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 (${\mathrm{N}}^3\mathrm{LO}$) 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 ${\mathrm{N}}^3\mathrm{LO}$ result for this quantity.

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N3LO 的冷夸克物质：软贡献

QCD 中热力学量的高阶微扰计算由于影响系统的软长波长模式的动态屏蔽物理学而变得复杂。在这里，我们提供了评估对 next-to-next-to-next-to-leading 顺序的这种软贡献的详细信息（${\mathrm{N}}^3\mathrm{LO}$) 高密度、零温度夸克物质 (QM) 的压力，补充了我们随附的信函 [T. 戈尔达等人。，物理。牧师莱特。 127 , 162003 (2021)]。我们的计算需要将硬热回路有效理论的压力确定为零温度下的完整双回路阶数，我们对此进行了相当详细的介绍。除此之外，我们全面讨论了 QM 压力的弱耦合扩展的结构，并为评估完整模型中缺失的贡献制定了路线图。${\mathrm{N}}^3\mathrm{LO}$ 这个数量的结果。