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The High-Temperature Limit of the SM(EFT)
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We derive the one-loop effective 3-dimensional Lagrangian that describes the high-temperature limit of the electroweak theory, to order $\mathcal{O}(g^6)$ in coupling constants $g$, including corrections due to Matsubara modes of both fermionic and bosonic degrees of freedom. We clarify certain aspects of the gauge-independence of physical parameters. We also extend the calculation to the Standard Model effective field theory, paving the way, in particular, for a precise study of the electroweak phase transition within this framework.
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