Semiclassical analysis of the phases of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>4</mml:mn><mml:mi>d</mml:mi></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>Higgs gauge systems with cutoff at the Gribov horizon

Capri, M. A. L.; Dudal, David; Gomez, A. J.; Guimaraes, M. S.; Justo, I. F.; Sorella, S. P.; Vercauteren, David

doi:10.1103/physrevd.88.085022

Cited by 29 publications

(49 citation statements)

References 71 publications

(170 reference statements)

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“…Computing the discriminant of the quartic polynomial in (26b) Similar results were also found in [20] and [21], where the Yang-Mills-Higgs theory was studied from the perspective of the Gribov problem. Despite the very different nature of the theory, a similar regime with two real masses, one with positive and one with negative residue, was also found there.…”

Section: The Gap Equation For the Gribov Parameter γsupporting

confidence: 64%

“…It is worth noticing that the Chern-Simons mass parameter M does not enter the gap equation (23). This is an expected result, due to the topological nature of the Chern-Simons term.…”

Section: The Gap Equation For the Gribov Parameter γmentioning

confidence: 77%

“…The poles of the propagator are functions of the parameters (g, M ). As such, the study of their behavior when varying (g, M ) is of great help in understanding the different regimes in which the theory may be found, as recently discussed in the case of Yang-Mills theories in the presence of Higgs fields [20,21,22,23] as well as of gauge theories at finite temperature [25]. The region in the plane (g, M ) in which the poles of the gauge propagator are complex has a natural interpretation as a confining region, since complex poles cannot be associated to a physical excitation of the spectrum.…”

Section: The Gap Equation For the Gribov Parameter γmentioning

confidence: 99%

“…Let us also mention that the Refined Gribov-Zwanziger framework has been employed in the study of the Casimir energy [19], producing the correct sign for the Casimir force within the MIT bag model, clarifying a long-standing problem. Also, in a series of papers [20,21,22,23], the Gribov-Zwanziger set up has been employed in order to study, in the continuum, the transition between the confining and non-confining regimes when Higgs fields are present. Also in this case, the non-perturbative gluon two-point correlation function obtained by taking into account the effects of the Gribov horizon turns out to be a useful quantity in order to obtain information about the transition from the confining to the Higgs regime.…”

Section: Introductionmentioning

confidence: 99%

“…Also in this case, the non-perturbative gluon two-point correlation function obtained by taking into account the effects of the Gribov horizon turns out to be a useful quantity in order to obtain information about the transition from the confining to the Higgs regime. As discussed in details in [20,21,22,23], the gluon correlation function undergoes a continuous change from a confining expression of the Gribov type, characterized by the presence of unphysical complex conjugate poles, to a Yukawa type propagator with a real pole, indicating that the theory is in the Higgs regime. The emerging picture is in full agreement with the renewed FradkinShenker work [24].…”

Section: Introductionmentioning

confidence: 99%

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Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

et al. 2014

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Section: The Gap Equation For the Gribov Parameter γsupporting

confidence: 64%

“…It is worth noticing that the Chern-Simons mass parameter M does not enter the gap equation (23). This is an expected result, due to the topological nature of the Chern-Simons term.…”

Section: The Gap Equation For the Gribov Parameter γmentioning

confidence: 77%

Section: The Gap Equation For the Gribov Parameter γmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

et al. 2014

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Gauge-invariant spectral description of the U (1) Higgs model from local composite operators

Dudal

Egmond

Guimaraes

et al. 2020

J. High Energ. Phys.

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The spectral properties of a set of local gauge-invariant composite operators are investigated in the U (1) Higgs model quantized in the 't Hooft R ξ gauge. These operators enable us to give a gauge-invariant description of the spectrum of the theory, thereby surpassing certain incommodities when using the standard elementary fields. The corresponding two-point correlation functions are evaluated at one-loop order and their spectral functions are obtained explicitly. As expected, the above mentioned correlation functions are independent from the gauge parameter ξ, while exhibiting positive spectral densities as well as gauge-invariant pole masses corresponding to the massive photon and Higgs physical excitations. I. INTRODUCTIONAn essential aspect of gauge theories is that all physical observable quantities have to be gauge-invariant [1,2]. However, in practice, the explicit calculations of the S-matrix elements and corresponding cross sections are done by employing the non-gauge-invariant elementary fields such as the W bosons and the Higgs field of the electroweak theory, giving results in quite accurate agreement with experimental ones.The success of making use of the non-gauge-invariant elementary fields can be traced back to the so called Nielsen identities [3][4][5][6][7] which follow from the Slavnov-Taylor identities encoding the BRST symmetry of quantized gauge theories. The Nielsen identities ensure that the pole masses of both transverse gauge bosons and Higgs field propagators do not depend on the gauge parameters entering the gauge fixing condition, a pivotal property shared by the Smatrix elements. Nevertheless, as one can easily figure out, the use of the non-gauge-invariant fields has its own limitations which show up in several ways. For example, the analysis of the spectral properties of the elementary two-point correlation functions in terms of the Källén-Lehmann ( KL) representation is often plagued by an undesired dependence of the spectral densities on the gauge parameters and/or the densities attaining negative values, obscuring their physical interpretation. Indeed, from e.g. non-perturbative lattice QCD studies, it is well known that not only direct particle-spectrum related properties are hiding in the spectral functions, but at finite temperature also information on transport properties in the quark-gluon plasma etc., see for instance [8][9][10][11][12]. The spectral functions considered are those of gauge-invariant operators. Moreover, it is also known that in certain classes of gauges, the Nielsen identities can suffer from fatal infrared singularities [3,13,14], obscuring what happens with e.g. the pole mass or effective potential governing the Higgs vacuum expectation value in such gauges.A formulation of the properties of the observable excitations in terms of gauge-invariant variables is thus very welcome. Such an endeavour has been addressed by several authors 1 [17-20], who have been able to construct, out of the elementary fields, a set of local gauge-invariant composite operat...

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Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory

Maas

Mufti

2014

J. High Energ. Phys.

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Yang-Mills-Higgs theory offers a rich set of physics. In particular, in some region of its parameter space it has QCD-like behavior, while in some other range it is Higgs-like. Furthermore, for the choice of the gauge group SU(2) and an SU(2) Higgs flavor symmetry it is the Higgs sector of the standard model. Therefore, it is possible to study a plethora of phenomena within a single theory. Here the standard-model version is studied using lattice gauge theory. Choosing non-aligned minimal Landau gauge, its propagators and three-point vertices will be determined in both the QCD-like and Higgslike domains. This permits to test various proposals for how confinement works, as well as how confinement and the Higgs effect differ. The correlations functions are found to exhibit a different behavior, depending on whether the lowest mass scalar flavor singlet is lighter than the vector triplet, heavier and stable, or unstable against decay into two vector triplets.

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Semiclassical analysis of the phases of4dSU(2)Higgs gauge systems with cutoff at the Gribov horizon

Cited by 29 publications

References 71 publications

Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

Gauge-invariant spectral description of the U (1) Higgs model from local composite operators

Two- and three-point functions in Landau gauge Yang-Mills-Higgs theory

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