Higher-order corrections to the bubble-nucleation rate at finite temperature

In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for gravitational-wave calculations. To be specific, the region of applicability and accuracy of the derivative expansion is discussed. The derivative expansion is then compared to a numerical implementation of the Gelfand-Yaglom theorem. Both methods are applied to popular first-order phase transition models, like a loop-induced barrier and a SM-EFT tree-level barrier. The results of these calculations are presented in easy-to-use parametrizations that can directly be used in gravitational-wave calculations. In addition, higher-order corrections for models with multiple scalar fields, such as singlet/triplet extensions, are studied. Lastly, the main goal of this paper is to investigate the convergence and uncertainty of all calculation. Doing so I argue that current calculations for the Standard Model with a tree-level barrier are inaccurate.

Automated summary

This paper discusses the consistent incorporation of higher-order corrections to the bubble-nucleation rate at finite temperature and examines different approaches to reduce uncertainties in gravitational-wave calculations. The applicability and accuracy of the derivative expansion are discussed and compared to a numerical implementation of the Gelfand-Yaglom theorem. First-order phase transition models are used to apply both methods and the results are presented in parametrizations for easy use in gravitational-wave calculations. Higher-order corrections for models with multiple scalar fields are also studied. The paper concludes that current calculations for the Standard Model with a tree-level barrier are inaccurate.