Emergent macroscopic descriptions of matter, such as hydrodynamics, are central to our description of complex physical systems across a wide spectrum of energy scales. The conventional understanding of these many-body phenomena has recently been shaken by a number of experimental findings. Collective behavior of matter has been observed in mesoscopic systems, such as high-energy hadron–hadron collisions, or ultracold gases with only a few strongly interacting fermions. In such systems, the separation of scales between macroscopic and microscopic dynamics (at the heart of any effective theory) is inapplicable. To address the conceptual challenges that arise from these observations and explore the universality of emergent descriptions of matter, the EMMI Rapid Reaction Task Force was assembled. This document summarizes the RRTF discussions on recent theoretical and experimental advances in this rapidly developing field. Leveraging technological breakthroughs in the control of quantum systems, we can now quantitatively explore what it means for a system to exhibit behavior beyond the sum of its individual parts. In particular, the report highlights how the (in)applicability of hydrodynamics and other effective theories can be probed across three principal frontiers: the size frontier, the equilibrium frontier, and the interaction frontier.

We investigate hydrodynamic contributions to short-range two-particle correlations in relativistic heavy-ion collisions using the Boltzmann-Langevin equation. We derive and solve the transport equation for equal-time two-point correlations, obtaining both local and non-local contributions that scale with transport coefficients. The non-local correlations emerging from 2-to-2 scattering dynamics provide a hydrodynamic signature in short-range correlation measurements.

We conduct a numerical study of relativistic viscous fluid dynamics in the density frame for one-dimensional fluid flows. The density frame is a formulation of relativistic viscous hydrodynamics that is first order in time, requires no auxiliary fields, and has no nonhydrodynamic modes. We compare our results to QCD kinetic theory simulations and find excellent agreement within the regime of applicability of hydrodynamics. Additionally, the density frame results remain well behaved and robust near the boundary of applicability. We also compare our findings to the second-order-in-time hydrodynamic theory developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) and a well-known M & uuml;ller-Israel-Stewart-type hydrodynamics code, MUSIC, which is commonly used to simulate heavy-ion collisions.

We present a detailed numerical and analytical study of the out-of-equilibrium dynamics of Model G, the dynamical universality class relevant to the chiral phase transition. We perform numerical 3D stochastic (Langevin) simulations of the O(4) critical point for large lattices in the chiral limit. We quench the system from the high-temperature unbroken phase to the broken phase and study the non-equilibrium dynamics of pion fields. Strikingly, the non-equilibrium evolution of the two-point functions exhibits a regime of growth, a parametrically large enhancement, and a subsequent slow relaxation to equilibrium. We analyze our numerical results using dynamic critical scaling and mean-field theory. The growth of the two point functions is determined by the non-linear dynamics of an ideal non-abelian superfluid, which is a limit of Model G that reflects the broken chiral symmetry. We also relate the non-equilibrium two-point functions to a long-lived parametric enhancement of soft pion yields relative to thermal equilibrium following a quench.

We discuss a universal nonequilibrium enhancement of long-wavelength Goldstone bosons induced by quenches to the broken phase in Model G—the dynamical universality class of an O ( 4 ) antiferromagnet and the chiral phase transition in QCD. Scaling arguments for the coarsening dynamics describing the formation of the chiral condensate predict a parametric enhancement in the infrared spectra of Goldstone bosons, a prediction confirmed by stochastic simulations of the transition. The details of the enhancement are determined by the nonlinear dynamics of a superfluid effective theory, which is a limit of Model G reflecting the broken O ( 4 ) symmetry. Our results translate to a parametric enhancement of low-momentum pions in heavy-ion collisions at the LHC, which are underpredicted in current hydrodynamic models without critical dynamics.

High-energy collisions involving the A=96 isobars ^96Zr and ^96Ru have been performed in 2018 at Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) as a means to search for the chiral magnetic effect in QCD. This would manifest itself as specific deviations from unity in the ratio of observables taken between ^96Zr+^96Zr and ^96Ru+^96Ru collisions. Measurements of such ratios (released at the end of 2021) indeed reveal deviations from unity, but these are primarily caused by the two collided isobars having different radial profiles and intrinsic deformations. To make progress in understanding RHIC data, nuclear physicists across the energy spectrum gathered in Heidelberg in 2022 as part of an EMMI Rapid Reaction Task Force (RRTF) to address the following question. Does the combined effort of low-energy nuclear structure physics and high-energy heavy-ion physics enable us to understand the observations made in isobar collisions at RHIC?

We propose an algorithm for simulating stochastic relativistic fluid dynamics based on Metropolis updates. Each step of the algorithm begins with an update based on ideal hydrodynamics. This is followed by proposing random (spatial) momentum transfers between fluid cells, keeping the total energy fixed. These proposals are then accepted or rejected using the change in entropy as a statistical weight. The algorithm reproduces relativistic viscous hydrodynamics in the "density frame," which is a formulation of viscous hydrodynamics we review and clarify here. This formulation is first order in time and requires no auxiliary dynamical fields such as II mu degrees. The only parameters are the shear and bulk viscosities and the equation of state. By adopting the 3 + 1 split of general relativity, we extend the Metropolis algorithm to general space-time coordinates, such as Bjorken coordinates, which are commonly used to simulate heavy-ion collisions.

We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charge between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a Metropolis step using the entropy as a statistical weight. This procedure reproduces the expected strains of dissipative relativistic hydrodynamics in a specific (and non-covariant) hydrodynamic frame known as the density frame. Numerical results, both with and without noise, are presented and compared to relativistic kinetics and analytical expectations. An all order resummation of the density frame gradient expansion reproduces the covariant dynamics in a specific model. In contrast to all other numerical approaches to relativistic dissipative fluids, the dissipative fluid formalism presented here is strictly first order in gradients and has no non-hydrodynamic modes. The physical naturalness and simplicity of the Metropolis algorithm, together with its convergence properties, make it a promising tool for simulating stochastic relativistic fluids in heavy ion collisions and for critical phenomena in the relativistic domain.

We present a detailed study of the finite momentum dynamics of the $O(4)$ critical point of QCD, which lies in the dynamic universality class of Model G. The critical scaling of the model is analyzed in multiple dynamical channels. For instance, the finite momentum analysis allows us to precisely extract the pion dispersion curve below the critical point. The pion velocity is in striking agreement with the predictions relation and static universality. The pion damping rate and velocity are both consistent with the dynamical critical exponent $\zeta = 3/2$ of Model G. Similarly, although the critical amplitude for the diffusion coefficient of the conserved $O(4)$ charges is small, it is clearly visible both in the restored phase and with finite explicit symmetry breaking, and its dynamical scaling is again consistent with $\zeta=3/2$. We determine a new set of universal dynamical critical amplitude ratios relating the diffusion coefficient to a suitably defined order parameter relaxation time. We also show that in a finite volume simulation, the chiral condensate diffuses on the coset manifold in a manner consistent with dynamical scaling, and with a diffusion coefficient that is determined by the transport coefficients of hydrodynamic pions. Finally, the amplitude ratios (together with other non-universal amplitudes also reported here) compile all relevant information for further studies of Model G both in and out of equilibrium.

Hot QCD physics studies the nuclear strong force under extreme temperature and densities. Experimentally these conditions are achieved via high-energy collisions of heavy ions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC). In the past decade, a unique and substantial suite of data was collected at RHIC and the LHC, probing hydrodynamics at the nucleon scale, the temperature dependence of the transport properties of quark-gluon plasma, the phase diagram of nuclear matter, the interaction of quarks and gluons at different scales and much more. This document, as part of the 2023 nuclear science long range planning process, was written to review the progress in hot QCD since the 2015 Long Range Plan for Nuclear Science, as well as highlight the realization of previous recommendations, and present opportunities for the next decade, building on the accomplishments and investments made in theoretical developments and the construction of new detectors. Furthermore, this document provides additional context to support the recommendations voted on at the Joint Hot and Cold QCD Town Hall Meeting, which are reported in a separate document.

We provide a generalized formulation of fluctuating hydrodynamics for the far-from-equilibrium noisy medium. As an example, we consider a noisy plasma experiencing Bjorken expansion, for which the leading order evolution is captured by the hydrodynamic attractor of classical hydrodynamics, while the quadratic couplings of fluctuations are solved effectively via a generalized version of the hydrodynamic kinetic equation. In the far-from-equilibrium plasma, backreaction of hydrodynamic fluctuations results in renormalization of transport properties, as well as long-time tails, of high orders. In particular, corresponding to a renormalized hydrodynamic attractor, evolution in a noisy plasma towards equilibrium becomes nonmonotonic.

An energetic parton travelling through a quark-gluon plasma loses energy via occasional hard scatterings and frequent softer interactions. Whether or not these interactions admit a perturbative description, the effect of the soft interactions can be factorized and encoded in a small number of transport coefficients. In this work, we present a hard-soft factorized parton energy loss model which combines a stochastic description of soft interactions and rate-based modelling of hard scatterings. We introduce a scale to estimate the regime of validity of the stochastic description, allowing for a better understanding of the model's applicability at small and large coupling. We study the energy and fermion-number cascade of energetic partons as an application of the model.

We perform a real-time simulation of the $O(4)$ critical point of QCD, which lies in the dynamic universality class of Model G. The axial charge and the order parameter $\phi_a =(\sigma, \vec{\pi})$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below $T_c$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $\zeta=1.47 \pm 0.01 ({\rm stat})$, which is compatible with the theoretical expectation of $\zeta = d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.

We determine the kinetic coefficients of ultrasoft pions using chiral perturbation theory at finite temperature close to the chiral limit. This is used to compute the axial charge diffusion and damping coefficients in the hydrodynamic effective theory for these pion waves. We show that to provide a leading order answer for these coefficients one needs to explore the dynamics of hard, soft, and ultrasoft pion modes, which are represented microscopically by the appropriate kinetic and hydrodynamic descriptions..

During the expansion of a heavy ion collision, the system passes close to the $O(4)$ critical point of QCD, and thus the fluctuations of the order parameter $(\sigma, \vec{\pi})$ are expected to be enhanced. Our goal is to compute how these enhanced fluctuations modify the transport coefficients of QCD near the pseudo-critical point. We also make a phenomenological estimate for how chiral fluctuations could effect the momentum spectrum of soft pions. We first formulate the appropriate stochastic hydrodynamic equations close to the $O(4)$ critical point. Then, working in mean field, we determine the correlation functions of the stress tensor and the currents which result from this stochastic real time theory, and use these correlation functions to determine the scaling behavior of the transport coefficients. The hydrodynamic theory also describes the propagation of pion waves, fixing the scaling behavior of the dispersion curve of soft pions. We present scaling functions for the shear viscosity and the charge conductivities near the pseudo-critical point, and estimate the absolute magnitude of the critical fluctuations to these parameters and the bulk viscosity. Using the calculated pion dispersion curve, we estimate the expected critical enhancement of soft pion yields, and this estimate provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations. Our results motivate further phenomenological and numerical work on the implications of chiral symmetry on real time properties of thermal QCD near the pseudo-critical point.

Interactions between hard partons and the quark-gluon plasma range from frequent soft interactions to rare hard interactions. While it is reasonable that hard interactions can be described perturbatively, soft interactions likely have significant non-perturbative effects. The cumulative effect of the soft interactions can be encoded into parton transport coefficients, which can be constrained from heavy ion measurements. In this work, we perform a simplified proof of principle calculations showing that the magnitude of the drag and diffusion of light partons can be constrained from the hadronic and jet $R_{AA}$, assuming a known temperature dependence of the soft transport coefficients. We show how this study can be implemented naturally in a parton energy loss model that factorizes systematically soft and hard partonic interactions. We use this proof of principle calculation to understand how reducing uncertainties on $R_{AA}$ can improve constraints on the parton's transport coefficients. We also observe the complementarity of jet and hadronic observables to constrain the light parton transport coefficients.

We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{\pi}$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.

We propose observables $v_0$ and $v_0(p_T)$ which quantify the relative fluctuations in the total transverse momentum at fixed multiplicity. We first study the factorization of the fixed multiplicity momentum dependent two particle correlation function into a product of $v_0(p_T^a)$ and $v_0(p_T^b)$ within realistic hydrodynamic simulations. Then we present computations of $v_0(p_T)$ for different particle types. We determine the relation between the integrated $v_0$ and previously measured observables, and compare results from a hybrid hydrodynamics based model to experimental data. The effects of bulk viscosity and an initial pre-equilibrium stage on the results are quantified. We find that $v_0$ is strongly correlated with the initial state entropy per elliptic area, $S/A$. Using this result, we explain how the observed correlations between the elliptic flow and the transverse momentum (both in simulations and experiment) reflect the initial state correlations between $1/A$ and ellipticity $\varepsilon_2$ at fixed multiplicity. We argue that the systematic experimental study of $v_0$, with the same sophistication as used for the other $v_n$, can contribute significantly to our understanding of quark gluon plasma properties.