Non-perturbative determination of the sphaleron rate for first-order phase transitions

2025/06/05 by Annala, Jaakko, Rummukainen, Kari, Tenkanen, Tuomas V. I.
#Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2506.04939

Abstract

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 ≡ λ₃/g²₃ and y≡ m²₃/g⁴₃, where λ₃, m²₃ and g₃ are the effective thermal scalar self-interaction coupling, the thermal mass and the effective gauge-coupling, respectively. By using non-perturbative 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) \lesssim 0.025 to guarantee preservation of the baryon asymmetry, which translates to v/T_c ≡ √(2 ⟨ ϕ^† ϕ⟩)/T_c \gtrsim 1.33 for the (gauge-invariant) 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.

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Related

• An Effective Sphaleron Awakens
• The Sphaleron Rate at the Electroweak Crossover
• The Electroweak Phase Transition in Extended Models
• Electroweak Baryogenesis: Advances in Sphaleron Rate Calculations and Implications of Thermal Phase Transitions
• Progress in the Theory of the Electroweak Phase Transition