Explaining higher-order correlations between elliptic and triangular flow Mubarak Alqahtani, Jean-Yves Ollitrault Physics Letters Section B Nuclear Elementary Particle and High Energy Physics, 2026 The ALICE and CMS Collaborations have analyzed a number of cumulants mixing elliptic flow ($v_2$) and triangular flow ($v_3$), involving up to $8$ particles, in Pb+Pb collisions at the LHC. We unravel an unexpected simplicity in these complex mathematical quantities for collisions at fixed impact parameter. We show that as one increases the order in $v_2$, for a given order in $v_3$, the changes in the cumulants are solely determined by the mean elliptic flow in the reaction plane, which originates from the almond-shaped geometry of the overlap area between the colliding nuclei. We derive simple analytic relations between cumulants of different orders on this basis. These relations are in good agreement with recent data from the CMS Collaboration. We argue that agreement will be further improved if the analysis is repeated with a finer centrality binning. We make quantitative predictions for cumulants of order 10 which have not yet been analyzed.
Understanding the correlation between elliptic and triangular flow Mubarak Alqahtani, Jean-Yves Ollitrault Physics Letters Section B Nuclear Elementary Particle and High Energy Physics, 2026 The relative correlation between the magnitudes of elliptic flow ( v 2 ) and triangular flow ( v 3 ) has been accurately measured in nucleus-nucleus collisions at the LHC collider. As a function of the centrality of the collision, it changes sign and varies non-monotonically. We show that this is naturally explained by two combined effects. The first effect is a skewness in initial-state fluctuations, which is quantified by the correlation between the geometry-driven elliptic deformation in the reaction plane and the fluctuation-driven triangularity ε 3 . We introduce an intensive measure of this skewness, which is generically of order unity and varies little above 5% centrality. We evaluate its magnitude using Monte Carlo simulations of the initial state, which show that it is sensitive to the nucleon width. The second effect is the fluctuation of impact parameter relative to centrality classifiers used by experiment. The ATLAS collaboration uses two different centrality classifiers, the multiplicity N ch and the transverse energy E T . We fit both sets of results for Pb+Pb collisions up to ≈ 40% centrality with a single parameter, the intensive mixed skewness. Its value inferred from experiment agrees with theoretical expectations.
Impact parameter dependence of anisotropic flow: Bayesian reconstruction in ultracentral nucleus-nucleus collisions Mubarak Alqahtani, Rajeev S. Bhalerao, Giuliano Giacalone, Andreas Kirchner, Jean-Yves Ollitrault Physical Review C, 2024 Peculiar phenomena have been observed in analyses of anisotropic flow ($v_n$) fluctuations in ultracentral nucleus-nucleus collisions: The fourth-order cumulant of the elliptic flow ($v_2$) distribution changes sign. In addition, the ATLAS collaboration has shown that cumulants of $v_n$ fluctuations of all orders depend significantly on the centrality estimator. We show that these peculiarities are due to the fact that the impact parameter $b$ always spans a finite range for a fixed value of the centrality estimator. We provide a quantitative determination of this range through a simple Bayesian analysis. We obtain excellent fits of STAR and ATLAS data, with a few parameters, by assuming that the probability distribution of $v_n$ solely depends on $b$ at a given centrality. This probability distribution is almost Gaussian, and its parameters depend smoothly on $b$, in a way that is constrained by symmetry and scaling laws. We reconstruct, thus, the impact parameter dependence of the mean elliptic flow in the reaction plane in a model-independent manner, and assess the robustness of the extraction using Monte Carlo simulations of the collisions where the impact parameter is known. We argue that the non-Gaussianity of $v_n$ fluctuations gives direct information on the hydrodynamic response to initial anisotropies, ATLAS data being consistent with a smaller response for $n=4$ than for $n=2$ and $n=3$, in agreement with hydrodynamic calculations.
Nonexistence results for a sequential fractional differential problem Mohammed D. Kassim, Mubarak Alqahtani, Nasser‐Eddine Tatar, Aymen Laadhari Mathematical Methods in the Applied Sciences, 2023 In this paper, we study a class of sequential fractional differential inequalities involving Caputo fractional derivatives with different orders. The nonexistence of nontrivial global solutions is investigated in a suitable space via the test function technique and some properties of fractional integrals. Our results are supported by numerical examples.
Far-from-equilibrium attractors with a realistic non-conformal equation of state Mubarak Alqahtani Nuclear Physics B, 2023 Using anisotropic hydrodynamics , we examine the existence of early-time attractors of non-conformal systems undergoing Bjorken expansion. In the case of a constant mass, we find that the evolution of the scaled longitudinal pressure is insensitive to variations of initial conditions converging onto an early-time universal curve and eventually merging with the late-time Navier-Stokes attractor (the hydrodynamic attractor). On the other hand, the bulk and the shear viscous corrections do not show an early-time attractor behavior. These results are consistent with previous studies considering a constant mass. When a realistic equation of state is included in the dynamics with a thermal mass, we demonstrate for the first time the absence of strict late-time universal attractors. However, a semi-universal feature of the evolution at very late times remains.
Kaonic Hanbury-Brown-Twiss radii at 200 GeV and 5.02 TeV Mubarak Alqahtani, Michael Strickland Physical Review C, 2023 We use 3+1D quasiparticle anisotropic hydrodynamics (aHydroQP) to make predictions for kaon Hanbury-Brown-Twiss (HBT) radii in 200 GeV and 5.02 TeV heavy-ion collisions. Using previously determined aHydroQP parameters, we compute kaonic HBT radii and their ratios as a function of the mean transverse momentum of the pair $k_T$. We first consider Au-Au collisions at 200 GeV, finding good agreement between aHydroQP predictions and experimental data up to $k_T \\sim 0.8$ GeV. We then present predictions for kaonic HBT radii and their ratios in 5.02 TeV Pb-Pb collisions. Our aHydroQP predictions exhibit $k_T$ scaling of the pion and kaon source radii, however, transverse mass $m_T$ scaling is broken.
Nonextensive hydrodynamics of boost-invariant plasmas Mubarak Alqahtani, Nasser Demir, Michael Strickland European Physical Journal C, 2022 We use quasiparticle anisotropic hydrodynamics to study the non-conformal and non-extensive dynamics of a system undergoing boost-invariant Bjorken expansion. To introduce nonextensivity, we use an underlying Tsallis distribution with a time-dependent nonextensivity parameter q. By taking moments of the quasiparticle Boltzmann equation in the relaxation-time approximation, we obtain dynamical equations which allow us to determine the time evolution of all microscopic parameters including q. We compare numerical solutions for bulk observables obtained using the nonextensive evolution with results obtained using quasiparticle anisotropic hydrodynamics with a Boltzmann distribution function ($$q \\rightarrow 1$$ q → 1 ). We show that the evolution of the temperature, pressure ratio, and scaled energy density, are quite insensitive to which distribution function is assumed. However, we find significant differences in the early-time evolution of the bulk pressure which are observed for even small deviations from the Boltzmann distribution function. Finally, we discuss the existence of non-conformal hydrodynamic attractors for the longitudinal and transverse pressures, the bulk and shear viscous corrections, and the nonextensivity parameter q.
Resummed Relativistic Dissipative Hydrodynamics Huda Alalawi, Mubarak Alqahtani, Michael Strickland Symmetry, 2022 In this review, we present the motivation for using relativistic anisotropic hydrodynamics to study the physics of ultrarelativistic heavy-ion collisions. We then highlight the main ingredients of the 3+1D quasiparticle anisotropic hydrodynamics model including the underlying symmetry assumptions and present phenomenological comparisons with experimental data at different collision energies. These comparisons show that anisotropic hydrodynamics can describe many bulk observables of the quark-gluon plasma.
Bulk observables at 5.02 TeV using quasiparticle anisotropic hydrodynamics Mubarak Alqahtani, Michael Strickland European Physical Journal C, 2021 We compare predictions of 3+1D quasiparticle anisotropic hydrodynamics (aHydroQP) for a large set of bulk observables with experimental data collected in 5.02 TeV Pb–Pb collisions. We make predictions for identified hadron spectra, identified hadron average transverse momentum, charged particle multiplicity as a function of pseudorapidity, the kaon-to-pion ($$K/\\pi $$ K / π ) and proton-to-pion ($$p/\\pi $$ p / π ) ratios, identified particle and charged particle elliptic flow, and HBT radii. We compare to data collected by the ALICE collaboration in 5.02 TeV Pb–Pb collisions. We find that, based on available data, these bulk observables are well described by aHydroQP with an assumed initial central temperature of $$T_0=630$$ T 0 = 630 MeV at $$\\tau _0 = 0.25$$ τ 0 = 0.25 fm/c and a constant specific shear viscosity of $$\\eta /s=0.159$$ η / s = 0.159 , which corresponds to a peak specific bulk viscosity of $$\\zeta /s = 0.048$$ ζ / s = 0.048 . In particular, we find that the momentum dependence of the kaon-to-pion ($$K/\\pi $$ K / π ) and proton-to-pion ($$p/\\pi $$ p / π ) ratios reported recently by the ALICE collaboration are extremely well described by aHydroQP in the 0–5% centrality class.
Fireball tomography from bottomonia elliptic flow in relativistic heavy-ion collisions P. Bhaduri, M. Alqahtani, N. Borghini, A. Jaiswal, M. Strickland European Physical Journal C, 2021 We calculate the elliptic flow of bottomonia produced in Pb$\\,+\\,$Pb collisions at $\\sqrt{s_{\\rm NN}}=5.02$ TeV. We consider temperature-dependent decay widths for the anisotropic escape of various bottomonium states and observe that the transverse momentum dependence of bottomonia elliptic flow provides a tomographic information about the QGP fireball at different stages of its evolution. For the space-time evolution of the fireball, we employ simulation results from the 3+1d quasiparticle anisotropic hydrodynamic model. We find that our results for transverse momentum dependence of bottomonia elliptic flow are in reasonable agreement with experimental results from the ALICE and CMS collaborations.