Bubble Wall Velocity at the Electroweak Phase Transition (original) (raw)
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Bubble Wall Velocity in a First Order Electroweak Phase Transition
Physical Review Letters, 1995
We calculate the velocity and thickness of a bubble wall at the electroweak phase transition in the Minimal Standard Model. We model the wall with semiclassical equations of motion and show that friction arises from the deviation of massive particle populations from thermal equilibrium. We treat these with Boltzmann equations in a fluid approximation in the background of the wall. Our analysis improves on the previous work by using the two loop effective potential, accounting for particle transport, and determining the wall thickness dynamically. We find that the wall is significantly thicker than at phase equilibrium, and that the velocity is fairly high, v w ≃ 0.7c, and quite weakly dependent on the Higgs mass.
How fast can the wall move? A study of the electroweak phase transition dynamics
Physical Review D, 1995
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 < 90GeV. 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.
Velocity of electroweak bubble walls
Nuclear Physics B, 2010
We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, 0.1 v w 0.6. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, 10 −2 v w 10 −1 , as required by electroweak baryogenesis.
An efficient approach to electroweak bubble velocities
2013
Extensions of the Standard Model are being considered as viable settings for a first-order electroweak phase transition which satisfy Sakharov's three conditions for the generation of the baryon asymmetry of the Universe. These extensions provide a sufficiently strong phase transition and remove the main obstacles which appear in the context of the Standard Model: A far-too-high lower bound on the Higgs mass, immediate wipeout of the newly-created baryon asymmetry, and insufficient CP violation. We describe the Universe hydrodynamically as a fluid coupled to the Higgs field via a phenomenological friction term, and study the time evolution of bubbles nucleated during the phase transition. We express the friction term in the hydrodynamic equations in terms of the particle content of the model, calibrate the friction on the basis of existing calculations for the Standard Model, and produce predictions for the velocity of the expanding bubble wall in the stationary regime. This way we develop a very efficient approach to compute bubble velocities. As an example, we apply our formalism to the first-order phase transition of a dimension-6 extension of the Standard Model which, within the present bounds on the Higgs mass, can reproduce the observed baryon asymmetry of the Universe. Depending on the strength of the phase transition, the wall velocity varies from about 0.3 to approaching the speed of light. Our method can easily be adapted to compute wall velocities in other interesting extensions of the Standard Model.
Hydrodynamics of the electroweak phase transition
2013
This work investigates the hydrodynamics of the expansion of the bubbles of the broken symmetry phase during the electroweak phase transition in the early universe, in which SU(2) electroweak symmetry is broken and fundamental particles acquire mass through the Higgs mechanism. The electroweak phase transition has received renewed attention as a viable setting for the production of the matter-antimatter asymmetry of the universe. The relevant mechanisms are strongly dependent on key parameters like the expansion velocity of the walls of bubbles of the new phase. In addition, the key dynamical parameters of the phase transition may generate signatures (like gravitational waves) which may become detectable in the near future. This work builds on existing hydrodynamical studies of the growth of bubbles of the broken symmetry phase and adapts them to novel scenarios, producing predictions of the wall velocity. The early universe at the time of the electroweak phase transition is modelled as a perfect relativistic fluid. A fundamental problem is to account for the interaction between the so-called cosmic 'plasma' and the bubble wall, which may slow down wall propagation and produce a steady state with finite velocity. This 'friction' is accounted for by a separate term in the hydrodynamical equations. This work adapts existing microphysical calculations of the friction to two physical models chosen because of their suitability as regards producing the baryon asymmetry of the universe: 1) An extension of the Standard Model with dimension-6 operators (for which this is the first calculation of the wall velocity ever produced) and 2) The Light Stop Scenario (LSS) of the Minimal Supersymmetric Standard Model (MSSM) (for which this is the first 2-loop calculation). The predicted values of the wall velocity are coherent and consistent with previous studies, confirming, in particular, the prediction of a low wall velocity for the LSS.
Journal of physics, 2010
Extensions of the Standard Model are being considered as viable settings for a first-order electroweak phase transition which would satisfy Sakharov's three conditions for the generation of the baryon asymmetry of the Universe. These extensions would provide a sufficiently strong phase transition and remove the main obstacles which appear in the context of the Standard Model: A far-too-high lower bound on the Higgs mass, immediate wipeout of the newly-created baryon asymmetry and insufficient CP violation. We apply standard semiclassical treatments of the hydrodynamics of a first-order phase transition to the case of a recently-introduced dimension-6 extension of the Standard Model which (within the present bounds on the Higgs mass) could produce the observed baryon asymmetry of the Universe. We express the friction term in the hydrodynamic equations in terms of the particle content of the model and produce predictions for the velocity of the expanding bubble wall in the stationary regime.
The bubble wall velocity in the minimal supersymmetric light stop scenario
Physical Review D, 2012
We build on existing calculations of the wall velocity of the expanding bubbles of the broken symmetry phase in a first-order electroweak phase transition within the light stop scenario (LSS) of the MSSM. We carry out the analysis using the 2-loop thermal potential for values of the Higgs mass consistent with present experimental bounds. Our approach relies on describing the interaction between the bubble and the hot plasma by a single friction parameter, which we fix by matching to an existing 1-loop computation and extrapolate it to our regime of interest. For a sufficiently strong phase transition (in which washout of the newly-created baryon asymmetry is prevented) we obtain values of the wall velocity, v w ≈ 0.05, far below the speed of sound in the medium, and not very much deviating from the previous 1-loop calculation. We also find that the phase transition is about 10% stronger than suggested by simply evaluating the thermal potential at the critical temperature.
Phenomenology of electroweak bubbles and gravity waves in the Littlest Higgs Model with T parity
We study the dynamics of electroweak bubbles in the scenario of a strong first order inverse electroweak phase transition at the TeV scale involving the global structure of the nonlinear sigma field in the littlest Higgs model with T parity. Employing the one-loop order finite temperature effective potential, we find that the pressure in the symmetric phase i.e., inside the bubble is always greater than that in the asymmetric phase i.e., outside the bubble, so that the bubbles are expanding. By calculating the fluid velocities in the two phases we arrive at the condition of a supersonic deflagrated motion of the bubble walls. We then discuss the generation of gravitational waves from the collisions of such bubbles as well as from the turbulence of the plasma.
Electroweak bubble nucleation, nonperturbatively
Physical Review D, 2001
We present a lattice method to compute bubble nucleation rates at radiatively induced first order phase transitions, in high temperature, weakly coupled field theories, nonperturbatively. A generalization of Langer's approach, it makes no recourse to saddle point expansions and includes completely the dynamical prefactor. We test the technique by applying it to the electroweak phase transition in the minimal standard model, at an unphysically small Higgs mass which gives a reasonably strong phase transition (λ/g 2 = 0.036, which corresponds to m H /m W = 0.54 at tree level but does not correspond to a positive physical Higgs mass when radiative effects of the top quark are included), and compare the results to older perturbative and other estimates. While two loop perturbation theory slightly under-estimates the strength of the transition measured by the latent heat, it over-estimates the amount of supercooling by a factor of 2.
Hydrodynamic stability analysis of burning bubbles in electroweak theory and in QCD
Physical Review D, 1993
Assuming that the electroweak and QCD phase transitions are first order, upon supercooling, bubbles of the new phase appear. These bubbles grow to macroscopic sizes compared to the natural scales associated with the Compton wavelengths of particle excitations. They propagate by burning the old phase into the new phase at the surface of the bubble. We study the hydrodynamic stability of the burning and find that for the velocities of interest for cosmology in the electroweak phase transition, the shape of the bubble wall is stable under hydrodynamic perturbations. Bubbles formed in the cosmological QCD phase transition are found to be a borderline case between stability and instability.