On the perturbative expansion at high temperature and implications for cosmological phase transitions

Abstract

We revisit the perturbative expansion at high temperature and investigate its convergence by inspecting the renormalisation scale dependence of the effective potential. Although at zero temperature the renormalisation group improved effective potential is scale independent at one-loop, we show how this breaks down at high temperature, due to the misalignment of loop and coupling expansions. Following this, we show how one can recover renormalisation scale independence at high temperature, and that it requires computations at two-loop order. We demonstrate how this resolves some of the huge theoretical uncertainties in the gravitational wave signal of first-order phase transitions, though uncertainties remain stemming from the computation of the bubble nucleation rate.

New early dark energy

“…, at the same time, the underlying perturbative treatment requires the scalar and vector loop expansion parameters to fulfill[90] (for a more recent discussion on the applicability of perturbation theory see[126,127])33 …”

Gravitational waves from first-order electroweak phase transition in a model with light sgoldstinos

“…This underlines considerable theoretical uncertainties pertinent to these predictions (see e.g. [69] for a recent discussion on this subject). 1, and sensitivity curves of LISA, BBO, DECIGO, Ultimate DECIGO experiments (dashed lines) [40,68].…”

The Electro-Weak Phase Transition at Colliders: Discovery Post-Mortem

“…Describing the nature of the electro-weak transition is an ongoing theoretical challenge. The current state-of-the-art technique is a gauge-invariant calculation at next-to-leading order (NLO) in dimensional reduction [71][72][73]. To derive the dynamics of the dimensionally-reduced potential at NLO requires the calculation of O( 102 ) diagrams which makes the application of the state of the art to large parameter scans in multiple models a work-in-progress.…”

“…To derive the dynamics of the dimensionally-reduced potential at NLO requires the calculation of O( 102 ) diagrams which makes the application of the state of the art to large parameter scans in multiple models a work-in-progress. Even at NLO, for sufficiently large couplings, perturbation theory begins to struggle to make sharp predictions [72] and, for weak transitions, infrared divergences in the physical Higgs mode can cause perturbation theory to qualitatively disagree with lattice results [74].…”

“…In doing so, one must make a somewhat unfortunate choice between gauge-dependent methods, or a gauge-independent method that does not include a resummation of divergent infrared modes at leading order [75]. The enormous unphysical scale dependence found in multiple studies due to the poor convergence of perturbation theory to O(g 4 ) [72] suggests that it is a heavy cost to neglect resummation terms at O(g 3 ). For a scalar singlet, unlike the standard model, the new contributions, either to a tree level barrier or the thermal barrier, are gauge independent due to the gauge singlet nature of the new field.…”