标题： 维度约化中的相变高达三圈 显示英文标题

标题： Phase Transitions in Dimensional Reduction up to Three Loops

摘要： 我们首次计算了在一个类似于SMEFT的Higgs部分的简单模型中，以$\lambda\sim m^2/T^2$三次方展开的相变参数，其中$m$是标量质量，$T$是温度。我们采用了维度约化方法，包括了6维项（以4维单位表示）的一环匹配修正，4维项的两环贡献以及平方质量的三环贡献。我们精确量化了不同修正的大小，包括重正化群运行以及由Coleman-Weinberg势提供的有效理论中的轻场量子效应，并简要讨论了引力波的含义。我们的结果显示，对于强相变，6维算符的一环修正可以与四次耦合的两环修正竞争，但远远超过三环热质量的修正。 显示英文摘要

摘要： We perform the first computation of phase-transition parameters to cubic order in $\lambda\sim m^2/T^2$, where $m$ is the scalar mass and $T$ is the temperature, in a simple model resembling the Higgs sector of the SMEFT. We use dimensional reduction, including 1-loop matching corrections for terms of dimension 6 (in 4-dimensional units), 2-loop contributions for dimension-4 ones and 3-loops for the squared mass. We precisely quantify the size of the different corrections, including renormalisation-group running as well as quantum effects from light fields in the effective theory provided by the Coleman-Weinberg potential, and discuss briefly the implications for gravitational waves. Our results suggest that, for strong phase transitions, 1-loop corrections from dimension-6 operators can compete with 2-loop ones from quartic couplings, but largely surpass those from 3-loop thermal masses.