Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review
Abstract
:1. Introduction
2. Symmetry Restoration and Order of Phase Transitions
3. Breakdown of Perturbative Expansion and Thermal Resummation
4. Electroweak Phase Transition
4.1. Standard Model
- The above demonstration does not take the thermal resummation into consideration. If one performs it by either the Parwani or AE scheme, E would be diminished by the resummation effect as discussed in Section 3.
- The effective potential is the sum of 1-particle-irreducible diagrams by definition, which is inherently gauge dependent, and so the VEV defined by the minimum of the effective potential depends on a choice of specific gauge. This is natural consequence since the normalization of the scalar fields (wavefunction renormalization) is missing. Notwithstanding, energies at stationary points are gauge independent obeyed by the NFK identity [109,110].
- Since the phase transition is generically non-perturbative phenomenon, lattice calculations are more suitable to obtain robust results. It is shown in Refs. [140,141,142,143] that EWPT turns into smooth crossover for GeV. After the Higgs boson discovery, EWPT is re-analyzed in Ref. [144] in a different context. The “critical temperature" is found to be GeV.
4.2. Standard Model with a Real Scalar
4.3. Perturbative Gauge-Invariant Treatment for the Thermal Phase Transitions
4.4. Comparisons among Various Calculation Schemes
5. Summary and Outlook
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Thermally Corrected Field-Dependent Masses in the rSM
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Senaha, E. Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review. Symmetry 2020, 12, 733. https://doi.org/10.3390/sym12050733
Senaha E. Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review. Symmetry. 2020; 12(5):733. https://doi.org/10.3390/sym12050733
Chicago/Turabian StyleSenaha, Eibun. 2020. "Symmetry Restoration and Breaking at Finite Temperature: An Introductory Review" Symmetry 12, no. 5: 733. https://doi.org/10.3390/sym12050733