Strongly interacting matter exhibits deconfined behavior in massive neutron stars.

Neutron-star cores contain matter at the highest densities in our Universe. This highly compressed matter may undergo a phase transition where nuclear matter melts into deconfined quark matter, liberating its constituent quarks and gluons. Quark matter exhibits an approximate conformal symmetry, predicting a specific form for its equation of state (EoS), but it is currently unknown whether the transition takes place inside at least some physical neutron stars. Here, we quantify this likelihood by combining information from astrophysical observations and theoretical calculations. Using Bayesian inference, we demonstrate that in the cores of maximally massive stars, the EoS is consistent with quark matter. We do this by establishing approximate conformal symmetry restoration with high credence at the highest densities probed and demonstrating that the number of active degrees of freedom is consistent with deconfined matter. The remaining likelihood is observed to correspond to EoSs exhibiting phase-transition-like behavior, treated as arbitrarily rapid crossovers in our framework.

How Perturbative QCD Constrains the Equation of State at Neutron-Star Densities.

We demonstrate in a general and analytic way how high-density information about the equation of state (EOS) of strongly interacting matter obtained using perturbative quantum chromodynamics constrains the same EOS at densities reachable in physical neutron stars. Our approach is based on utilizing the full information of the thermodynamic potentials at the high-density limit together with thermodynamic stability and causality. This requires considering the pressure as a function of chemical potential p(µ) instead of the commonly used pressure as a function of energy density p(ε). The results can be used to propagate the perturbative quantum chromodynamics calculations reliable around 40n_{s} to lower densities in the most conservative way possible. We constrain the EOS starting from only a few times the nuclear saturation density n≳2.2n_{s}, and at n=5n_{s} we exclude at least 65% of otherwise allowed area in the ε-p plane. This provides information complementary to astrophysical observations that should be taken into account in any complete statistical inference study of the EOS. These purely theoretical results are independent of astrophysical neutron-star input, and hence, they can also be used to test theories of modified gravity and beyond the standard model physics in neutron stars.

Soft Interactions in Cold Quark Matter.

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.

Discovering Partonic Rescattering in Light Nucleus Collisions.

We demonstrate that oxygen-oxygen collisions at the LHC provide unprecedented sensitivity to parton energy loss in a system whose size is comparable to those created in very peripheral heavy-ion collisions. With leading and next-to-leading order calculations of nuclear modification factors, we show that the baseline in the absence of partonic rescattering is known with up to 2% theoretical accuracy in inclusive oxygen-oxygen collisions. Surprisingly, a Z-boson normalized nuclear modification factor does not lead to higher theoretical accuracy within current uncertainties of nuclear parton distribution functions. We study a broad range of parton energy loss models and we find that the expected signal of partonic rescattering can be disentangled from the baseline by measuring charged hadron spectra in the range 20 GeV

Nonequilibrium Attractor in High-Temperature QCD Plasmas.

We establish the existence of a far-from-equilibrium attractor in weakly coupled gauge theory undergoing one-dimensional Bjorken expansion. We demonstrate that the resulting far-from-equilibrium evolution is insensitive to certain features of the initial condition, including both the initial momentum-space anisotropy and initial occupancy. We find that this insensitivity extends beyond the energy-momentum tensor to the detailed form of the one-particle distribution function. Based on our results, we assess different procedures for reconstructing the full one-particle distribution function from the energy-momentum tensor along the attractor and discuss implications for the freeze-out procedure used in the phenomenological analysis of ultrarelativistic nuclear collisions.

Early- and Late-Time Behavior of Attractors in Heavy-Ion Collisions.

Whether, how, and to what extent solutions of Bjorken-expanding systems become insensitive to aspects of their initial conditions is of importance for heavy-ion collisions. Here we study 1+1D and phenomenologically relevant boost-invariant 3+1D systems in which initial conditions approach a universal attractor. In Israel-Stewart theory (IS) and kinetic theory where the universal attractor extends to arbitrarily early times, we show that all initial conditions approach the attractor at early times by a power law while their approach is exponential at late times. In these theories, the physical mechanisms of hydrodynamization operational at late times do not drive the approach to the attractor at early times, and the early-time attractor is reached prior to hydrodynamization. In marked contrast, the attractor in strongly coupled systems is realized concurrent with hydrodynamization. This qualitative difference may offer a basis for discriminating weakly and strongly coupled scenarios of heavy-ion collisions.

Chemical Equilibration in Hadronic Collisions.

We study chemical equilibration in out-of-equilibrium quark-gluon plasma using the first principles method of QCD effective kinetic theory, accurate at weak coupling. In longitudinally expanding systems-relevant for relativistic nuclear collisions-we find that for realistic couplings chemical equilibration takes place after hydrodynamization, but well before local thermalization. We estimate that hadronic collisions with final state multiplicities dN_{ch}/dη≳10^{2} live long enough to reach approximate chemical equilibrium, which is consistent with the saturation of strangeness enhancement observed in proton-proton, proton-nucleus, and nucleus-nucleus collisions.

Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory.

High-energy nuclear collisions produce a nonequilibrium plasma of quarks and gluons which thermalizes and exhibits hydrodynamic flow. There are currently no practical frameworks to connect the early particle production in classical field simulations to the subsequent hydrodynamic evolution. We build such a framework using nonequilibrium Green's functions, calculated in QCD kinetic theory, to propagate the initial energy-momentum tensor to the hydrodynamic phase. We demonstrate that this approach can be easily incorporated into existing hydrodynamic simulations, leading to stronger constraints on the energy density at early times and the transport properties of the QCD medium. Based on (conformal) scaling properties of the Green's functions, we further obtain pragmatic bounds for the applicability of hydrodynamics in nuclear collisions.

Next-to-Next-to-Next-to-Leading Order Pressure of Cold Quark Matter: Leading Logarithm.

At high baryon chemical potential µ_{B}, the equation of state of QCD allows a weak-coupling expansion in the QCD coupling α_{s}. The result is currently known up to and including the full next-to-next-to-leading order α_{s}^{2}. Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates nonperturbative treatment of the scale α_{s}^{1/2}µ_{B}. We apply a hard-thermal-loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and we use it to determine the leading-logarithm contribution to next-to-next-to-next-to-leading order: α_{s}^{3}ln^{2}α_{s}. This result is the first improvement to the equation of state of massless cold quark matter in 40 years. The new term is negligibly small and thus significantly increases our confidence in the applicability of the weak-coupling expansion.

Gravitational-Wave Constraints on the Neutron-Star-Matter Equation of State.

The detection of gravitational waves originating from a neutron-star merger, GW170817, by the LIGO and Virgo Collaborations has recently provided new stringent limits on the tidal deformabilities of the stars involved in the collision. Combining this measurement with the existence of two-solar-mass stars, we generate a generic family of neutron-star-matter equations of state (EOSs) that interpolate between state-of-the-art theoretical results at low and high baryon density. Comparing the results to ones obtained without the tidal-deformability constraint, we witness a dramatic reduction in the family of allowed EOSs. Based on our analysis, we conclude that the maximal radius of a 1.4-solar-mass neutron star is 13.6 km, and that the smallest allowed tidal deformability of a similar-mass star is Λ(1.4 M_{⊙})=120.

Cool Quark Matter.

We generalize the state-of-the-art perturbative equation of state of cold quark matter to nonzero temperatures, needed in the description of neutron star mergers and core collapse processes. The new result is accurate to O(g^{5}) in the gauge coupling, and is based on a novel framework for dealing with the infrared sensitive soft field modes of the theory. The zero Matsubara mode sector is treated via a dimensionally reduced effective theory, while the soft nonzero modes are resummed using the hard thermal loop approximation. This combination of known effective descriptions offers unprecedented access to small but nonzero temperatures, both in and out of beta equilibrium.

Isotropization and Hydrodynamization in Weakly Coupled Heavy-Ion Collisions.

We numerically solve the (2+1)-dimensional effective kinetic theory of weak coupling QCD under longitudinal expansion, relevant for early stages of heavy-ion collisions. We find agreement with viscous hydrodynamics and classical Yang-Mills simulations in the regimes where they are applicable. By choosing initial conditions that are motivated by a color-glass-condensate framework, we find that for Q_{s}=2 GeV and α_{s}=0.3 the system is approximately described by viscous hydrodynamics well before τ≲1.0 fm/c.

Approach to equilibrium in weakly coupled non-Abelian plasmas.

We follow the time evolution of non-Abelian gauge bosons from far-from-equilibrium initial conditions to thermal equilibrium by numerically solving an effective kinetic equation that becomes accurate in the weak coupling limit. We consider isotropic initial conditions that are either highly overoccupied or underoccupied. We find that overoccupied systems thermalize through a self-similar cascade reaching equilibrium in multiples of a thermalization time t(eq)≈72./(1+0.12logλ(-1))×1/λ(2)T, whereas underoccupied systems undergo a "bottom-up" thermalization in a time t(eq)≈[34.+21.log(Q/T)]/(1+0.037logλ(-1))×(Q/T)(1/2)/λ(2)T, where Q is the characteristic momentum scale of the initial condition. We apply this result to model initial stages of heavy-ion collisions and find rapid thermalization roughly in a time Qt(eq)≲10 or t(eq)≲1 fm/c.