Modern hydrodynamic simulations of core-collapse supernovae and neutron-star mergers require knowledge not only of the equilibrium properties of strongly interacting matter, but also of the system’s response to perturbations, encoded in various transport coefficients. Using perturbative and holographic tools, we derive here an improved weak-coupling and a new strong-coupling result for the most important transport coefficient of unpaired quark matter, its bulk viscosity. These results are combined in a simple analytic pocket formula for the quantity that is rooted in perturbative quantum chromodynamics at high densities but takes into account nonperturbative holographic input at neutron-star densities, where the system is strongly coupled. This expression can be used in the modeling of unpaired quark matter at astrophysically relevant temperatures and densities.

South Korea

Mexico

Jesús Cruz Rojas

Germany

Tyler Gorda

Spain

Carlos Hoyos

Finland

Niko Jokela

Matti Järvinen

Norway

Aleksi Kurkela

Risto Paatelainen

Saga Säppi

Aleksi Vuorinen

Estimate for the Bulk Viscosity of Strongly Coupled Quark Matter Using Perturbative QCD and Holography

We introduce the parton cascade Alpaca, which evolves parton ensembles corresponding to single events according to the effective kinetic theory of QCD at high temperature formulated by Arnold, Moore and Yaffe by explicitly simulating elastic scattering, splitting and merging. By taking the ensemble average over many events the phase space density (as evolved by the Boltzmann equation) is recovered, but the parton cascade can go beyond the evolution of the mean because it can be turned into a complete event generator that produces fully exclusive final states including fluctuations and correlations. The parton cascade does not require the phase space density as input (except for the initial condition at the starting time). Rather, effective masses and temperature, which are functions of time and are defined as integrals over expressions involving the distribution function, are estimated in each event from just the parton ensemble of that event. We validate the framework by showing that ensembles sampled from a thermal distribution stay in thermal equilibrium even after running the simulation for a long time. This is a non-trivial result, because it requires all parts of the simulation to intertwine correctly.

Sweden

Robin Törnkvist

Korinna Zapp

AMY Lorentz invariant parton cascade: the thermal equilibrium case

The equation of state of neutron-star cores can be constrained by requiring a consistent connection to the perturbative Quantum Chromodynamics (QCD) calculations at high densities. The constraining power of the QCD input depends on uncertainties from missing higher-order terms, the choice of the unphysical renormalization scale, and the reference density where QCD calculations are performed. Within a Bayesian approach, we discuss the convergence of the perturbative QCD series, quantify its uncertainties at high densities, and present a framework to systematically propagate the uncertainties down to neutron-star densities. We find that the effect of the QCD input on the neutron-star inference is insensitive to the various unphysical choices made in the uncertainty estimation.

Oleg Komoltsev

Aleksas Mazeliauskas

Bayesian uncertainty quantification of perturbative QCD input to the neutron-star equation of state

We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in QED. The calculation is performed within the real-time formalism utilizing dimensional regularization in <math><mn>4</mn><mo>−</mo><mn>2</mn><mi>ϵ</mi></math> dimensions, while the result is reported including explicit <math><mi>O</mi><mo>(</mo><mi>ϵ</mi><mo>)</mo></math> terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a companion paper. These results pave the way for a similar future calculation in quantum chromodynamics.

Juuso Österman

Italy

Philipp Schicho

Kaapo Seppänen

Soft photon propagation in a hot and dense medium to next-to-leading order

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>) in the fine-structure constant <math><msub><mi>α</mi><mi>e</mi></msub></math>, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the <math><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>e</mi><mn>3</mn></msubsup><mi>ln</mi><msub><mi>α</mi><mi>e</mi></msub><mo>)</mo></math> term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective-field-theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> calculation for cold and dense quark matter.

Degenerate fermionic matter at <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>: Quantum electrodynamics

We provide the first next-to-leading-order (NLO) weak-coupling description of the thermalization process of far-from-equilibrium systems in non-Abelian gauge theory. We study isotropic systems starting from either over- or underoccupied initial conditions and follow their time evolution toward thermal equilibrium by numerically solving the QCD effective kinetic theory at NLO accuracy. We find that the NLO corrections remain well under control for a wide range of couplings and that the overall effect of NLO corrections is to reduce the time needed to reach thermal equilibrium in the systems considered.

China

Yu Fu

France

Jacopo Ghiglieri

Shahin Iqbal

Thermalization of non-Abelian gauge theories at next-to-leading order

Motivated by recent interest in collectivity in small systems, we calculate the harmonic flow response to initial geometry deformations within weakly coupled QCD kinetic theory using the first correction to the free-streaming background. We derive a parametric scaling formula that relates harmonic flow in systems of different sizes and different generic initial gluon distributions. We comment on similarities and differences between the full QCD effective kinetic theory and the toy models used previously. Finally we calculate the centrality dependence of the integrated elliptic flow v 2 in oxygen-oxygen, proton-lead and proton-proton collision systems.

CERN

Collective flow in single-hit QCD kinetic theory

High-order perturbative calculations for thermodynamic quantities in QCD are complicated by the physics of dynamical screening that affects the soft, long-wavelength modes of the system. Here, we provide details for the evaluation of this soft contribution to the next-to-next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>) pressure of high-density, zero-temperature quark matter (QM), complementing our accompanying Letter [T. Gorda et al., Phys. Rev. Lett. 127, 162003 (2021)]. Our calculation requires the determination of the pressure of the hard-thermal-loop effective theory to full two-loop order at zero temperature, which we go through in considerable detail. In addition to this, we comprehensively discuss the structure of the weak-coupling expansion of the QM pressure, and lay out a roadmap towards the evaluation of the contributions missing from a full <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> result for this quantity.

Cold quark matter at <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>: Soft contributions

Accurate knowledge of the thermodynamic properties of zero-temperature, high-density quark matter plays an integral role in attempts to constrain the behavior of the dense QCD matter found inside neutron-star cores, irrespective of the phase realized inside the stars. In this Letter, we consider the weak-coupling expansion of the dense QCD equation of state and compute the next-to-next-to-next-to-leading-order contribution arising from the non-Abelian interactions among long-wavelength, dynamically screened gluonic fields. Accounting for these interactions requires an all-loop resummation, which can be performed using hard-thermal-loop (HTL) kinematic approximations. Concretely, we perform a full two-loop computation using the HTL effective theory, valid for the long-wavelength, or soft, modes. We find that the soft sector is well behaved within cold quark matter, contrary to the case encountered at high temperatures, and find that the new contribution decreases the renormalization-scale dependence of the equation of state at high density.

Soft Interactions in Cold Quark Matter

Medium induced parton energy loss is not conclusively established either in very peripheral heavy-ion collisions or in proton-ion collisions. However, the standard interpretation of azimuthal momentum anisotropies in these systems implies some partonic rescattering. The upcoming light-ion runs at the Large Hadron Collider (LHC) provide a unique opportunity to search for parton energy loss in different systems of similar size. Here, we make predictions for the expected parton energy loss signal in the charged hadron spectra in a system size scan at LHC. We test a large set of model assumptions against the transverse momentum and centrality dependence of the charged hadron nuclear modification factor in lead-lead and xenon-xenon collisions at the LHC. We then attempt to make a model agnostic prediction for the charged hadron nuclear modification factor in oxygen-oxygen collisions.

Alexander Huss

Wilke van der Schee

Urs Achim Wiedemann

Predicting parton energy loss in small collision systems