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.
