We complete the perturbative program for equilibrium thermodynamics of cosmological first-order phase transitions of gauge-Higgs theories that map into the (three-dimensional) superrenormalizable SU⁡(2)+doublet effective theory at high temperatures. To this end, we determine their finite-temperature effective potential at next-to-next-to-next-to-next-to-leading order (N4⁢LO). The computation of the three-loop effective potential required to reach this order is also presented for U(1) gauge theories and is readily extendable to generic models in dimensionally reduced effective theories. Our N4⁢LO result is the last perturbative order before confinement renders electroweak gauge-Higgs theories nonperturbative at four loops. By contrasting our analysis with nonperturbative lattice results, we find a remarkable agreement. As a direct application for predictions of gravitational waves produced by a first-order transition, our computation provides the final fully perturbative results for the phase transition strength and speed of sound.

中文翻译：

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三个回路的宇宙学相变：对微扰理论的最终裁决


我们完成了规范-希格斯理论的宇宙学一阶相变的平衡热力学的扰动程序，该程序映射到高温下的（三维）超重整化 SU（2）+双合态有效理论。为此，我们确定了它们在 next-to-next-to-next-to-next-to-leading 阶 （N4LO） 下的有限温度有效电位。达到该阶所需的三环有效电位的计算也适用于 U（1） 规范理论，并且很容易扩展到维约化有效理论中的通用模型。我们的 N4LO 结果是约束使电弱规范-希格斯理论在四个回路上无扰动之前的最后一个扰动阶数。通过将我们的分析与非扰动晶格结果进行对比，我们发现了显著的一致性。作为预测一阶跃迁产生的引力波的直接应用，我们的计算为相变强度和声速提供了最终的完全微扰结果。