Jaakko Annala, Kari Rummukainen, Tuomas V. I. Tenkanen
In many extensions of the Standard Model electroweak phase transitions at high temperatures can be described in a minimal dimensionally reduced effective theory with SU(2) gauge field and fundamental Higgs scalar. In this effective theory, all thermodynamic information is governed by two dimensionless ratios x ≡ λ 3 / g 3 2 and y ≡ m 3 2 / g 3 4 , where λ 3 , m 3 2 , and g 3 are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using nonperturbative lattice simulations to determine the rate of sphaleron transitions in the entire ( x , y ) -plane corresponding to the Higgs phase, and by applying previous lattice results for the bubble nucleation, we find a condition x ( T c ) ≲ 0.025 to guarantee preservation of the baryon asymmetry, which translates to v / T c ≡ 2 Δ ⟨ ϕ † ϕ ⟩ / T c ≳ 1.33 for the (gauge-invariant) discontinuity in Higgs condensate. This indicates that viability of the electroweak baryogenesis requires the phase transition to be slightly stronger than previously anticipated. Finally, we present a general template for analysing such viability in a wide class of beyond the Standard Model theories, in which new fields are heavy enough to be integrated out at high temperature.