Higgs-Yukawa model on the lattice

Chu, David Y.-J.; Jansen, Karl; Knippschild, Bastian; Lin, C.-J. David

doi:10.1051/epjconf/201817508017

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…Interestingly, one is seen only at or below a Higgs mass around 80 GeV, and thus in a regime which seems to be dominated by QCD-like physics, as discussed in section 3.8. Furthermore, it appears that a Higgs-sector with an extended potential seems to be able to provide a more favorable thermodynamic behavior [410,413], as is also indicated by non-gauge theories [414][415][416]. This may indicate a possible gateway to beyond-the-standard model physics or at least to a non-standard realization of BEH physics [410].…”

Section: The Finite-temperature Transitionmentioning

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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Section: The Finite-temperature Transitionmentioning

confidence: 99%

Brout–Englert–Higgs physics: From foundations to phenomenology

Maas

2019

Progress in Particle and Nuclear Physics

107

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“…Other techniques for measuring operator anomalous dimensions and extrapolating to the conformal limit have been explored [115,116]. Scaling methods have also been used successfully in lattice studies of Higgs-Yukawa theory in four dimensions [117][118][119][120][121]; the appearance of conformal fixed points in Higgs-Yukawa theory could have important implications for the Standard Model and new-physics extensions.…”

Section: Conformal Field Theories On the Latticementioning

confidence: 99%

Lattice gauge theory for physics beyond the Standard Model

et al. 2019

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“…Before the discovery of the scalar resonance around 125 GeV, this triviality property was used to predict an upper bound for the Higgs-boson mass [13] which then later could indeed be computed on the lattice [14][15][16]. Given the experimental measurement of the Higgs-boson mass, now it can be an ingredient for the investigation of the appearance of new physics beyond the SM [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point

Chu

Jansen²,

Knippschild

et al. 2019

J. High Energ. Phys.

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We analyse finite-size scaling behaviour of a four-dimensional Higgs-Yukawa model near the Gaussian infrared fixed point. Through improving the mean-field scaling laws by solving one-loop renormalisation group equations, the triviality property of this model can be manifested in the volume-dependence of moments of the scalar-field zero mode. The scaling formulae for the moments are derived in this work with the inclusion of the leading-logarithmic corrections. To test these formulae, we confront them with data from lattice simulations in a simpler model, namely the O(4) pure scalar theory, and find numerical evidence of good agreement. Our results of the finite-size scaling can in principle be employed to establish triviality of Higgs-Yukawa models, or to search for alternative scenarios in studying their fixed-point structure, if sufficiently large lattices can be reached.

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Higgs-Yukawa model on the lattice

Cited by 5 publications

References 20 publications

Brout–Englert–Higgs physics: From foundations to phenomenology

Brout–Englert–Higgs physics: From foundations to phenomenology

Lattice gauge theory for physics beyond the Standard Model

Finite-size scaling for four-dimensional Higgs-Yukawa model near the Gaussian fixed point

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