Finite Temperature Effective Potential to Order $g^4,\la^2$ and the Electroweak Phase Transition

TL;DR

The paper addresses the finite-temperature electroweak phase transition by computing the Standard Model effective potential to order $g^4,\lambda^2$ with full zero-temperature renormalization, using a Dyson–Schwinger equation framework to resum relevant diagrams. It demonstrates that higher-order corrections markedly strengthen the first-order transition due to infrared effects in the non-Abelian gauge sector and scalar IR behavior near the critical temperature, providing detailed analyses of surface tension, latent heat, and the $\varphi$-VEV in both a pure SU(2)-Higgs model and the full Standard Model. The authors supply an explicit analytic formula for the potential and compare to lower-order results and to the Abelian case, highlighting significant scheme and IR-sensitivity issues that limit perturbative reliability. The work underscores the importance of infrared dynamics and motivates nonperturbative approaches to achieve robust predictions for the electroweak phase transition relevant to baryogenesis and early-universe cosmology. The results offer a foundation for further analytic and numerical exploration of finite-temperature effects in the electroweak sector.

Abstract

The standard model effective potential is calculated at finite temperature to order $g^4,\la^2$ and a complete zero temperature renormalization is performed. In comparison with lower order calculations the strength of the first order phase transition has increased dramatically. This effect can be traced back to infrared contributions from typical non-Abelian diagrams and to the infrared behaviour of the scalar sector close to the critical temperature. Several quantities, e.g. surface tension, latent heat and field expectation value are analyzed for an SU(2)-Higgs model and for the full standard model in detail. An explicit formula enabling further analytic or numerical study is presented. (DESY-94-025)