucl -ex]. [3] J.G. Contreras, J.D. Tapia Takaki, Ultra-peripheral heavy-ion collisions at the LHC, Int. J. Mod. Phys. A 30 (2015) 1542012. [4] S.R. Klein, H. Mäntysaari, Imaging the nucleus with high-energy photons, Nat. Rev. Phys. 1 (2019) 662–674, arXiv :1910 .10858 [hep -ex]. [5] S.R. Klein, J. Nystrand, Interference in exclusive vector meson production in heavy ion collisions, Phys. Rev. Lett. 84 (2000) 2330–2333, arXiv :hep -ph /9909237. [6] A.J. Baltz, S.R. Klein, J. Nystrand, Coherent vector meson photoproduction with nuclear breakup in relativistic heavy ion collisions, Phys. Rev. Lett. 89 (2002) 012301, arXiv :nucl -th /0205031. [7] I.A. Pshenichnov, J.P. Bondorf, I.N. Mishustin, A. Ventura, S. Masetti, Mutual heavy ion dissociation in peripheral collisions at ultrarelativistic energies, Phys. Rev. C 64 (2001) 024903, arXiv :nucl -th /0101035. [8] I.A. Pshenichnov, Electromagnetic excitation and fragmentation of ultrarelativistic nuclei, Phys. Part. Nucl. 42 (2011) 215–250. [9] M. Broz, J.G. Contreras, J.D. Tapia Takaki, A generator of forward neutrons for ultraperipheral collisions: n𝐎 𝐎n, Comput. Phys. Commun. (2020) 107181, arXiv :1908 . 08263 [nucl -th]. [10] S.R. Klein, J. Nystrand, J. Seger, Y. Gorbunov, J. Butterworth, STARlight: a Monte Carlo simulation program for ultra-peripheral collisions of relativistic ions, Comput. Phys. Commun. 212 (2017) 258–268, arXiv :1607 .03838 [hep -ph]. [11] STAR Collaboration, B.I. Abelev, et al., Observation of two-source interference in the photoproduction reaction Au Au —>Au Au 𝜌0, Phys. Rev. Lett. 102 (2009) 112301, arXiv :0812 .1063 [nucl -ex]. [12] C. Li, J. Zhou, Y.-J. Zhou, Probing the linear polarization of photons in ultraperipheral heavy ion collisions, Phys. Lett. B 795 (2019) 576–580, arXiv :1903 .10084 [hep -ph]. [13] C. Li, J. Zhou, Y.-J. Zhou, Impact parameter dependence of the azimuthal asymmetry in lepton pair production in heavy ion collisions, Phys. Rev. D 101 (2020) 034015, arXiv :1911 .00237 [hep -ph]. [14] STAR Collaboration, J. Adam, et al., Measurement of 𝑒+𝑒−momentum and angular distributions from linearly polarized photon collisions, Phys. Rev. Lett. 127 (2021) 052302, arXiv :1910 .12400 [nucl -ex]. [15] H. Xing, C. Zhang, J. Zhou, Y.-J. Zhou, The cos 2𝜙azimuthal asymmetry in 𝜌0meson production in ultraperipheral heavy ion collisions, J. High Energy Phys. 10 (2020) 064, arXiv :2006 .06206 [hep -ph]. [16] W. Zha, J.D. Brandenburg, L. Ruan, Z. Tang, Z. Xu, Exploring the double-slit interference with linearly polarized photons, Phys. Rev. D 103 (2021) 033007, arXiv : 2006 .12099 [hep -ph]. [17] Y. Hagiwara, C. Zhang, J. Zhou, Y.-J. Zhou, Coulomb nuclear interference effect in dipion production in ultraperipheral heavy ion collisions, Phys. Rev. D 103 (2021) 074013, arXiv :2011 .13151 [hep -ph]. [18] Y. Hagiwara, C. Zhang, J. Zhou, Y.-J. Zhou, Probing the gluon tomography in photoproduction of dipion, Phys. Rev. D 104 (2021) 094021, arXiv :2106 .13466 [hep -ph]. [19] J.D. Brandenburg, Z. Xu, W. Zha, C. Zhang, J. Zhou, Y. Zhou, Exploring gluon tomography with polarization dependent diffractive J/𝜓production, Phys. Rev. D 106 (2022) 074008, arXiv :2207 .02478 [hep -ph]. [20] STAR Collaboration, M. Abdallah, et al., Tomography of ultrarelativistic nuclei with polarized photon-gluon collisions, Sci. Adv. 9 (2023) eabq3903, arXiv :2204 .01625 [nucl -ex]. [21] CMS Collaboration, A. Tumasyan, et al., Azimuthal correlations within exclusive dijets with large momentum transfer in photon-lead collisions, Phys. Rev. Lett. 131 (2023) 051901, arXiv :2205 .00045 [nucl -ex]. [22] ALICE Collaboration, B. Abelev, et al., Measurement of the cross section for electromagnetic dissociation with neutron emission in Pb–Pb collisions at √𝑠NN = 2.76 TeV, Phys. Rev. Lett. 109 (2012) 252302, arXiv :1203 .2436 [nucl -ex]. [23] ALICE Collaboration, S. Acharya, et al., Neutron emission in ultraperipheral Pb–Pb collisions at √𝑠NN = 5.02 TeV, Phys. Rev. C 107 (2023) 064902, arXiv :2209 .04250 [nucl -ex]. [24] ALICE Collaboration, J. Adam, et al., Coherent 𝜌0photoproduction in ultraperipheral Pb–Pb collisions at √𝑠NN =2.76 TeV, J. High Energy Phys. 09 (2015) 095, arXiv :1503 .09177 [nucl -ex]. [25] ALICE Collaboration, S. Acharya, et al., Coherent photoproduction of 𝜌0vector mesons in ultra-peripheral Pb–Pb collisions at √sNN = 5.02 TeV, J. High Energy Phys. 06 (2020) 035, arXiv :2002 .10897 [nucl -ex]. [26] ALICE Collaboration, S. Acharya, et al., First measurement of coherent 𝜌0photoproduction in ultra-peripheral Xe–Xe collisions at √𝑠NN =5.44 TeV, Phys. Lett. B 820 (2021) 136481, arXiv :2101 .02581 [nucl -ex]. [27] V. Rebyakova, M. Strikman, M. Zhalov, Coherent 𝜌and J/𝜓photoproduction in ultraperipheral processes with electromagnetic dissociation of heavy ions at RHIC and LHC, Phys. Lett. B 710 (2012) 647–653, arXiv :1109 .0737 [hep -ph]. [28] ALICE Collaboration, K. Aamodt, et al., The ALICE experiment at the CERN LHC, J. Instrum. 3 (2008) S08002. [29] ALICE Collaboration, B. Abelev, et al., Performance of the ALICE experiment at the CERN LHC, Int. J. Mod. Phys. A 29 (2014) 1430044, arXiv :1402 .4476 [nucl -ex]. [30] ALICE Collaboration, K. Aamodt, et al., Alignment of the ALICE inner tracking system with cosmic-ray tracks, J. Instrum. 5 (2010) P03003, arXiv :1001 .0502 [physics .ins - det]. [31] J. Alme, et al., The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Methods A 622 (2010) 316–367, arXiv :1001 .1950 [physics .ins -det]. [32] ALICE Collaboration, E. Abbas, et al., Performance of the ALICE VZERO system, J. Instrum. 8 (2013) P10016, arXiv :1306 .3130 [nucl -ex]. [33] LHC Forward Physics Working Group Collaboration, K. Akiba, et al., LHC forward physics, J. Phys. G, Nucl. Part. Phys. 43 (2016) 110201, arXiv :1611 .05079 [hep -ph]. [34] S.R. Klein, J. Nystrand, Exclusive vector meson production in relativistic heavy ion collisions, Phys. Rev. C 60 (1999) 014903, arXiv :hep -ph /9902259 [hep -ph]. [35] L.C. Maximon, R.A. Schrack, The form factor of the Fermi model spatial distribution, J. Res. Natl. Bur. Stand. B 70 (1966) 85–94. [36] A.S. Krass, Interference effects in photoproduction of 𝜚0mesons, Phys. Rev. 159 (1967) 1496–1500. [37] M. Ross, L. Stodolsky, Photon dissociation model for vector-meson photoproduction, Phys. Rev. 149 (1966) 1172–1181. [38] Particle Data Group Collaboration, R.L. Workman, et al., Review of particle physics, PTEP 2022 (2022) 083C01. [39] G. Baur, K. Hencken, A. Aste, D. Trautmann, S.R. Klein, Multiphoton exchange processes in ultraperipheral relativistic heavy ion collisions, Nucl. Phys. A 729 (2003) 787–808, arXiv :nucl -th /0307031. [40] H. Mäntysaari, F. Salazar, B. Schenke, C. Shen, W. Zhao, Effects of nuclear structure and quantum interference on diffractive vector meson production in ultraperipheral nuclear collisions, Phys. Rev. C 109 (2024) 024908, arXiv :2310 .15300 [nucl -th]. [41] F. Gelis, E. Iancu, J. Jalilian-Marian, R. Venugopalan, The color glass condensate, Annu. Rev. Nucl. Part. Sci. 60 (2010) 463–489, arXiv :1002 .0333 [hep -ph]. [42] C.A. Bertulani, G. Baur, Electromagnetic processes in relativistic heavy ion collisions, Phys. Rep. 163 (1988) 299. [43] A.J. Baltz, M.J. Rhoades-Brown, J. Weneser, Heavy ion partial beam lifetimes due to Coulomb induced processes, Phys. Rev. E 54 (1996) 4233–4239. [44] A.J. Baltz, M. Strikman, Suppression of heavy ion 𝛾𝛾 production of the Higgs particle by Coulomb dissociation, Phys. Rev. D 57 (1998) 548–549, arXiv :hep -ph /9705220. [45] J. Nystrand, A.J. Baltz, S.R. Klein, Aspects of Coulomb dissociation and interference in peripheral nucleus-nucleus collisions, in: Workshop on Electromagnetic Probes of Fundamental Physics, 3, 2002, pp. 161–170, arXiv :nucl -th /0203062. Physics Letters B 858 (2024) 139017 8 ALICE Collaboration ALICE Collaboration S. Acharya127,, D. Adamová 86,, A. Agarwal135, G. Aglieri Rinella 32,, L. Aglietta 24,, M. Agnello29,, N. Agrawal25,, Z. Ahammed 135,, S. Ahmad15,, S.U. Ahn71,, I. Ahuja 37,, A. Akindinov141,, V. Akishina38, M. Al-Turany97,, D. Aleksandrov 141,, B. Alessandro56,, H.M. Alfanda6,, R. Alfaro Molina67,, B. Ali 15,, A. Alici25,, N. Alizadehvandchali 116,, A. Alkin 104,, J. Alme 20,, G. Alocco52,, T. Alt64,, A.R. Altamura 50,, I. Altsybeev95,, J.R. Alvarado 44,, C.O.R. Alvarez 44, M.N. Anaam 6,, C. Andrei45,, N. Andreou 115,, A. Andronic126,, E. Andronov141,, V. Anguelov 94,, F. Antinori 54,, P. Antonioli51,, N. Apadula 74,, L. Aphecetche103,, H. Appelshäuser 64,, C. Arata 73,, S. Arcelli25,, M. Aresti 22,, R. Arnaldi56,, J.G.M.C.A. Arneiro 110,, I.C. Arsene19,, M. Arslandok 138,, A. Augustinus32,, R. Averbeck 97,, M.D. Azmi15,, H. Baba 124, A. Badalà53,, J. Bae 104,, Y.W. Baek40,, X. Bai120,, R. Bailhache 64,, Y. Bailung 48,, R. Bala91,, A. Balbino 29,, A. Baldisseri 130,, B. Balis2,, D. Banerjee4,, Z. Banoo 91,, V. Barbasova 37, F. Barile 31,, L. Barioglio56,, M. Barlou 78, B. Barman41, G.G. Barnaföldi46,, L.S. Barnby115,, E. Barreau 103,, V. Barret127,, L. Barreto 110,, C. Bartels 119,, K. Barth32,, E. Bartsch 64,, N. Bastid127,, S. Basu 75,, G. Batigne 103,, D. Battistini 95,, B. Batyunya 142,, D. Bauri47, J.L. Bazo Alba101,, I.G. Bearden 83,, C. Beattie138,, P. Becht97,, D. Behera 48,, I. Belikov129,, A.D.C. Bell Hechavarria 126,, F. Bellini25,, R. Bellwied 116,, S. Belokurova 141,, L.G.E. Beltran109,, Y.A.V. Beltran 44,, G. Bencedi46,, A. Bensaoula116, S. Beole24,, Y. Berdnikov 141,, A. Berdnikova94,, L. Bergmann 94,, M.G. Besoiu63,, L. Betev 32,, P.P. Bhaduri 135,, A. Bhasin91,, B. Bhattacharjee41,, L. Bianchi 24,, N. Bianchi49,, J. Bielčík 35,, J. Bielčíková 86,, A.P. Bigot129,, A. Bilandzic95,, G. Biro 46,, S. Biswas4,, N. Bize 103,, J.T. Blair 108,, D. Blau141,, M.B. Blidaru 97,, N. Bluhme38, C. Blume64,, G. Boca 21,55,, F. Bock 87,, T. Bodova 20,, J. Bok 16,, L. Boldizsár46,, M. Bombara37,, P.M. Bond 32,, G. Bonomi134,55,, H. Borel130,, A. Borissov 141,, A.G. Borquez Carcamo94,, H. Bossi 138,, E. Botta 24,, Y.E.M. Bouziani64,, L. Bratrud 64,, P. Braun-Munzinger 97,, M. Bregant110,, M. Broz 35,, G.E. Bruno96,31,, V.D. Buchakchiev36,, M.D. Buckland 23,, D. Budnikov141,, H. Buesching 64,, S. Bufalino 29,, P. Buhler102,, N. Burmasov 141,, Z. Buthelezi 68,123,, A. Bylinkin20,, S.A. Bysiak 107, J.C. Cabanillas Noris109,, M.F.T. Cabrera 116, M. Cai 6,, H. Caines 138,, A. Caliva28,, E. Calvo Villar 101,, J.M.M. Camacho109,, P. Camerini23,, F.D.M. Canedo 110,, S.L. Cantway138,, M. Carabas 113,, A.A. Carballo 32,, F. Carnesecchi32,, R. Caron 128,, L.A.D. Carvalho110,, J. Castillo Castellanos 130,, M. Castoldi32,, F. Catalano32,, S. Cattaruzzi 23,, C. Ceballos Sanchez142,, R. Cerri 24,, I. Chakaberia 74,, P. Chakraborty 136,47,, S. Chandra135,, S. Chapeland32,, M. Chartier 119,, S. Chattopadhay 135, S. Chattopadhyay135,, S. Chattopadhyay 99,, M. Chen39, T. Cheng97,6,, C. Cheshkov 128,, V. Chibante Barroso32,, D.D. Chinellato 111,, E.S. Chizzali95, ,II, J. Cho58,, S. Cho 58,, P. Chochula32,, Z.A. Chochulska 136, D. Choudhury41, P. Christakoglou84,, C.H. Christensen 83,, P. Christiansen75,, T. Chujo 125,, M. Ciacco 29,, C. Cicalo52,, M.R. Ciupek97, G. Clai51,III, F. Colamaria 50,, J.S. Colburn100, D. Colella31,, M. Colocci 25,, M. Concas 32,, G. Conesa Balbastre73,, Z. Conesa del Valle 131,, G. Contin23,, J.G. Contreras35,, M.L. Coquet 103,130,, P. Cortese133,56,, M.R. Cosentino 112,, F. Costa 32,, S. Costanza21,55,, C. Cot 131,, J. Crkovská 94,, P. Crochet127,, R. Cruz-Torres 74,, P. Cui6,, M.M. Czarnynoga136, A. Dainese54,, G. Dange 38, M.C. Danisch94,, A. Danu 63,, P. Das 80,, P. Das4,, S. Das 4,, A.R. Dash126,, S. Dash47,, A. De Caro28,, G. de Cataldo 50,, J. de Cuveland38, A. De Falco 22,, D. De Gruttola28,, N. De Marco 56,, C. De Martin23,, S. De Pasquale 28,, R. Deb134,, R. Del Grande95,, L. Dello Stritto 32,, W. Deng6,, K.C. Devereaux18, P. Dhankher18,, D. Di Bari 31,, A. Di Mauro 32,, B. Diab130,, R.A. Diaz 142,7,, T. Dietel114,, Y. Ding 6,, J. Ditzel64,, R. Divià 32,, Ø. Djuvsland 20, U. Dmitrieva 141,, A. Dobrin63,,