How fast can the wall move? A study of the electroweak phase transition dynamics

Abstract

We consider the dynamics of bubble growth in the Minimal Standard Model at the electroweak phase transition and determine the shape and the velocity of the phase boundary, or bubble wall. We show that in the semi-classical approximation the friction on the wall arises from the deviation of massive particle populations from thermal equilibrium. We treat these with Boltzmann equations in a fluid approximation. This approximation is reasonable for the top quarks and the light species while it underestimates the friction from the infrared $W$ bosons and Higgs particles. We use the two-loop finite temperature effective potential and find a subsonic bubble wall for the whole range of Higgs masses $0<m_H<90$GeV. The result is weakly dependent on $m_H$: the wall velocity $v_w$ falls in the range $0.36<v_w<0.44$, while the wall thickness is in the range $29>LT>23$. The wall is thicker than the phase equilibrium value because out of equilibrium particles exert more friction on the back than on the base of a moving wall. We also consider the effect of an infrared gauge condensate which may exist in the symmetric phase; modelling it simplemindedly, we find that the wall may become supersonic, but not ultrarelativistic.

42 pages, plain latex, with three figures. Minor editing August 1 (we figured out how to do analytically some integrals we previously did numerically, made corresponding (slight) changes to numerical results, and corrected some typos.)

References in corpus (8)

• 3D Physics and the Electroweak Phase Transition: Perturbation Theory
• The Growth of Bubbles in Cosmological Phase Transitions
• Bubble Wall Velocity at the Electroweak Phase Transition
• Finite Temperature Effective Potential to Order $g^4,\la^2$ and the Electroweak Phase Transition
• The Electroweak Phase Transition at $m_H\simeq m_W$
• The Effects of Electro-weak Phase Transition Dynamics on Baryogenesis and Primordial Nucleosynthesis
• On Non-Perturbative Effects at the High-Temperature Electroweak Phase Transition
• The Strongly Interacting Electroweak Phase Transition

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