Cold quark matter at N3LO: Soft contributions

High-order perturbative calculations for thermodynamic quantities in QCD are complicated by the physics of dynamical screening that affects the soft, long-wavelength modes of the system. Here, we provide details for the evaluation of this soft contribution to the next-to-next-to-next-to-leading order ((NLO)-L-3) pressure of high-density, zero-temperature quark matter (QM), complementing our accompanying Letter [T. Gorda et al., Phys. Rev. Lett. 127, 162003 (2021)]. Our calculation requires the determination of the pressure of the hard-thermal-loop effective theory to full two-loop order at zero temperature, which we go through in considerable detail. In addition to this, we comprehensively discuss the structure of the weak-coupling expansion of the QM pressure, and lay out a roadmap towards the evaluation of the contributions missing from a full (NLO)-L-3 result for this quantity.

Automated summary

This article provides a detailed overview of the soft contribution required for next-to-next-to-next-to-leading order pressure calculations in high-density, zero-temperature quark matter (QM), involving the determination of the pressure of the hard-thermal-loop effective theory to full two-loop order at zero temperature and an in-depth discussion of the weak-coupling expansion structure of QM pressure.