Quantum Corrections to the Electroweak Sphaleron Transition

Baacke, J.; Junker, S.

doi:10.1142/s0217732393003251

Cited by 22 publications

(25 citation statements)

References 8 publications

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“…Recently both the bosonic and fermionic determinants in the background of the sphaleron have been calculated for any temperatures in Refs [105,106]. Probably, this is the most involved and non-trivial computation done for the sphaleron rate until now.…”

Section: The Sphaleron Rate In the Broken Phasementioning

confidence: 99%

Electroweak baryon number non-conservation in the early Universe and in high-energy collisions

Рубаков¹,

1996

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We review recent progress in the study of the anomalous baryon number non-conservation at high temperatures and in high-energy collisions. Recent results on high temperature phase transitions are described, and applications to the electroweak baryogenesis are considered. The current status of the problem of electroweak instanton-like processes at high energies is outlined.Electroweak baryon number non-conservation in the early Universe and in high-energy collisions 7.1 Strength of the phase transition; 7.2 Sources of CP-violation in the electroweak theory and its extensions; 7.3 Electroweak baryogenesis: how to state the problem; 7.4 Uniform scalar fields; 7.5 Asymmetry from fermion±domain wall interactions; 7.6 Strength of CP-violation and baryon asymmetry 8. Instanton-like processes in high energy collisions 491 8.1 Summary of perturbative analysis about the instanton; 8.2 Unitarity; 8.3 From many 3 many to few 3 many 9. Conclusions 499 References 500 Electroweak baryon number non-conservation in the early Universe and in high-energy collisions 463 { At very large m H am W the situation is more complicated [54, 55], but the estimate (2.11) remains valid. { Of course, this travel does not typically proceed exactly through the sphaleron configuration. Some (not necessarily small) deformations of sphalerons are considered in Refs [56 ± 58] where topological properties of these configurations are investigated. 464 V A Rubakov, M E Shaposhnikov Physics ± Uspekhi 39 (5) May, 1996 Electroweak baryon number non-conservation in the early Universe and in high-energy collisions 465 V A Rubakov, M E Shaposhnikov Physics ± Uspekhi 39 (5) V A Rubakov, M E Shaposhnikov Physics ± Uspekhi 39 (5)

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Section: The Sphaleron Rate In the Broken Phasementioning

confidence: 99%

Electroweak baryon number non-conservation in the early Universe and in high-energy collisions

Рубаков¹,

1996

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“…Previously, this approach has been used to derive approximate analytic results for the one-loop fluctuation determinant beyond the thin-wall approximation [89], as well as one-loop corrections to sphaleron rates [90][91][92]. The latter have also been calculated by direct integration of the Green's function [93][94][95][96][97].…”

Section: Introductionmentioning

confidence: 99%

Green’s function method for handling radiative effects on false vacuum decay

2015

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We introduce a Green's function method for handling radiative effects on false vacuum decay. In addition to the usual thin-wall approximation, we achieve further simplification by treating the bubble wall in the planar limit. As an application, we take the λΦ 4 theory, extended with N additional heavier scalars, wherein we calculate analytically both the functional determinant of the quadratic fluctuations about the classical soliton configuration and the first correction to the soliton configuration itself.

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“…The method for calculating the fluctuation determinants based on the resolvent has been applied to tunneling problems in Refs. [37,[50][51][52][53]. We consider the following eigenvalue equations where i = 1, 2 and s ∈ R is an auxiliary parameter.…”

Section: B2 Integration Over the Resolventmentioning

confidence: 99%

Functional methods for false-vacuum decay in real time

Garbrecht

Tamarit

2019

J. High Energ. Phys.

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We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space. We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest-descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed. As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering. While this amplitude may in principle be obtained by analytic continuation of its Euclidean counterpart, we work out in detail how it can be computed to one-loop order at the level of the path integral, i.e. evaluating the Gaußian integrals of fluctuations about the relevant complex saddle points. To that effect, we show how the eigenvalues and eigenfunctions on a thimble can be obtained by analytic continuation of the Euclidean eigensystem, and we determine the path-integral measure on thimbles. This way, using real-time methods, we recover the one-loop result by Callan and Coleman for the decay rate. As a byproduct of our derivation, we note that the optical theorem suggests an interpretation of the false-vacuum energy in flat space in terms of the normalization of the position or field eigenstate associated with the false vacuum, with unit norm corresponding to zero energy up to volume-suppressed effects. We finally demonstrate our real-time methods explicitly, including the construction of the eigensystem of the complex saddle, on the archetypical example of tunneling in a quasi-degenerate quartic potential. arXiv:1905.04236v1 [hep-th]

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Quantum Corrections to the Electroweak Sphaleron Transition

Cited by 22 publications

References 8 publications

Electroweak baryon number non-conservation in the early Universe and in high-energy collisions

Electroweak baryon number non-conservation in the early Universe and in high-energy collisions

Green’s function method for handling radiative effects on false vacuum decay

Functional methods for false-vacuum decay in real time

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