The high-temperature limit of the SM(EFT)

A bstract We derive the one-loop effective 3-dimensional Lagrangian that describes the high-temperature limit of the electroweak theory, to order $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( 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.