We combine, for the first time, event-by-event <math><msub><mrow><mi>T</mi></mrow><mrow><mi>R</mi></mrow></msub><mi>ENTo</mi></math> initial conditions with the relativistic viscous hydrodynamic model v-USPhydro and the Monte Carlo event generator JEWEL to make predictions for the nuclear modification factor <math><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> and jet azimuthal anisotropies <math><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mrow><mo>{</mo><mn>2</mn><mo>}</mo></mrow></math> in <math><msqrt><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>N</mi><mi>N</mi></mrow></msub></mrow></msqrt><mo>=</mo><mn>5.02</mn><mspace width="0.2em"></mspace><mrow><mi>TeV</mi></mrow></math> PbPb collisions for multiple centralities and values of the jet cone radius R. The R-dependence of <math><msub><mrow><mi>R</mi></mrow><mrow><mi>A</mi><mi>A</mi></mrow></msub></math> and <math><msub><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msub><mrow><mo>{</mo><mn>2</mn><mo>}</mo></mrow></math> strongly depends on the presence of recoiling scattering centers. We find a small jet <math><msub><mrow><mi>v</mi></mrow><mrow><mn>3</mn></mrow></msub><mrow><mo>{</mo><mn>2</mn><mo>}</mo></mrow></math> in mid-central collisions and consistent results in wide jet <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> regions and centralities with ATLAS data.

Brazil

Leonardo Barreto

Fabio M. Canedo

Marcelo G. Munhoz

United States

Jorge Noronha

Jacquelyn Noronha-Hostler

Jet cone radius dependence of And at PbPb 5.02 TeV from JEWEL+T ENTo+v-USPhydro

We point out that there is an upper bound on the speed of sound squared given by <math><msubsup><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mo>≤</mo><mn>0.781</mn></math> valid for all known systems described by relativistic transient hydrodynamics where calculations of certain ratios of hydrodynamic transport coefficients can be performed from first principles. Assuming this bound is valid for ultradense matter implies that the maximum mass of isolated (non-rotating) neutron stars cannot be larger than 2.7 solar masses.

Mauricio Hippert

Paul Romatschke

Upper bound on the speed of sound in nuclear matter from transport

We derive the set of inequalities that is necessary and sufficient for nonlinear causality and linear stability of first-order relativistic hydrodynamics with either a <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>V</mi></mrow></msub></mrow></math> conserved current or a <math><mi>U</mi><mo>(</mo><mn>1</mn><msub><mo>)</mo><mi>A</mi></msub></math> current with a chiral anomaly or both. Our results apply to generic hydrodynamic frames in which no relations among the transport parameters are imposed. Furthermore, our analysis yields, to the best of our knowledge, the first theory of viscous chiral hydrodynamics proven to be causal and stable. We find that causality demands the absence of vorticity-induced heat flux, forcing a departure from the thermodynamic frame in the chiral case. The inequalities for causality and stability define a hypervolume in the space of transport parameters, wherein each point corresponds to a consistent formulation. Notably, causality is determined by just three combinations of transport parameters. We present our results in a form amenable to numerical hydrodynamic simulations.

Nick Abboud

Enrico Speranza

Causal and stable first-order chiral hydrodynamics

We analytically determine all the eigenvalues and eigenfunctions of the linearized Boltzmann collision operator (computed using Boltzmann statistics) in massless scalar <math><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math> theory. This is used to determine this system's shear viscosity and particle diffusion transport coefficients in analytical form. The corresponding relaxation time approximation for this linearized Boltzmann equation is also derived.

Gabriel S. Denicol

Spectrum of the Boltzmann collision operator for Theory in the Classical Regime

Causality is necessary for retarded Green’s functions to remain retarded in all inertial frames in relativity, which ensures that dissipation of fluctuations is a Lorentz invariant concept. For first-order Bemfica, Disconzi, Noronha, and Kovtun theories with stochastic fluctuations, introduced via the Schwinger-Keldysh formalism, we show that imposing causality and stability leads to correlation functions of hydrodynamic fluctuations that only display the expected physical properties at small frequencies and wave number, i.e., within the expected regime of validity of the first-order approach. For second-order theories of the Israel and Stewart type, constructed using the information current such that entropy production is always non-negative, a stochastic formulation is presented using the Martin-Siggia-Rose approach where imposing causality and stability leads to correlators with the desired properties. We also show how Green’s functions can be determined from such an action. We identify a <math><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry, analogous to the Kubo-Martin-Schwinger symmetry, under which this Martin-Siggia-Rose action is invariant. This modified Kubo-Martin-Schwinger symmetry provides a new guide for the effective action formulation of hydrodynamic systems with dynamics not solely governed by conservation laws. Furthermore, this symmetry ensures that the principle of detailed balance is valid in a covariant manner. We employ the new symmetry to further clarify the connection between the Schwinger-Keldysh and Martin-Siggia-Rose approaches, establishing a precise link between these descriptions in second-order theories of relativistic hydrodynamics. Finally, the modified Kubo-Martin-Schwinger symmetry is used to determine the corresponding action describing diffusion in Israel-Stewart theories in a general hydrodynamic frame.

Nicki Mullins

Lorenzo Gavassino

Relativistic hydrodynamic fluctuations from an effective action: Causality, stability, and the information current

We compute the radius of convergence of the linearized relativistic hydrodynamic expansion around a nontrivially rotating strongly coupled <math><mi>N</mi><mo>=</mo><mn>4</mn></math> super-Yang-Mills plasma. Our results show that the validity of hydrodynamics is sustained and can even get enhanced for conformal field theory (CFT) in a rotating state. Analytic equations for the hydrodynamic dispersion relations and transport coefficients of the rotating plasma as a function of their values in a plasma at rest are given.

Netherlands

Casey Cartwright

Markus Garbiso Amano

Matthias Kaminski

Convergence of hydrodynamics in a rotating strongly coupled plasma

We prove that ideal chiral hydrodynamics, as derived from chiral kinetic theory, is acausal and its initial-value problem is ill posed, both in the linearized case around a local equilibrium solution and also in the full nonlinear regime. Therefore, such theory cannot be used to determine how the chiral anomaly affects the hydrodynamic evolution. We show that these fundamental issues can be fixed by using different definitions (frames) for the hydrodynamic fields. This leads to a causal theory of ideal chiral hydrodynamics where the vorticity strength is constrained by the coefficient that encodes the anomaly.

Fábio S. Bemfica

Marcelo M. Disconzi

Challenges in solving chiral hydrodynamics

We investigate the far-from-equilibrium behavior of the Boltzmann equation for a gas of massless scalar field particles with quartic (tree level) self-interactions (<math><mrow><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math>) in Friedmann-Lemaitre-Robertson-Walker spacetime. Using a new covariant generating function for the moments of the Boltzmann distribution function, we analytically determine a subset of the spectrum and the corresponding eigenfunctions of the linearized Boltzmann collision operator. We show how the covariant generating function can be also used to find the exact equations for the moments in the full nonlinear regime. Different than the case of a ultrarelativistic gas of hard spheres (where the total cross section is constant), for <math><mi>λ</mi><msup><mi>ϕ</mi><mn>4</mn></msup></math> the fact that the cross section decreases with energy implies that moments of arbitrarily high order directly couple to low order moments. Numerical solutions for the scalar field case are presented and compared to those found for a gas of hard spheres.

Far-from-equilibrium kinetic dynamics of <math><mi>λ</mi><msup><mi>ϕ</mi><mn>4</mn></msup></math> theory in an expanding universe

New constraints are found that must necessarily hold for Israel-Stewart-like theories of fluid dynamics to be causal far away from equilibrium. Conditions that are sufficient to ensure causality, local existence, and uniqueness of solutions in these theories are also presented. Our results hold in the full nonlinear regime, taking into account bulk and shear viscosities (at zero chemical potential), without any simplifying symmetry or near-equilibrium assumptions. Our findings provide fundamental constraints on the magnitude of viscous corrections in fluid dynamics far from equilibrium.

Vu Hoang

Maria Radosz

Nonlinear Constraints on Relativistic Fluids Far from Equilibrium

We show that the recently formulated causal and stable first-order hydrodynamics has the same dynamics as Israel-Stewart theory for boost-invariant, Bjorken expanding systems with an ideal gas equation of state and a regulating sector determined by a constant relaxation time. In this case, the general solution of the new first-order formulation can be determined analytically.