# Contents

## Idea

The Higgs field or Higgs boson is a scalar physical field/fundamental particle in a gauge theory such as the standard model of particle physics supposedly responsible for the spontaneously broken symmetry of the electroweak field (electroweak symmetry breaking) and for giving elementary particles their masses by the Higgs mechanism.

## Properties

The observed rest mass of the Higgs particle is about $125$ GeV.

## Models

There is no lack of proposals for realizing the Higgs field in various big schemes of mathematical structures modelling physics.

For instance

• in the technicolor model the Higgs field is not a fundamental particle but a compound of fermions. This realizes the Higgs effect entirely in ordinary gauge theory;

• in string theory (see string phenomenology) a Higgs can arise in all sorts of ways. Notably in “intersecting brane models” it arises from strings localized at intersecting points (for a typical kind of survey see for instance around slide 33 here)

• in noncommutative geometry it has been shown that the Higgs may be modeled as a component of the gauge bosons assuming that the KK-reduction is over a certain non-commutative space of classical dimension 0.

## History

The Higgs mechanism was proposed in 1963-1964 by a fair number of authors essentially simultaneously, see the References below. The explicit prediction of the Higgs boson implied by this mechanism though seems to be solely due to (Higgs 64).

The Higgs boson (or at least something very much like it) was finally detected in 2013 at the LHC experiment.

So for the Higgs particle prediction and experimental detection lie apart by about 50 years. Compare maybe to the neutrino, which was predicted in 1930 and detected in 1956, about 26 years later.

standard model of particle physics and cosmology

theory:Einstein-Yang-Mills-Dirac-Higgs
gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field $e$principal connection $\nabla$spinor $\psi$scalar field $H$
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
$L =$$R(e) vol(e) +$$\langle F_\nabla \wedge \star_e F_\nabla\rangle +$$(\psi , D_{(e,\nabla)} \psi) vol(e) +$$\nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$

## References

### General

The original articles explaining what is now called the Higgs mechanism by spontaneous symmetry breaking were

• P. Anderson, Plasmons, gauge invariance and mass, Physical Review 130: 439. (1963)

• François Englert, Robert Brout, Broken Symmetry and the Mass of Gauge Vector Mesons, Physical Review Letters 13 (9): 321–23. (1964)

• Gerald Guralnik, C. R. Hagen, ; T. W. B. Kibble, Global Conservation Laws and Massless Particles Physical Review (1964)

• Peter Higgs, Broken Symmetries and the Masses of Gauge Bosons, Physical Review Letters 13 (16): 508–509. (1964)

While all these articles essentially describe the Higgs mechanism, appearently only the one by Peter Higgs explicitly points out that this mechanism predicts the existence of a new, then unobserved, boson, the one therefore now called the Higgs boson.

The general theory of spontaneous symmetry breaking is reviewed in

• Jeremy Bernstein, Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that, Rev. Mod. Phys. 46, 7–48 (1974) (pdf)

The phenomenology of Higgs models is discussed in

• Marcela Carena, Howard E. Haber, Higgs Boson Theory and Phenomenology, Prog.Part.Nucl.Phys.50:63-152,2003 (arXiv:hep-ph/0208209)

### Vacuum (in-)stability

Discussion of the apparent lack of vacuum stability for the observed Higgs potential includes the following:

• J.R. Espinosa, G. Giudice, A. Riotto, Cosmological implications of the Higgs mass measurement, JCAP 0805:002, 2008 (arXiv:0710.2484)

• John Ellis, J.R. Espinosa, G.F. Giudice, A. Hoecker, A. Riotto, The Probable Fate of the Standard Model, Phys. Lett. B679:369-375, 2009 (arXiv:0906.0954)

• Dario Buttazzo, Giuseppe Degrassi, Pier Paolo Giardino, Gian Giudice, Filippo Sala, Alberto Salvio, Alessandro Strumia, Investigating the near-criticality of the Higgs boson (arXiv:1307.3536)

• Anson Hook, John Kearney, Bibhushan Shakya, Kathryn M. Zurek, Probable or Improbable Universe? Correlating Electroweak Vacuum Instability with the Scale of Inflation, J. High Energ. Phys. (2015) 2015: 61 (arXiv:1404.5953)

• Jose R. Espinosa, Gian F. Giudice, Enrico Morgante, Antonio Riotto, Leonardo Senatore, Alessandro Strumia, Nikolaos Tetradis, The cosmological Higgstory of the vacuum instability (arXiv:1505.04825)

• William E. East, John Kearney, Bibhushan Shakya, Hojin Yoo, Kathryn M. Zurek, Spacetime Dynamics of a Higgs Vacuum Instability During Inflation, Phys. Rev. D 95, 023526 (2017) (arXiv:1607.00381)

### In G2-MSSM

Discussion of the Higgs mechanism in the G2-MSSM and related models is due to

• Gordon Kane, String theory and generic predictions for our world – superpartner masses, LHC signatures, dark matter, EWSB, cosmological history of universe, etc, talk at String phenomenology 2011, August 2011 (pdf)

• Gordon Kane, Piyush Kumar, Ran Lu, Bob Zheng, Higgs Mass Prediction for Realistic String/M Theory Vacua, Phys. Rev. D 85, 075026 (arXiv:1112.1059)

(a useful informed comment is here)

and related to the issue of the vacuum stability in

Revised on February 21, 2018 13:12:55 by Urs Schreiber (91.230.41.206)