From pQCD to neutron stars: matching equations of state to constrain global star properties

Abstract

The equation of state (EoS) of quantum chromodynamics (QCD) at zero temperature can be calculated in two different perturbative regimes: for small values of the baryon chemical potential $\mu$, one may use chiral perturbation theory (ChEFT); and for large values of $\mu$, one may use perturbative QCD (pQCD). There is, however, a gap for $\mu \in (0.97\text{ GeV},2.6\text{ GeV})$, where these theories becomes non-perturbative, and where there is currently no known microscopic description of QCD matter. Unfortunately, this interval obscures the values of $\mu$ found within the cores of neutron stars (NSs). In this thesis, we argue that thermodynamic matching of the ChEFT and pQCD EoSs is a legitimate way to obtain quantitative constraints on the non-pertubative QCD EoS. Moreover, we argue that this method is effective, verifiable, and systematically improvable. First, we carry out a simplified matching procedure in QCD-like theories that can be simulated on the lattice without a sign problem. Our calculated pressure band serves as a prediction for lattice-QCD practitioners and will allow them to verify or refute the simplified procedure. Second, we apply the state-of-the-art matched EoS of Kurkela et al. (2014) to rotating NSs. This allows us to obtain bounds on observable NS properties, as well as point towards future observations that would more tightly constrain the current state-of-the-art EoS band. Finally, as evidence of the ability to improve the procedure, we carry out calculations in pQCD to improve the zero-temperature pressure. We calculate the full $\mathcal{O}(g^6{\ln }^{2}g)$ contribution to the pQCD pressure for $n_f$ massless quarks, as well as a significant portion of the $\mathcal{O}(g^6\ln g)$ piece and even some of the $\mathcal{O}(g^6)$ piece.

Ph.D. Thesis, 108 pages, 13 figures, 1 appendix

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