Standard Model of particle physics
Elementary particles of the Standard Model
Background Particle physics Standard Model Quantum field theory Gauge theory Spontaneous symmetry breaking Higgs mechanism
Constituents Electroweak interaction Quantum chromodynamics CKM matrix Standard Model mathematics
Limitations Strong CP problem Hierarchy problem Neutrino oscillations Physics beyond the Standard Model
Scientists Rutherford Thomson Chadwick Bose Sudarshan Davis Jr Anderson Fermi Dirac Feynman Rubbia Gell-Mann Kendall Taylor Friedman Powell Anderson Glashow Iliopoulos Lederman Maiani Meer Cowan Nambu Chamberlain Cabibbo Schwartz Perl Majorana Weinberg Lee Ward Salam Kobayashi Maskawa Mills Yang Yukawa 't Hooft Veltman Gross Pais Pauli Politzer Reines Schwinger Wilczek Cronin Fitch Vleck Higgs Englert Brout Hagen Guralnik Kibble de Mayolo Lattes Zweig
v t e

Quantum field theory
Feynman diagram
History
Background Field theory Electromagnetism Weak force Strong force Quantum mechanics Special relativity General relativity Gauge theory Yang–Mills theory
Symmetries Symmetry in quantum mechanics C-symmetry P-symmetry T-symmetry Lorentz symmetry Poincaré symmetry Gauge symmetry Explicit symmetry breaking Spontaneous symmetry breaking Noether charge Topological charge
Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation value Feynman diagram Lattice field theory LSZ reduction formula Partition function Propagator Quantization Regularization Renormalization Vacuum state Wick's theorem
Equations Dirac equation Klein–Gordon equation Proca equations Wheeler–DeWitt equation Bargmann–Wigner equations
Standard Model Quantum electrodynamics Electroweak interaction Quantum chromodynamics Higgs mechanism
Incomplete theories String theory Supersymmetry Technicolor Theory of everything Quantum gravity
Scientists Adler Anderson Anselm Bargmann Becchi Belavin Bell Berezin Bethe Bjorken Bleuer Bogoliubov Brodsky Brout Buchholz Cachazo Callan Coleman Dashen DeWitt Dirac Doplicher Dyson Englert Faddeev Fadin Fayet Fermi Feynman Fierz Fock Frampton Fritzsch Fröhlich Fredenhagen Furry Glashow Gelfand Gell-Mann Glimm Goldstone Gribov Gross Gupta Guralnik Haag Heisenberg Hepp Higgs Hagen 't Hooft Iliopoulos Ivanenko Jackiw Jaffe Jona-Lasinio Jordan Jost Källén Kendall Kinoshita Klebanov Kontsevich Kuraev Landau Lee Lehmann Leutwyler Lipatov Łopuszański Low Lüders Maiani Majorana Maldacena Migdal Mills Møller Naimark Nambu Neveu Nishijima Oehme Oppenheimer Osterwalder Parisi Pauli Peskin Plefka Polyakov Pomeranchuk Popov Proca Rubakov Ruelle Salam Schrader Schwarz Schwinger Segal Seiberg Semenoff Shifman Shirkov Skyrme Sommerfield Stora Stueckelberg Sudarshan Symanzik Thirring Tomonaga Tyutin Vainshtein Veltman Virasoro Ward Weinberg Weisskopf Wentzel Wess Wetterich Weyl Wick Wightman Wigner Wilczek Wilson Witten Yang Yukawa Zamolodchikov Zamolodchikov Zee Zimmermann Zinn-Justin Zuber Zumino
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In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other being fermions) would be considered massless, but measurements show that the W⁺, W⁻, and Z⁰ bosons actually have relatively large masses of around 80 GeV/c². The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field (the Higgs field) which permeates all of space to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. In the Standard Model, the phrase "Higgs mechanism" refers specifically to the generation of masses for the W^±, and Z weak gauge bosons through electroweak symmetry breaking.^[1] The Large Hadron Collider at CERN announced results consistent with the Higgs particle on 14 March 2013, making it extremely likely that the field, or one like it, exists, and explaining how the Higgs mechanism takes place in nature. The view of the Higgs mechanism as involving spontaneous symmetry breaking of a gauge symmetry is technically incorrect since by Elitzur's theorem gauge symmetries can never be spontaneously broken. Rather, the Fröhlich–Morchio–Strocchi mechanism reformulates the Higgs mechanism in an entirely gauge invariant way, generally leading to the same results.^[2]

The mechanism was proposed in 1962 by Philip Warren Anderson,^[3] following work in the late 1950s on symmetry breaking in superconductivity and a 1960 paper by Yoichiro Nambu that discussed its application within particle physics.

A theory able to finally explain mass generation without "breaking" gauge theory was published almost simultaneously by three independent groups in 1964: by Robert Brout and François Englert;^[4] by Peter Higgs;^[5] and by Gerald Guralnik, C. R. Hagen, and Tom Kibble.^[6][7][8] The Higgs mechanism is therefore also called the Brout–Englert–Higgs mechanism, or Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism,^[9] Anderson–Higgs mechanism,^[10] Anderson–Higgs–Kibble mechanism,^[11] Higgs–Kibble mechanism by Abdus Salam^[12] and ABEGHHK'tH mechanism (for Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and 't Hooft) by Peter Higgs.^[12] The Higgs mechanism in electrodynamics was also discovered independently by Eberly and Reiss in reverse as the "gauge" Dirac field mass gain due to the artificially displaced electromagnetic field as a Higgs field.^[13]

On 8 October 2013, following the discovery at CERN's Large Hadron Collider of a new particle that appeared to be the long-sought Higgs boson predicted by the theory, it was announced that Peter Higgs and François Englert had been awarded the 2013 Nobel Prize in Physics.^[a][14]

Standard Model

The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, and is an essential part of the Standard Model.

In the Standard Model, at temperatures high enough that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature, the Higgs field develops a vacuum expectation value; some theories suggest the symmetry is spontaneously broken by tachyon condensation, and the W and Z bosons acquire masses (also called "electroweak symmetry breaking", or EWSB). In the history of the universe, this is believed to have happened about a picosecond (10⁻¹² s) after the hot big bang, when the universe was at a temperature 159.5 ± 1.5 GeV.^[15]

Fermions, such as the leptons and quarks in the Standard Model, can also acquire mass as a result of their interaction with the Higgs field, but not in the same way as the gauge bosons.

Structure of the Higgs field

In the standard model, the Higgs field is an SU(2) doublet (i.e. the standard representation with two complex components called isospin), which is a scalar under Lorentz transformations. Its electric charge is zero; its weak isospin is 1/2 and the third component of weak isospin is −1/2; and its weak hypercharge (the charge for the U(1) gauge group defined up to an arbitrary multiplicative constant) is 1. Under U(1) rotations, it is multiplied by a phase, which thus mixes the real and imaginary parts of the complex spinor into each other, combining to the standard two-component complex representation of the group U(2).

The Higgs field, through the interactions specified (summarized, represented, or even simulated) by its potential, induces spontaneous breaking of three out of the four generators ("directions") of the gauge group U(2). This is often written as SU(2)_L × U(1)_Y, (which is strictly speaking only the same on the level of infinitesimal symmetries) because the diagonal phase factor also acts on other fields – quarks in particular. Three out of its four components would ordinarily resolve as Goldstone bosons, if they were not coupled to gauge fields.

However, after symmetry breaking, these three of the four degrees of freedom in the Higgs field mix with the three W and Z bosons (
W⁺
,
W⁻
and
Z⁰
), and are only observable as components of these weak bosons, which are made massive by their inclusion; only the single remaining degree of freedom becomes a new scalar particle: the Higgs boson. The components that do not mix with Goldstone bosons form a massless photon.

The photon as the part that remains massless

The gauge group of the electroweak part of the standard model is SU(2)_L × U(1)_Y. The group SU(2) is the group of all 2-by-2 unitary matrices with unit determinant; all the orthonormal changes of coordinates in a complex two dimensional vector space.

Rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor ( 0, v ) . The generators for rotations about the x, y, and z axes are by half the Pauli matrices σ_x, σ_y, and σ_z, so that a rotation of angle θ about the z-axis takes the vacuum to

${\displaystyle \ {\Bigl (}\ 0\ ,\ v\ e^{-{\tfrac {1}{2}}\ i\ \theta }\ {\Bigr )}~.}$

While the T_x and T_y generators mix up the top and bottom components of the spinor, the T_z rotations only multiply each by opposite phases. This phase can be undone by a U(1) rotation of angle  1 / 2  θ . Consequently, under both an SU(2) T_z-rotation and a U(1) rotation by an amount  1 / 2  θ , the vacuum is invariant.

This combination of generators

${\displaystyle \ Q=T_{3}+{\tfrac {\ 1\ }{2}}\ Y_{\mathsf {W}}\ }$

defines the unbroken part of the gauge group, where Q is the electric charge, T₃ is the generator of rotations around the 3-axis in the SU(2) and Y_W is the weak hypercharge generator of the U(1). This combination of generators (a 3 rotation in the SU(2) and a simultaneous U(1) rotation by half the angle) preserves the vacuum, and defines the unbroken gauge group in the standard model, namely the electric charge group. The part of the gauge field in this direction stays massless, and amounts to the physical photon. By contrast, the broken trace-orthogonal charge ${\displaystyle \ T_{3}-{\tfrac {\ 1\ }{2}}\ Y_{\mathsf {W}}=2\ T_{3}-Q\ }$ couples to the massive
Z⁰
 boson.

Consequences for fermions

In spite of the introduction of spontaneous symmetry breaking, the mass terms preclude chiral gauge invariance. For these fields, the mass terms should always be replaced by a gauge-invariant "Higgs" mechanism. One possibility is some kind of Yukawa coupling (see below) between the fermion field ψ and the Higgs field φ, with unknown couplings G_ψ, which after symmetry breaking (more precisely: After expansion of the Lagrange density around a suitable ground state) again results in the original mass terms, which are now, however (i.e., by introduction of the Higgs field) written in a gauge-invariant way. The Lagrange density for the Yukawa interaction of a fermion field ψ and the Higgs field φ is

${\displaystyle \ {\mathcal {L}}_{\mathrm {Fermion} }(\phi ,A,\psi )~=~{\overline {\psi }}\ \gamma ^{\mu }\ D_{\mu }\ \psi ~+~G_{\psi }\ {\overline {\psi }}\ \phi \ \psi \ ,}$

where again the gauge field A only enters via the gauge covariant derivative operator D_μ (i.e., it is only indirectly visible). The quantities γ_μ are the Dirac matrices, and G_ψ is the already-mentioned Yukawa coupling parameter for ψ. Now the mass-generation follows the same principle as above, namely from the existence of a finite expectation value ${\displaystyle \ |\langle \phi \rangle |~.}$ Again, this is crucial for the existence of the property mass.

History of research

Background

Spontaneous symmetry breaking offered a framework to introduce bosons into relativistic quantum field theories. However, according to Goldstone's theorem, these bosons should be massless.^[16] The only observed particles which could be approximately interpreted as Goldstone bosons were the pions, which Yoichiro Nambu related to chiral symmetry breaking.

A similar problem arises with Yang–Mills theory (also known as non-abelian gauge theory), which predicts massless spin-1 gauge bosons. Massless weakly-interacting gauge bosons lead to long-range forces, which are only observed for electromagnetism and the corresponding massless photon. Gauge theories of the weak force needed a way to describe massive gauge bosons in order to be consistent.

Discovery

That breaking gauge symmetries did not lead to massless particles was observed in 1961 by Julian Schwinger,^[17] but he did not demonstrate massive particles would eventuate. This was done in Philip Warren Anderson's 1962 paper^[3] but only in non-relativistic field theory; it also discussed consequences for particle physics but did not work out an explicit relativistic model. The relativistic model was developed in 1964 by three independent groups:

• Robert Brout and François Englert^[4]
• Peter Higgs^[5]
• Gerald Guralnik, Carl Richard Hagen, and Tom Kibble.^[6][7][8]

Slightly later, in 1965, but independently from the other publications^{[18][19][20][21][22][23]} the mechanism was also proposed by Alexander Migdal and Alexander Polyakov,^[24] at that time Soviet undergraduate students. However, their paper was delayed by the editorial office of JETP, and was published late, in 1966.

The mechanism is closely analogous to phenomena previously discovered by Yoichiro Nambu involving the "vacuum structure" of quantum fields in superconductivity.^[25] A similar but distinct effect (involving an affine realization of what is now recognized as the Higgs field), known as the Stueckelberg mechanism, had previously been studied by Ernst Stueckelberg.

These physicists discovered that when a gauge theory is combined with an additional field that spontaneously breaks the symmetry group, the gauge bosons can consistently acquire a nonzero mass. In spite of the large values involved (see below) this permits a gauge theory description of the weak force, which was independently developed by Steven Weinberg and Abdus Salam in 1967. Higgs's original article presenting the model was rejected by Physics Letters. When revising the article before resubmitting it to Physical Review Letters, he added a sentence at the end,^[26] mentioning that it implies the existence of one or more new, massive scalar bosons, which do not form complete representations of the symmetry group; these are the Higgs bosons.

The three papers by Brout and Englert; Higgs; and Guralnik, Hagen, and Kibble were each recognized as "milestone letters" by Physical Review Letters in 2008.^[27] While each of these seminal papers took similar approaches, the contributions and differences among the 1964 PRL symmetry breaking papers are noteworthy. All six physicists were jointly awarded the 2010 J. J. Sakurai Prize for Theoretical Particle Physics for this work.^[28]

Benjamin W. Lee is often credited with first naming the "Higgs-like" mechanism, although there is debate around when this first occurred.^[29][30][31] One of the first times the Higgs name appeared in print was in 1972 when Gerardus 't Hooft and Martinus J. G. Veltman referred to it as the "Higgs–Kibble mechanism" in their Nobel winning paper.^[32][33]

Simple explanation of the theory, from its origins in superconductivity

The proposed Higgs mechanism arose as a result of theories proposed to explain observations in superconductivity. A superconductor does not allow penetration by external magnetic fields (the Meissner effect). This strange observation implies that the electromagnetic field somehow becomes short ranged during this phenomenon. Successful theories arose to explain this during the 1950s, first for fermions (Ginzburg–Landau theory, 1950), and then for bosons (BCS theory, 1957).

In these theories, superconductivity is interpreted as arising from a charged condensate. Initially, the condensate value does not have any preferred direction. This implies it is scalar, but its phase is capable of defining a gauge, in gauge based field theories. To do this, the field must be charged. A charged scalar field must also be complex (or described another way, it contains at least two components, and a symmetry capable of rotating each into the other(s)). In naïve gauge theory, a gauge transformation of a condensate usually rotates the phase. However, in these circumstances, it instead fixes a preferred choice of phase. However it turns out that fixing the choice of gauge so that the condensate has the same phase everywhere, also causes the electromagnetic field to gain an extra term. This extra term causes the electromagnetic field to become short range.

Goldstone's theorem also plays a role in such theories. The connection is technically, when a condensate breaks a symmetry, then the state reached by acting with a symmetry generator on the condensate has the same energy as before. This means that some kinds of oscillation will not involve change of energy. Oscillations with unchanged energy imply that excitations (particles) associated with the oscillation are massless.

Once attention was drawn to this theory within particle physics, the parallels were clear. A change of the usually long range electromagnetic field to become short ranged, within a gauge invariant theory, was exactly the needed effect sought for the weak force bosons (because a long range force has massless gauge bosons, and a short ranged force implies massive gauge bosons, suggesting that a result of this interaction is that the field's gauge bosons acquired mass, or a similar and equivalent effect). The features of a field required to do this was also quite well defined - it would have to be a charged scalar field, with at least two components, and complex in order to support a symmetry able to rotate these into each other.

Examples

The Higgs mechanism occurs whenever a charged field has a vacuum expectation value. In the non-relativistic context this is a superconductor, more formally known as the Landau model of a charged Bose–Einstein condensate. In the relativistic condensate, the condensate is a scalar field that is relativistically invariant.

Landau model

The Higgs mechanism is a type of superconductivity which occurs in the vacuum. It occurs when all of space is filled with a sea of particles which are charged, or, in field language, when a charged field has a nonzero vacuum expectation value. Interaction with the quantum fluid filling the space prevents certain forces from propagating over long distances (as it does inside a superconductor; e.g., in the Ginzburg–Landau theory).

A superconductor expels all magnetic fields from its interior, a phenomenon known as the Meissner effect. This was mysterious for a long time, because it implies that electromagnetic forces somehow become short-range inside the superconductor. Contrast this with the behavior of an ordinary metal. In a metal, the conductivity shields electric fields by rearranging charges on the surface until the total field cancels in the interior.

But magnetic fields can penetrate to any distance, and if a magnetic monopole (an isolated magnetic pole) is surrounded by a metal the field can escape without collimating into a string. In a superconductor, however, electric charges move with no dissipation, and this allows for permanent surface currents, not just surface charges. When magnetic fields are introduced at the boundary of a superconductor, they produce surface currents which exactly neutralize them.

The Meissner effect arises due to currents in a thin surface layer, whose thickness can be calculated from the simple model of Ginzburg–Landau theory, which treats superconductivity as a charged Bose–Einstein condensate.

Suppose that a superconductor contains bosons with charge q . The wavefunction of the bosons can be described by introducing a quantum field, ${\displaystyle \ \psi \ ,}$ which obeys the Schrödinger equation as a field equation. In units where the reduced Planck constant, ħ, is set to 1:

${\displaystyle i\frac{\mathrm{\partial <!--\; \partial \; -->}}{\mathrm{\partial <!--\; \partial \; -->}t}\mathrm{\psi <!--\; \psi \; -->}=\frac{}{}}$Zdroj:https://en.wikipedia.org?pojem=Higgs_mechanism
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