arXiv 2602.069622026-02hep-phhep-th

规范耦合中硬热对相变可观测量的次领头阶贡献

Hard thermal contributions to phase transition observables at NNLO

Université de Genève（日内瓦大学）；Universidad de Granada（格拉纳达大学）

Fabio Bernardo, Mikael Chala, Luis Gil, Philipp Schicho

备注：: 44 pages, 5 figures, 1 table, journal version
DOI：: 10.1007/JHEP06(2026)281

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AI总结：

研究构建规范 - 希格斯模型高温有效场论，通过积分硬模式到三圈水平等方法，量化高维算符和高圈修正影响，推导相关质量和耦合，展示规范独立性，还发现主积分相关问题及QCD德拜质量的缺失贡献。

摘要：

为构建规范 - 希格斯模型在规范耦合下到$\mathcal{O}(g^6)$的高温有效场论，我们将硬模式积分到三圈水平并使用次领头阶有效势。对于阿贝尔希格斯模型，我们量化了高维算符和高圈修正对与引力波可观测量相关的热力学参数的影响。我们推导了${\rm U(1)}$和${\rm SU}(N)$规范 - 希格斯模型的三圈标量和德拜质量以及阿贝尔情形的两圈四次耦合，展示了物理参数的规范独立性，还证明匹配不需要新的主积分，同时4维和3维可重整性的一致性指出了这些主积分中先前缺失的贡献。作为副产品，我们报告了对三圈QCD德拜质量先前缺失的贡献。

英文摘要：

To construct the high-temperature effective field theory of gauge-Higgs models up to $\mathcal{O}(g^6)$ in the gauge coupling, we integrate out hard modes to three-loop level and use the next-to-next-to-leading order effective potential. For the Abelian Higgs model, we quantify the impact of both higher-dimensional operators and higher-loop corrections on thermodynamic parameters relevant for gravitational-wave observables, finding that one-loop dimension-six effects typically dominate over two- and three-loop corrections to super-renormalizable parameters for the strongest transitions. We derive the three-loop scalar and Debye masses for the ${\rm U(1)}$ and ${\rm SU}(N)$ gauge-Higgs models, as well as the two-loop quartic couplings for the Abelian case, show gauge independence of physical parameters, and demonstrate that no new master integrals are required for the matching, while consistency of 4d and 3d renormalizability points to previously missing contributions in these master integrals. As a byproduct, we report a previously missing contribution to the three-loop QCD Debye mass.

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