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At least 559 records · Page 31

Measurement of two-photon decay width of χ c2 (1 P ) in γγ → χ c2 (1 P ) → J/ψγ at Belle

We report the measurement of the two-photon decay width of χ c2 (1P) in two-photon processes at the Belle experiment. We analyze the process γγ → χ c2 (1P) → J/ψγ, J/ψ → ℓ + ℓ - (ℓ = e or μ) using a data sample of 971 fb -1 collected with the Belle detector at the KEKB e + e - collider. In this analysis, the product of the two-photon decay width of χ c2 (1P) and the branching fraction is determined to be ${\Gamma}_{\gamma \gamma}({\chi}_{c2}(1P))\mathcal{B}({\chi}_{c2}(1P)\to J/\psi \gamma) \mathcal{B} (J/\psi \to {\ell}^{+}{\ell}^{-})=$ 14.8 ± 0.3(stat.) ± 0.7(syst.) eV, which corresponds to Γ γγ (χ c2 (1P)) = 653 ± 13(stat.) ± 31(syst.) ± 17(B.R.) eV, where the third uncertainty is from $\mathcal{B}$ (χ c2 (1P) → J/ψγ) and $\mathcal{B}$ (J/ψ → ℓ + ℓ - ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Jet fragmentation transverse momentum distributions in pp and p-Pb collisions at $ \sqrt{s}$, $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV

Jet fragmentation transverse momentum ( j T ) distributions are measured in proton-proton (pp) and proton-lead (p-Pb) collisions at s NN = 5 . 02 TeV with the ALICE experiment at the LHC. Jets are reconstructed with the ALICE tracking detectors and electromagnetic calorimeter using the anti- k T algorithm with resolution parameter R = 0 . 4 in the pseudorapidity range |η| < 0 . 25. The j T values are calculated for charged particles inside a fixed cone with a radius R = 0 . 4 around the reconstructed jet axis. The measured j T distributions are compared with a variety of parton-shower models. Herwig and P ythia 8 based models describe the data well for the higher j T region, while they underestimate the lower j T region. The j T distributions are further characterised by fitting them with a function composed of an inverse gamma function for higher j T values (called the “wide component”), related to the perturbative component of the fragmentation process, and with a Gaussian for lower j T values (called the “narrow component”), predominantly connected to the hadronisation process. The width of the Gaussian has only a weak dependence on jet transverse momentum, while that of the inverse gamma function increases with increasing jet transverse momentum. For the narrow component, the measured trends are successfully described by all models except for Herwig. For the wide component, Herwig and PYTHIA 8 based models slightly underestimate the data for the higher jet transverse momentum region. These measurements set constraints on models of jet fragmentation and hadronisation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

First Search for Axion Dark Matter with a MADMAX Prototype

This Letter presents the first search for dark matter axions with mass in the ranges 76.56 to 76.82 μ⁢eV and 79.31 to 79.53 μ⁢eV using a prototype setup for the MAgnetized Disk and Mirror Axion eXperiment (MADMAX). The experimental setup employs a dielectric haloscope consisting of three sapphire disks and a mirror to resonantly enhance the axion-induced microwave signal within the magnetic dipole field provided by the 1.6 T Morpurgo magnet at CERN. Over 14.5 days of data collection, no axion signal was detected. A 95% CL upper limit on the axion-photon coupling strength down to |𝑔 𝑎⁢𝛾 |∼2×10 −11 GeV −1 is set in the targeted mass ranges, surpassing previous constraints, assuming a local axion dark matter density 𝜌 𝑎 of 0.3 GeV/cm 3 . This study marks the first axion dark matter search using a dielectric haloscope.

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Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of beauty production via non-prompt D 0 mesons in Pb-Pb collisions at $ \sqrt{{\textrm{s}}_{\textrm{NN}}} $ = 5.02 TeV

The production of non-prompt D 0 mesons from beauty-hadron decays was measured at midrapidity (|y| < 0.5) in Pb-Pb collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}}$= 5.02 TeV with the ALICE experiment at the LHC. Their nuclear modification factor (R AA ), measured for the first time down to p T = 1 GeV/c in the 0–10% and 30–50% centrality classes, indicates a significant suppression, up to a factor of about three, for p T > 5 GeV/c in the 0–10% central Pb-Pb collisions. The data are described by models that include both collisional and radiative processes in the calculation of beauty-quark energy loss in the quark-gluon plasma, and quark recombination in addition to fragmentation as a hadronisation mechanism. The ratio of the non-prompt to prompt D 0 -meson R AA is larger than unity for p T > 4 GeV/c in the 0–10% central Pb-Pb collisions, as predicted by models in which beauty quarks lose less energy than charm quarks in the quark-gluon plasma because of their larger mass.

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Measurement of beauty and charm production in pp collisions at $\sqrt{s}$ = 5.02 TeV via non-prompt and prompt D mesons

The pT-differential production cross sections of prompt and non-prompt (produced in beauty-hadron decays) D mesons were measured by the ALICE experiment at midrapidity (|y| < 0.5) in proton-proton collisions at s√ = 5.02 TeV. The data sample used in the analysis corresponds to an integrated luminosity of (19.3 ± 0.4) nb -1 . D mesons were reconstructed from their decays D 0 → K - π + , D + → K - π + π + , and D$^+_s$→ φπ + → K - K + π + and their charge conjugates. Compared to previous measurements in the same rapidity region, the cross sections of prompt D + and D$^+_s$ mesons have an extended pT coverage and total uncertainties reduced by a factor ranging from 1.05 to 1.6, depending on pT, allowing for a more precise determination of their pT-integrated cross sections. The results are well described by perturbative QCD calculations. The fragmentation fraction of heavy quarks to strange mesons divided by the one to non-strange mesons, f s /(f u + f d ), is compatible for charm and beauty quarks and with previous measurements at different centre-of-mass energies and collision systems. The $b\bar{b}$ production cross section per rapidity unit at midrapidity, estimated from non-prompt D-meson measurements, is d$σ_{b\bar{b}}$/d$y$| |y|<0.5 = $34.5 ± 2.4(stat)^{+4.7}_{-2.9}$(tot.syst) μb. It is compatible with previous measurements at the same centre-of-mass energy and with the cross section pre- dicted by perturbative QCD calculations.

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Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗

Search for B 0 → K *0 𝜏 + ⁢𝜏 − Decays at the Belle II Experiment

We present a search for the rare flavor-changing neutral-current decay 𝐵 0 →𝐾 *0 ⁢𝜏 + ⁢𝜏 − with data collected by the Belle II experiment at the SuperKEKB electron-positron collider. The analysis uses a 365 fb −1 data sample recorded at the center-of-mass energy of the ϒ⁡(4⁢𝑆) resonance. One of the 𝐵 mesons produced in the ϒ⁡(4⁢𝑆)→𝐵 0 $⁢\overline{𝐵}$ 0 process is fully reconstructed in a hadronic decay mode, while its companion 𝐵 meson is required to decay into a 𝐾 *0 and two 𝜏 leptons of opposite charge. The 𝜏 leptons are reconstructed in final states with a single electron, muon, charged pion or charged 𝜌 meson, and additional neutrinos. We set an upper limit on the branching fraction of ℬ⁡(𝐵 0 →𝐾 *0 ⁢𝜏 + ⁢𝜏 − )<1.8×10 −3 at the 90% confidence level, which is the most stringent constraint reported to date.

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The Search for Feebly Interacting Particles

At the dawn of a new decade, particle physics faces the challenge of explaining the mystery of dark matter, the origin of matter over antimatter in the Universe, the apparent fine-tuning of the electroweak scale, and many other aspects of fundamental physics. Perhaps the most striking frontier to emerge in the search for answers involves New Physics at mass scales comparable to that of familiar matter—below the GeV scale but with very feeble interaction strength. New theoretical ideas to address dark matter and other fundamental questions predict such feebly interacting particles (FIPs) at these scales, and existing data may even provide hints of this possibility. Emboldened by the lessons of the LHC, a vibrant experimental program to discover such physics is underway, guided by a systematic theoretical approach that is firmly grounded in the underlying principles of the Standard Model. We give an overview of these efforts, their motivations, and the decadal goals that animate the community involved in the search for FIPs, and we focus in particular on accelerator-based experiments.

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Unveiling hidden physics at the LHC

The field of particle physics is at the crossroads. The discovery of a Higgs-like boson completed the Standard Model (SM), but the lacking observation of convincing resonances Beyond the SM (BSM) offers no guidance for the future of particle physics. On the other hand, the motivation for New Physics has not diminished and is, in fact, reinforced by several striking anomalous results in many experiments. Here we summarise the status of the most significant anomalies, including the most recent results for the flavour anomalies, the multi-lepton anomalies at the LHC, the Higgs-like excess at around 96 GeV, and anomalies in neutrino physics, astrophysics, cosmology, and cosmic rays. While the LHC promises up to 4 ab –1 of integrated luminosity and far-reaching physics programmes to unveil BSM physics, we consider the possibility that the latter could be tested with present data, but that systemic shortcomings of the experiments and their search strategies may preclude their discovery for several reasons, including: final states consisting in soft particles only, associated production processes, QCD-like final states, close-by SM resonances, and SUSY scenarios where no missing energy is produced. New search strategies could help to unveil the hidden BSM signatures, devised by making use of the CERN open data as a new testing ground. We discuss the CERN open data with its policies, challenges, and potential usefulness for the community. We showcase the example of the CMS collaboration, which is the only collaboration regularly releasing some of its data. We find it important to stress that individuals using public data for their own research does not imply competition with experimental efforts, but rather provides unique opportunities to give guidance for further BSM searches by the collaborations. Wide access to open data is paramount to fully exploit the LHCs potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Observation of the ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$ decay and measurement of its branching ratio

A measurement of the ${K}^{+}\to {\pi}^{+}\nu \overline{\nu}$ decay by the NA62 experiment at the CERN SPS is presented, using data collected in 2021 and 2022. This dataset was recorded, after modifications to the beamline and detectors, at a higher instantaneous beam intensity with respect to the 2016–2018 data taking. Combining NA62 data collected in 2016–2022, a measurement $\mathcal{B} ({K}^{+}\to {\pi}^{+}\nu \overline{\nu}) = \large{(}13.0^{+3.3}_{-3.0}\large{)}$ x $10^{-11}$ of is reported. With 51 signal candidates observed and an expected background of $18^{+3}_{-2}$ events, $\mathcal{B} ({K}^{+}\to {\pi}^{+}\nu \overline{\nu})$ becomes the smallest branching ratio measured with a signal significance above 5σ.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Constitutive Relation in Transitional Granular Flows

To study the constitutive behavior of granular materials, the presence of gravity is detrimental. Although empirical relations have been obtained for engineering designs to control granular flows on Earth, it is not known how well these Earthbound relations can be used in another gravity field. Fundamental understanding must be derived to reliably design for granular flows in space exploration. There are two extremes of granular flows of which significant amount of knowledge is available. One deals with a dense and quasi-static situation where the deformation rate nearly vanishes. The other deals with dilute and rapidly fluctuating grain velocities where particle inertia dominates. This project, funded by the NASA Microgravity Fluid Physics Program, aims to study this transitional regime via physical experiments and computer simulations. A conceptual model has been established as described below. There are two natural time scales in a granular flow. One is the travel time between two consecutive collisions and the other is the duration of a collision contact. At a very low shear-rate, the shear-induced particle velocity is low. Hence the travel time between collisions is longer than the contact time between colliding particles. Binary collisions prevail. As the shear-rate increases, the traveling time between collisions reduces and the probability of multiple collisions goes up. These particle groups disperse shortly after and new groups form. When shear-rate is further increased, clusters grow in size due to an increasing chance for free particles to join before groups have the time to disperse. The maximum cluster size may depend on the global concentration and material properties. As the solid concentration approaches zero, the cluster size goes to one particle diameter. The maximum possible cluster size under any condition is the container size, provided that the shear flow is inside a container. The critical shear-rates that dictate the initiation of the multiple contacts, and the size and lifetime of the collision clusters, are functions of the concentration also. A 'regime' theory has been proposed by Babic et al. This theory suggested that both the solid concentration, C, and the non-dimensional shear-rate, B, are important in determining the regimes of the granular constitutive law. Additional information is included in the original extended abstract.

Shen, Hayley H.↗

Study of η(1405)/η(1475) in $J/\psi \to \gamma {K}_S^0{K}_S^0{\pi}^0$ decay

Using a sample of (10 . 09 ± 0 . 04) × 10 9 J/ψ decays collected with the BESIII detector, partial wave analyses of the decay $ J/\psi \to \gamma {K}_S^0{K}_S^0{\pi}^0$ are performed within the ${K}_S^0{K}_S^0{\pi}^0$ invariant mass region below 1.6 GeV/ c 2 . The covariant tensor amplitude method is used in both mass independent and mass dependent approaches. Both analysis approaches exhibit dominant pseudoscalar and axial vector components, and show good consistency for the other individual components. Furthermore, the mass dependent analysis reveals that the ${K}_S^0{K}_S^0{\pi}^0$ invariant mass spectrum for the pseudoscalar component can be well described with two isoscalar resonant states using relativistic Breit-Wigner model, i.e., the η (1405) with a mass of $1391.7\pm {0.7}_{-0.3}^{+11.3}$ MeV/ c 2 and a width of $60.8\pm {1.2}_{-12.0}^{+5.5}$ MeV, and the η (1475) with a mass of $1507.6\pm {1.6}_{-32.2}^{+15.5}$ MeV/ c 2 and a width of $115.8\pm {2.4}_{-10.9}^{+14.8}$ MeV. The first and second uncertainties are statistical and systematic, respectively. Alternate models for the pseudoscalar component are also tested, but the description of the ${K}_S^0{K}_S^0{\pi}^0$ invariant mass spectrum deteriorates significantly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higher harmonic non-linear flow modes of charged hadrons in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV

Anisotropic flow coefficients, v n , non-linear flow mode coefficients, χ n,mk , and correlations among different symmetry planes, ρ n,mk are measured in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV. Results obtained with multi-particle correlations are reported for the transverse momentum interval 0.2 < p T < 5.0 GeV/c within the pseudorapidity interval 0.4 < |η| < 0.8 as a function of collision centrality. The v n coefficients and χ n,mk and ρ n,mk are presented up to the ninth and seventh harmonic order, respectively. Calculations suggest that the correlations measured in different symmetry planes and the non-linear flow mode coefficients are dependent on the shear and bulk viscosity to entropy ratios of the medium created in heavy-ion collisions. The comparison between these measurements and those at lower energies and calculations from hydrodynamic models places strong constraints on the initial conditions and transport properties of the system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at $ \sqrt{s} $ = 13 TeV

Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at √s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-(Δη ~ 0) and long-range (1.6 < |Δη| < 1.8) in pseudorapidity are extracted on the near-side (Δ~ 0). They are reported as a function of transverse momentum (p T ) in the range 1 < p T < 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-p T leading particles or jets for varying p T thresholds. The results demonstrate that the long-range “ridge” yield, possibly related to the collective behavior of the system, is present in events with high-p T processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the p T dependency, while overestimating the event-scale dependency.

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Measurements of the groomed and ungroomed jet angularities in pp collisions at $ \sqrt{s}$ = 5.02 TeV

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into final-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at $\sqrt{s}$ = 5.02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (|η| < 0.9). The anti-$k_T$ algorithm is used with jet resolution parameters R = 0.2 and R = 0.4 for several transverse momentum $p^{ch jet}_{T}$ intervals in the 20–100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underlying event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, λ α , and groomed jet angularities, λ α,g , to investigate the interplay between perturbative and nonperturbative effects at low jet momenta. Various angular exponent parameters α = 1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic accuracy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

W ± -boson production in p–Pb collisions at $ \sqrt{s_{\textrm{NN}}} $ = 8.16 TeV and Pb–Pb collisions at $ \sqrt{s_{\textrm{NN}}} $ = 5.02 TeV

The production of the W ± bosons measured in p–Pb collisions at a centre-of-mass energy per nucleon–nucleon collision $\sqrt{s_{NN}}$ = 8.16 TeV and Pb–Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV with ALICE at the LHC is presented. The W ± bosons are measured via their muonic decay channel, with the muon reconstructed in the pseudorapidity region -4 < η$_{lab}^{μ}$ < -2.5 with transverse momentum p$_{T}^{μ}$ > 10 GeV/c. While in Pb–Pb collisions the measurements are performed in the forward (2.5 < y$_{cms}^{μ}$ < 4) rapidity region, in p–Pb collisions, where the centre-of-mass frame is boosted with respect to the laboratory frame, the measurements are performed in the backward (-4.46 < y$_{cms}^{μ}$ < -2.96) and forward (2.03 < y$_{cms}^{μ}$ < 3.53) rapidity regions. The W - and W + production cross sections, lepton-charge asymmetry, and nuclear modification factors are evaluated as a function of the muon rapidity. In order to study the production as a function of the p–Pb collision centrality, the production cross sections of the W - and W + bosons are combined and normalised to the average number of binary nucleon–nucleon collision $\langle$N coll $\rangle$. In Pb–Pb collisions, the same measurements are presented as a function of the collision centrality. Study of the binary scaling of the W ± -boson cross sections in p–Pb and Pb–Pb collisions is also reported. The results are compared with perturbative QCD calculations, with and without nuclear modifications of the Parton Distribution Functions (PDFs), as well as with available data at the LHC. Significant deviations from the theory expectations are found in the two collision systems, indicating that the measurements can provide additional constraints for the determination of nuclear PDFs and in particular of the light-quark distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Non-linear flow modes of identified particles in Pb-Pb collisions at $ \sqrt{s_{\mathrm{NN}}} $ = 5.02 TeV

The pT-differential non-linear flow modes, v 4,22 , v 5,32 , v 6,33 and v 6,222 for π ± , K ± , K$^0_S$ , $p + \bar{p}, Λ + \bar{Λ}$ and &straightphi;-meson have been measured for the first time at $\sqrt{s_{NN}}$ = 5.02 TeV in Pb-Pb collisions with the ALICE detector at the Large Hadron Collider. The results were obtained with a multi-particle technique, correlating the identified hadrons with reference charged particles from a different pseudorapidity region. These non-linear observables probe the contribution from the second and third order initial spatial anisotropy coefficients to higher flow harmonics. All the characteristic features observed in previous p T -differential anisotropic flow measurements for various particle species are also present in the non-linear flow modes, i.e. increase of magnitude with increasing centrality percentile, mass ordering at low p T and particle type grouping in the intermediate p T range. Hydrodynamical calculations (iEBE-VISHNU) that use different initial conditions and values of shear and bulk viscosity to entropy density ratios are confronted with the data at low transverse momenta. These calculations exhibit a better agreement with the anisotropic flow coefficients than the non-linear flow modes. These observations indicate that non-linear flow modes can provide additional discriminatory power in the study of initial conditions as well as new stringent constraints to hydrodynamical calculations.

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