Thermal resummation and phase transitions

The consequences of phase transitions in the early universe are becoming testable in a variety of manners, from colliders physics to gravitational wave astronomy. In particular one phase transition we know of, the electroweak phase transition (EWPT), could potentially be first order in BSM scenarios and testable in the near future. If confirmed this could provide a mechanism for baryogenesis, which is one of the most important outstanding questions in physics. To reliably make predictions it is necessary to have full control of the finite temperature scalar potentials. However, as we show the standard methods used in BSM physics to improve phase transition calculations, resumming hard thermal loops, introduces significant errors into the scalar potential. In addition, the standard methods make it impossible to match theories to an EFT description reliably. In this paper we define a thermal resummation procedure based on partial dressing (PD) for general BSM calculations of phase transitions beyond the high-temperature approximation. Additionally, we introduce the modified optimized partial dressing (OPD) procedure, which is numerically nearly as efficient as old incorrect methods, while yielding identical results to the full PD calculation. This can be easily applied to future BSM studies of phase transitions in the early universe. As an example, we show that in unmixed singlet scalar extensions of the SM, the (O)PD calculations make new phenomenological predictions compared to previous analyses. An important future application is the study of EFTs at finite temperature.