Abstract
Symmetries at finite temperature are of great importance to understand dynamics of spontaneous symmetry breaking phenomena, especially phase transitions in early Universe. Some symmetries such as the electroweak symmetry can be restored in hot environment. However, it is a nontrivial question that the phase transition occurs via first or second order, or even smooth crossover, which strongly depends on underlying physics. If it is first order, gravitational waves can be generated, providing a detectable signal of this epoch. Moreover, the baryon asymmetry of the Universe can also arise under some conditions. In this article, the electroweak phase transition is reviewed, focusing particularly on the case of the first-order phase transition. Much attention is paid to multi-step phase transitions in which additional symmetry breaking such as a spontaneous Z 2 breaking plays a pivotal role in broadening the possibility of the first-order electroweak phase transition. On the technical side, we review thermal resummation that mitigates a bad infrared behavior related to the symmetry restoration. In addition, gauge and scheme dependences of perturbative calculations are also briefly discussed.
Highlights
Symmetry and its breaking are key concepts in particle physics and cosmology
Much attention has been given to the latter since the baryon asymmetry of the Universe (BAU) [6], which cannot be realized in the standard model (SM) of particle physics, could arise if electroweak phase transition (EWPT) is first order with expanding bubble walls (referred to as electroweak baryogenesis (EWBG) [7], for reviews, see Refs. [8,9,10,11,12,13,14,15,16])
Symmetry 2020, 12, 733 are classified in the next-to-minimal supersymmetric SM, and it is shown that a global U (1) breaking induced by a gauge singlet scalar preceding EWPT can help to achieve the first-order EWPT
Summary
Symmetry and its breaking are key concepts in particle physics and cosmology. The former provides foundation of underlying theories while the latter is often indispensable to describes diversity in nature. Symmetry 2020, 12, 733 are classified in the next-to-minimal supersymmetric SM, and it is shown that a global U (1) breaking induced by a gauge singlet scalar preceding EWPT can help to achieve the first-order EWPT This mechanism is widely applied to a plethora of models beyond the SM. A standard prescription is called thermal resummation in which perturbative expansion is re-organized in such a way that dominant temperature corrections are summed over and absorbed into zeroth-order terms. In addition to this problem, ordinary perturbative calculations of EWPT are plagued by a gauge dependence problem, which is attributed to the gauge-dependent order parameter, viz, the Higgs vacuum expectation value (VEV).
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