High-density QCD matter from first principles

The aim of the project "Dense QCD matter from first principles", or DenseMatter in short, was to apply the ab-initio machinery of perturbative thermal field theory to a quantitative description of ultra-high-density quark matter (QM), possible present inside the cores of the most massive stable neutron stars. This line of work is extremely topical, as recent years have witnessed major breakthroughs in the observational study of neutron stars that have indeed become the leading laboratory for dense Quantum Chromodynamics (QCD) matter. In particular, the first detection of gravitational waves (GWs) from the merger of two distant neutron stars, recorded in August 2017, marked the birth of a new era of multimessenger astronomy, which will have a lasting impact on both astrophysics and the physics of the strong nuclear interaction.

The two most important concrete objectives of the DenseMatter project were the elevation of the weak-coupling expansion of the pressure (or equation of state) of cold and dense quark matter to the full four-loop order, and utilizing the result for obtaining the most accurate equation of state for neutron-star matter. The former of these two projects was naturally split into three parts, as the four-loop pressure of quark matter can be shown to contain three distinctive contributions, corresponding to the so-called soft and hard excitations of the system as well as their mixing. Similarly, the NS matter EoS determination was foreseen to consist of an initial phase where an interpolation routine for the quantity was developed, followed by regular updates when new observational or theoretical results emerged, so this project wwould also naturally split to several subprojects.

The final, extremely ambitious goal of the DenseMatter project was to apply the results of its two main parts to determine the inner structure of massive NSs by confirming whether deconfined QM resides inside them or not. This is one of the most prominent open problems in nuclear astrophysics, and one whose conclusive resolution would be a breakthrough of momentous nature beyond this subfield of physics.

The project got off to a flying start when just a few months after its onset the first-ever detection of gravitational waves from a binary neutron-star merger was announced by the LIGO and Virgo collaborations. Due to the preparatory work our group had been performing in the neutron-star-matter equation of state subproject, we were able to immediately apply the new measurement of the tidal deformability of an approx. 1.4 -solar-mass neutron star in the model-independent determination of the neutron-star-matter equation of state. This result was published in Physical Review Letters and became one of the most popular theory papers utilizing the LIGO/Virgo measurement, having gathered over 700 citations to date (February 2023).

Having observed a curious "bending" of the model-independent pressure as a function of density somewhat below the highest densities realized in physical neutron stars, reminiscent of the effect of a phase transition, we decided to immediately tackle the main goal of the DenseMatter project: the physical phase realized deep in the cores of the most massive stable neutron stars. To this end, we developed a new, more versatile way of interpolating the equation of state, and tracked a larger number of physical quantities in the original PRL publication. These results came out in a 2020 Nature Physics article titled "Evidence for quark-matter cores in massive neutron stars" that indeed presented first-ever model-independent evidence for the likely presence of deconfined matter inside the massive stable neutron stars. This paper also proved to be very successful, and has gathered almost 400 citations in less than three years, and the conclusions were further strengthened in a later Physical Review X article in 2022. Finally, we are currently finalizing an article that presents an important generalization of the Nature Physics research, involving the use of Bayesian inference and equations of state obtained using Gaussian processes. Here, we will be able to attach a likelihood estimate for the existence of quark-matter cores, which according to our preliminary results will likely land in the ballpark of 90%.

Due to the shift of attention towards NS physics, our activities on the perturbative-QCD front were slightly delayed, and the completion of the full four-loop pressure is still lacking. We have, however, made significant progress in this direction as well, and e.g. published two PRL articles on the way. In the first of these two papers, we determined a new term of order g^6ln^2(g) in the weak-coupling expansion of the quark-matter pressure, with g denoting the gauge coupling of the theory, while in the latter we derived the entire soft contribution to the quantity at order g^6. In the related but slightly simpler theory of Quantum Electrodynamics, we have also recently determined the so-called mixed contributions to the pressure up to O(g^6), originating from the interplay of the hard and soft momentum scales of the system, and are currently finalizing a similar computation in QCD.

Finally, going slightly beyond the initial plans, we have continued our earlier programme to develop a holographic description of dense QCD matter, especially in the context of neutron stars. Here, our single most important contribution has been to derive the first results for the most important transport coefficients describing cold and dense quark matter. These results were published in PRL in 2020, and the project is currently being pursued further for the bulk viscosity.

As detailed above, the most important milestone results from the project undoubtedly include the derivation of the most accurate model-independent equation of state of neutron-star matter as well as obtaining first-ever robust evidence for the presence of quark matter inside the most massive neutron stars in existence. More broadly, one could argue that the DenseMatter project has significantly promoted a new model-independent appraoch to the microphysics of neutron stars, based on solid first-principles results from nuclear and particle theory as well as their model-agnostic interpolation. This approach has slowly become the gold standard in the field, with multiple research groups adapting the methods that were initially introduced by us.

Similarly, our derivation of new terms for the weak-coupling expansion of the equation of state of cold and dense quark matter is an achievement that will live on even when higher-order results are eventually reached using the methods we have developed especially for our 2021 PRL. Indeed, in this article and its longer companion paper, we laid out in detail how the full four-loop pressure can eventually be determined and how the sometimes intricate cancellation of the infrared and ultraviolet divergences of the various parts of the final result will need to play out.

Periodic Reporting for period 4 - DenseMatter (High-density QCD matter from first principles)

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