---
author:
- 'Ioan Ghisoiu,'
- 'Tyler Gorda,'
- 'Aleksi Kurkela,'
- 'Paul Romatschke,'
- 'Matias Säppi,'
- and Aleksi Vuorinen
title: 'On high-order perturbative calculations at finite density'
---

Introduction \[sec:intro\]
==========================

Understanding the properties of cold and dense strongly interacting matter is known to be a very challenging task. With the Sign Problem preventing a lattice approach [@deForcrand:2010ys], the first-principles methods available for describing, e.g., the internal composition of neutron stars, are limited to Chiral Effective Theory at low baryon densities [@Machleidt:2011zz] and perturbative QCD at ultrahigh density [@Kraemmer:2003gd]. In order to decrease the currently sizable error bars of the Equation of State (EoS) of neutron star matter [@Hebeler:2013nza], it is thus clear that these two approaches should be actively pushed to higher orders. Indeed, it has been shown recently that a systematic interpolation between the low- and high-density limits can be efficiently used to restrict the behavior of the neutron star EoS at all densities, provided that the asymptotic limits are accurate enough [@Kurkela:2014vha; @Fraga:2015xha].

The current state-of-the-art result for the perturbative EoS of zero-temperature quark matter is from a three-loop, or ${\mathcal O}(\alpha_s^2)$, calculation that was first performed at vanishing quark masses [@Freedman:1976ub; @Vuorinen:2003fs], but later 