The renormalization flow in the adjoint SU(2) lattice Higgs model

Baier, Rudolf; Lang, C. B.; Reusch, H. J.

doi:10.1016/0550-3213(88)90074-0

Cited by 9 publications

(7 citation statements)

References 46 publications

(49 reference statements)

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“…This is discussed in detail in appendix A. Especially, we found that with better thermalization properties the results on the phase diagram from exploratory investigations [19][20][21][22][23] changed, and especially the phase transition shifted to larger values of κ for larger volumes. The reason for this is likely the presence of the massless gauge-invariant vector particle, and thus slow decorrelation and large finite-volume effects.…”

Section: Phase Diagram and Simulation Pointsmentioning

confidence: 76%

“…Our lattice implementation will be given in Section 3, with some details relegated to appendix A. In particular, we found that early investigations of the phase diagram of this theory [19][20][21][22][23] likely underestimated systematic effects due to the finite volume and length of Monte Carlo trajectories, similar to what has happened in the fundamental case [24]. These effects are quite severe, and thus also in our case we cannot yet offer a full systematic analysis in terms of discretization artifacts, though volume effects will be investigated in great detail.…”

Section: Introductionmentioning

confidence: 99%

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A composite massless vector boson

Afferrante,

Maas,

Törek

2020

Preprint

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In a non-perturbative gauge-invariant formulation of grand-unified theories all low energy vector states need to be composite with respect to the high-scale gauge group, including the photon. We investigate this by using lattice methods to spectroscopically analyze the vector channel in a toy grand-unified theory, an SU(2) adjoint Higgs model. Our results support indeed the existence of a massless composite vector particle.

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Section: Phase Diagram and Simulation Pointsmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

A composite massless vector boson

Afferrante,

Maas,

Törek

2020

Preprint

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“…These two transitions are connected by a phase transition line that separates the Higgs and confining phases. There is evidence for a tricritical point at finite (κ, β) at which the transition changes from first to second order [31], but it is not known if the tricritical line extends to λ = 0.…”

Section: Discussionmentioning

confidence: 99%

Mass of a quantum 't Hooft-Polyakov monopole

Rajantie

2006

J. High Energy Phys.

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The quantum mechanical mass of 't Hooft-Polyakov monopoles in the fourdimensional Georgi-Glashow is calculated non-perturbatively using lattice Monte Carlo simulations. This is done by imposing twisted boundary conditions that ensure there is one unit of magnetic charge on the lattice, and measuring the free energy difference between this ensemble and the vacuum. In the weak-coupling limit, the results can be used to determine the quantum correction to the classical mass, once renormalisation of couplings is taken properly into account. The methods can also be used to study the masses at strong coupling, i.e., near the critical point, where there are hints of a possible electric-magnetic duality.

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“…These results will be reviewed in the following. Almost all of these investigations have been performed in four dimensions for the standard model case [46, 144, 158-160, 162, 186-191, 194-200, 203, 204, 206], and only very few addressed other theories [180,184,185,192,193,201,202,205,[207][208][209][210][211][212].…”

Section: The Phase Diagram From the Latticementioning

confidence: 99%

Brout–Englert–Higgs physics: From foundations to phenomenology

Maas

2019

Progress in Particle and Nuclear Physics

107

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Brout-Englert Higgs physics is one of the most central and successful parts of the standard model. It is also part of a multitude of beyond-the-standard-model scenarios.The aim of this review is to describe the field-theoretical foundations of Brout-Englert-Higgs physics, and to show how the usual phenomenology arises from it. This requires to give a precise and gauge-invariant meaning to the underlying physics. This is complicated by the fact that concepts like the Higgs vacuum expectation value or the separation between confinement and the Brout-Englert-Higgs effect loose their meaning beyond perturbation theory. This is addressed by carefully constructing the corresponding theory space and the quantum phase diagram of theories with elementary Higgs fields and gauge interactions.The physical spectrum needs then to be also given in terms of gauge-invariant, i. e. composite, states. Using gauge-invariant perturbation theory, as developed by Fröhlich, Morchio, and Strocchi, it is possible to rederive conventional perturbation theory in this framework. This derivation explicitly shows why the description of the standard model in terms of the unphysical, gaugedependent, elementary states of the Higgs and W -bosons and Z-boson, but also of the elementary fermions, is adequate and successful.These are unavoidable consequences of the field theory underlying the standard model, from which the usual picture emerges. The validity of this emergence can only be tested non-perturbatively. Such tests, in particular using lattice gauge theory, will be reviewed as well. They fully confirm the underlying mechanisms.In this course it will be seen that the structure of the standard model is very special, and qualitative changes occur beyond it. The extension beyond the standard model will therefore also be reviewed. Particular attention will be given to structural differences arising for phenomenology. Again, non-perturbative tests of these results will be reviewed.Finally, to make this review self-contained a brief discussion of issues like the triviality and hierarchy problem, and how they fit into a fundamental field-theoretical formulation, is included. If there is no gauge-invariant way of defining the vacuum expectation value of the Higgs, the whole standard procedure [14] of doing BEH physics seems to collapse on itself at first. This seems to question the whole basis of the current theoretical description of experiments, despite its huge success [10]. But it does not. Rather, it can be shown that a treatment taking the gauge-dependence into account will lead to, essentially, the same results for the standard model.How this works out is exactly the core of this review: The construction of a fully gauge-invariant description of this physics, and how the standard phenomenology follows from it. This starts in section 3. There, a gauge-invariant description of the theory (3) will be set up. This is the first step of developing a comprehensive, field-theoretical consistent view on BEH physics. This view is continued by establis...

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The renormalization flow in the adjoint SU(2) lattice Higgs model

Cited by 9 publications

References 46 publications

A composite massless vector boson

A composite massless vector boson

Mass of a quantum 't Hooft-Polyakov monopole

Brout–Englert–Higgs physics: From foundations to phenomenology

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