Gauge invariance of the one-loop effective action of the Higgs field in the SU(2) Higgs model
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Abstract:
The one-loop effective action of the Abelian and non-Abelian Higgs models has been studied in various gauges, in the context of instanton and sphaleron transition, bubble nucleation, and most recently in nonequilibrium dynamics. Gauge invariance is expected on account of Nielsen's theorem if the classical background field is an extremum of the classical action, i.e., a solution of the classical equation of motion. We substantiate this general statement for the one-loop effective action, as computed using mode functions. We show that in the gauge-Higgs sector there are two types of modes that satisfy the same equation of motion as the Faddeev-Popov modes. We apply the general analysis to the computation of the fluctuation determinant for bubble nucleation in the SU(2) Higgs model in the 't Hooft gauge with general gauge parameter $\ensuremath{\xi}.$ We show that due to the cancellation of the modes mentioned above, the fluctuation determinant is independent of $\ensuremath{\xi}.$Keywords:
Sphaleron
In this paper we generalize the quantum gauge transformation of Maxwell theory obtained through gaugeon formalism.The generalization is made by making the bosonic transformation parameter field-dependent.The Jacobian of vacuum functional under field-dependent quantum gauge transformation is calculated explicitly.We show that the quantum gauge transformation with a particular choice of field-dependent parameter connects the gaugeon actions of Maxwell theory in two different gauges.We establish the result by connecting two well-known gauges, namely, Lorentz gauge and axial gauge.I.
Quantum gauge theory
BRST quantization
Lorenz gauge condition
Gauge covariant derivative
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Two classical static configurations of the SU (2) gauge-Higgs system are known: the sphaleron and the string-monopole configuration. In addition, a third configuration, new sphaleron, has been conjectured to exist. A series of field configurations at spatial infinity is examined, such that the ansatz for the sphaleron and that for the string-monopole configuration are given by the n = 2 and n = 1 sectors of the series respectively and the n = 4 sector is the ansatz for the new sphaleron. A specific gauge transformation, which is singular and relates the Dirac and the 't Hooft-Polyakov monopoles, and Hopf projection map, which induces noncontractable structure in field configuration space, are investigated to produce the series. It is conjectured that the SU (2) gauge-Higgs system might admit more classical configurations. A peculiar property of the sphaleron that, in spite of sitting at a saddle point of energy, it enjoys maximal symmetry of the gauge-Higgs system is discussed.
Sphaleron
Ansatz
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Sphaleron
Baryon asymmetry
Parametric oscillator
Baryon number
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We report on work studying the properties of the sphaleron in models of the electroweak interactions with two Higgs doublets in as model-independent a way as possible: by exploring the physical parameter space described by the masses and mixing angles of the Higgs particles. If one of the Higgs particles is heavy, there can be several sphaleron solutions, distinguished by their properties under parity and the behaviour of the Higgs field at the origin. In general, these solutions are not spherically symmetric, although the departure from spherical symmetry is small.
Sphaleron
Parity (physics)
Tachyonic field
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The Higgs triplet model (HTM) extends the Standard Model (SM) by one complex triplet scalar (also known as the type-II seesaw model), offering a simple and viable way to account for nonzero neutrino masses. On the other hand, the nontrivial couplings of the triplet to the gauge fields and to the SM Higgs field are expected to influence the topological vacuum structure of the SM, and consequently, the energy and the field configuration of the electroweak sphaleron. The sphaleron process plays a crucial role in dynamically generating the baryon asymmetry of the Universe. In this work, we study the vacuum structure of the gauge and Higgs fields and calculate the saddle-point sphaleron configuration in the HTM. The coupled nonlinear equations of motion of the sphaleron are solved using the spectral method. We find the inclusion of the triplet scalar could in principle significantly change the sphaleron energy compared with the SM. Nevertheless, at zero temperature, the current stringent experimental constraint on the vacuum expectation value of the triplet suppresses the difference. Interestingly, we find that there still exists some narrow parameter space where the sphaleron energy can be enhanced up to $30\%$ compared with the SM case.
Sphaleron
Vacuum expectation value
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A bstract The Higgs triplet model (HTM) extends the Standard Model (SM) by one complex triplet scalar (also known as the type-II seesaw model), offering a simple and viable way to account for nonzero neutrino masses. On the other hand, the nontrivial couplings of the triplet to the gauge fields and to the SM Higgs field are expected to influence the topological vacuum structure of the SM, and consequently, the energy and the field configuration of the electroweak sphaleron. The sphaleron process plays a crucial role in dynamically generating the baryon asymmetry of the Universe. In this work, we study the vacuum structure of the gauge and Higgs fields and calculate the saddle-point sphaleron configuration in the HTM. The coupled nonlinear equations of motion of the sphaleron are solved using the spectral method. We find the inclusion of the triplet scalar could in principle significantly change the sphaleron energy compared with the SM. Nevertheless, at zero temperature, the current stringent experimental constraint on the vacuum expectation value of the triplet suppresses the difference. Interestingly, we find that there still exists some narrow parameter space where the sphaleron energy can be enhanced up to 30% compared with the SM case.
Sphaleron
Vacuum expectation value
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Quantum gauge theory
BRST quantization
Lattice gauge theory
Faddeev–Popov ghost
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Quantum gauge theory
BRST quantization
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Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant fields. We show that all the formulations, such as the Coulomb, the axial, and the Lorentz gauges, can be constructed and that the explicit LSZ mapping connecting Heisenberg operators to those of the asymptotic fields is possible. We also make some comments on gauge transformations in quantized field theory.
BRST quantization
Lorenz gauge condition
Classical electromagnetism
Quantum gauge theory
Stochastic electrodynamics
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We report here on the effect that CP-violation from a two Higgs doublet potential has on the sphaleron, a field configuration which mediates baryon and lepton number violation in electroweak theories. We parametrized the Higgs potential in terms of physical Higgs masses and mixing angles, one of which is CP-violating. From considering boundedness of potential we were able to derive the allowed range of the CP-violating mixing angle for given Higgs masses. We found the sphaleron and its barrier in the pure SU(2) theory in the presence of CP-violation by extending the usual spherically symmetric ansatz. From the sphaleron solution we used the method of gradient flow to find the static minimum energy path between vacua of the theory with different Chern-Simons number. We determined the sphaleron energy as a function of CP-violating mixing angle and showed that it can increase by 10–20% [1].
Sphaleron
CP violation
Ansatz
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