Date of Award

Spring 1-1-2016

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Paul Romatschke

Second Advisor

Anna Hasenfratz

Third Advisor

Thomas DeGrand

Fourth Advisor

Michael Hermele

Fifth Advisor

Benjamin Brown


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 µ, one may use chiral perturbation theory (ChEFT); and for large values of µ, one may use perturbative QCD (pQCD). Each of these theories is controlled, predictive, and has much theoretical development. There is, however, a gap for µ ∈ (0.97 GeV, 2.6 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 µ 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 in this intermediate region. Within this framework, one pieces together the EoSs coming from ChEFT (or another low-energy description) and pQCD in a thermodynamically consistent manner to obtain a band of allowed EoSs. This method trades qualitative modeling for quantitative constraints: one attempts no microscopic characterization of the underlying matter.

In this thesis, we argue that this method is an effective, verifiable, and systematically improvable way to explore and characterize the interior of NSs. 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 O(g6 ln2 g) contribution to the pQCD pressure for nf massless quarks, as well as a significant portion of the O(g6 ln g) piece and even some of the O(g6) piece.