Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions

Gongyo, Shinya; Zwanziger, Daniel

doi:10.1007/jhep01(2015)002

Cited by 5 publications

(21 citation statements)

References 56 publications

(99 reference statements)

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“…Our analytic computation is so far only possible at large-N , so it cannot be directly compared to the N = 2 results of [3]. Nevertheless, we will see that the behavior of the Higgs phase we find at large N is qualitatively similar to the N = 2 results of [3].…”

Section: Introductionmentioning

confidence: 57%

“…In this letter we propose that placing the model in a small volume can further suppress the divergence. Given the values of the couplings, e, g 0 used in [3], the mass becomes small enough to be measured in Montecarlo simulations. We show that the dependence of the gluon mass on the volume agrees qualitatively with the results of [3].…”

Section: Jhep12(2015)064mentioning

confidence: 99%

“…For the lattice computations of ref. [3], for example, the values used were n = 256, 512, 1024. As an arbitrary example, for the sake of illustrating our point, let's imagine a lattice spacing is chosen such that ma = 10 −14 (this is the assumption that m is small enough that all these volumes are still in the regime where mV < 1).…”

Section: The Higgs Phase and Gluon Massmentioning

confidence: 99%

“…A numerical lattice study of the phase diagram of the same theory, with gauge group SU(2), was published by S. Gongyo and D. Zwanziger [3]. In this reference, they found evidence for both the confined and the Higgs phase, even in 1+1 dimensions.…”

Section: Introductionmentioning

confidence: 95%

“…Inspired by the nontrivial results of [3], we extend the approach started in [2] to study analytically the (1+1)-dimensional theory with a lattice discretization and at finite volume. Our analytic computation is so far only possible at large-N , so it cannot be directly compared to the N = 2 results of [3].…”

Section: Introductionmentioning

confidence: 99%

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Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Cubero

2015

J. High Energ. Phys.

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We examine the phase structure of massive Yang-Mills theory in 1+1 dimensions. This theory is equivalent to a gauged principal chiral sigma model. It has been previously shown that the gauged theory has only a confined phase, and no Higgs phase in the continuum, and at infinite volume. There are no massive gluons, but only hadron-like bound states of sigma-model particles. The reason is that the gluon mass diverges, being proportional to the two-point correlation function of the renormalized field of the sigma model at x = 0. We use exact large-N results to show that after introducing a lattice regularization and typical values of the coupling constants used in Monte Carlo simulations, the gluon mass becomes finite, and even sometimes small. A smooth crossover into a Higgs phase can then appear. For small volumes and large N , we find an analytic expression for the gluon mass, which depends on the coupling constants and the volume. We argue that this Higgs phase is qualitatively similar to the one observed in lattice computations at N = 2.

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Section: Introductionmentioning

confidence: 57%

Section: Jhep12(2015)064mentioning

confidence: 99%

Section: The Higgs Phase and Gluon Massmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Cubero

2015

J. High Energ. Phys.

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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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Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD

Gongyo

Suganuma

2013

Phys. Rev. D

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In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge with Uð1Þ 3 Â Uð1Þ 8 Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on 16 4 at ¼ 6:0 and 32 4 at ¼ 5:8 and 6.0 at the quenched level. In the four-dimensional Euclidean spacetime, the effective mass of diagonal gluons is estimated as M diag ' 0:3 GeV and that of off-diagonal gluons as M off ' 1 GeV in the region of r ¼ 0:4-1:0 fm. In the momentum space, the effective mass of diagonal gluons is estimated as M diag ' 0:3 GeV and that of off-diagonal gluons as M off ' 1 GeV in the region of p < 1:1 GeV. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by Z=ðp 2 þ m 2 Þ with fit parameters, Z, m, and in the region of p < 3:0 GeV. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions.

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Phase structure and the gluon propagator of SU(2) gauge-Higgs model in two dimensions

Cited by 5 publications

References 56 publications

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Confinement-Higgs phase crossover as a lattice artifact in 1 + 1 dimensions

Brout–Englert–Higgs physics: From foundations to phenomenology

Gluon propagators in maximally Abelian gauge in SU(3) lattice QCD

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