Classical field dynamics of the electroweak phase transition

Abstract

We investigate the thermodynamics and dynamics of the electroweak phase transition by modelling the infrared physics with classical Yang-Mills Higgs theory. We discuss the accuracy of this approach and conclude that, for quantities whose determination is dominated by the infrared, the classical method should be correct up to parametrically suppressed (ie O(α)) corrections. For a Higgs self-coupling which at tree level corresponds to m H 50GeV, we determine the jump in the order parameter to be δφ = 1.5gT , the surface tension to be σ = 0.07g 4 T 3 , and the friction coefficient on the moving bubble wall due to infrared bosons to be η ≡ P/v w = 0.03 ± .004g 6 T 4 . We also investigate the response of Chern-Simons number to a spatially uniform chemical potential and find that it falls off a short distance inside the bubble wall, both in equilibrium and below the equilibrium temperature.

Electroweak bubble nucleation, nonperturbatively

“…The surface tension can be obtained much more economically with an alternative method due to Moore and Turok [49]. This method is based on analyzing the spectrum of the transverse fluctuations of the phase interfaces; the magnitude of the fluctuations is inversely proportional to σ/T .…”

Low-cost fermions in classical field simulations

“…We have to make sure to satisfy Eq. (15). For this we define the Fourier transformed stochastic fields: …”

“…A second strength of the classical approximation is that equilibrium is not a prerequisite. Solving the real time Yang-Mills equations with far-from-equilibrium initial conditions one could gain access to the evolution of the Chern-Simons number [14,15,16]. For this to accomplish the third strength of the classial equations has been ex- * Electronic address: s.borsanyi@sussex.ac.uk † Electronic address: m.b.hindmarsh@sussex.ac.uk ploited: its preservation of gauge invariance under timeindependent transformations.…”

Simulations of Bose Fields at Finite Temperature

“…In the limit where the modes of the system are highly occupied ͑N k ¿ 1͒, the classical fluctuations of the field overwhelm the quantum fluctuations, and these modes may therefore be represented by a coherent wave function. This is analogous to the situation in laser physics, where the highly occupied laser modes can be well described by classical equations.Using this argument, Damle et al have performed calculations of the approach to equilibrium of a near ideal superfluid [15], and similar approximations to other quantum field equations have been successful elsewhere [16]. also use the GPE to represent the classical modes of a Bose-condensed system.…”

“…Using this argument, Damle et al have performed calculations of the approach to equilibrium of a near ideal superfluid [15], and similar approximations to other quantum field equations have been successful elsewhere [16]. References [17][18][19] also use the GPE to represent the classical modes of a Bose-condensed system.…”