Triangularity and Dipole Asymmetry in Heavy Ion Collisions

Abstract

We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity $<r^3\cos 3(\varphi -{\psi }_{3,3})>$ and the dipole asymmetry $<r^3\cos (\varphi -{\psi }_{1,3})>$ of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry ${\psi }_{1,3}$ has a $20$ preference out of plane. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles ${\psi }_{1,3}$ and ${\psi }_{3,3}$ are strongly correlated. We study the ideal hydrodynamic response to these cumulants and determine the associated $v_1/{\epsilon }_1$ and $v_3/{\epsilon }_3$ for a massless ideal gas equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and Roland fit of two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole asymmetry and the correlations between ${\psi }_{1,3}$ and ${\psi }_{3,3}$ by measuring a two particle correlation with respect to the participant plane, $<\cos ({\varphi }_a-3{\varphi }_b+2{\Psi }_{PP})>$. The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, $<\cos(ϕ_a + ϕ_\b - 2Ψ_{PP})>$.

32 pages, 16 figures

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• Directed flow from parton spin-orbit coupling in $pp$ and $pA$ collisions
• Mode-by-mode hydrodynamics: ideas and concepts
• Imprints of octupole collectivity in uranium-238 on relativistic heavy-ion flow observables
• Event-shape dependence of symmetry plane correlations using the Gaussian estimator in Pb-Pb collisions at the LHC using a multiphase transport model
• Measuring differential particle correlations in relativistic nuclear collisions
• SPARKX: A Software Package for Analyzing Relativistic Kinematics in Collision Experiments
• First measurement of symmetric cumulants of hexagonal flow harmonics in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Elliptic anisotropy of open-charm hadrons from parton scatterings in p--Pb collisions at energies available at the CERN Large Hadron Collider
• Nonlinear coupling of flow harmonics in heavy-ion collisions
• Calculation of Power Spectrum in the Little Bangs
• The impact of nuclear deformation on relativistic heavy-ion collisions: assessing consistency in nuclear physics across energy scales
• Effect of charged particle's multiplicity fluctuations on flow harmonics in even-by-event hydrodynamics
• Investigations of the linear and non-linear flow harmonics using the A Multi-Phase Transport model
• Exploring parameter dependence of heavy-flavor dynamics in small collision systems
• The QGP dynamics in relativistic heavy-ion collisions
• Coarse Graining in Hydrodynamics and Effects of Fluctuations
• Results on angular correlations with ALICE
• Azimuthal correlations and collective effects in a heavy-ion collisions at the LHC energies
• Event-shaped-dependent cumulants in p-Pb collisions at 5.02 TeV
• Studies of three-particle correlations and reaction-plane correlators from STAR
• How many particles do make a fluid? Qualifying collective behavior in expanding ultracold gases
• Jet modifications in event-by-event hydrodynamically evolving media
• Mode-by-mode evolution of Pb-Pb collisions at 5.02 TeV in a hybrid model
• Hydrodynamic Overview at Hot Quarks 2016
• Hadronic Rescattering in pA and AA Collisions