Everything about The Higgs Mechanism totally explained
The
Higgs mechanism, also called the
Brout-Englert-Higgs mechanism,
Higgs-Kibble mechanism or
Anderson-Higgs mechanism, was proposed in 1964 by
Robert Brout and
Francois Englert, independently by
Peter Higgs and by
Gerald Guralnik,
C. R. Hagen, and
Tom Kibble following earlier work by
Yoichiro Nambu on the structure of the vacuum. It was inspired by the
BCS theory of superconductivity, the preceding
Ginzburg-Landau theory, and the suggestion by
Philip Anderson that superconductivity could be important for relativistic physics. It was anticipated by
earlier work of
Ernst Stückelberg on massive quantum electrodynamics. It was named the
Higgs mechanism by
Gerardus 't Hooft in 1971.
The Higgs mechanism is a form of superconductivity in the vacuum. It considers all of space filled with a relativistically invariant quantum fluid called the
Higgs field, whose motion prevents certain forces from propagating over long distances. Part of the Higgs field mixes with the force-carrying
gauge fields to produce massive
gauge bosons, while the rest of the Higgs field describes a new particle, called the
Higgs boson. The range of the force and the mass of the gauge bosons are inverses in
natural units, but the mass of the Higgs boson is different and depends on the details.
The Higgs mechanism is the only way elementary vector particles, like the
or the
, can have a mass. Interactions with the associated Higgs boson gives mass to the
quarks and
leptons in the
standard model. The Higgs mechanism is an example of
tachyon condensation where the tachyon is the
Higgs field.
Although the evidence for the Higgs
mechanism is overwhelming, accelerators have yet to produce a Higgs
boson, for example by determining its mass. Even then it wouldn't be clear if the Higgs is an elementary or a composite particle. For example, one might speculate that, similar to Cooper pairs, which are the carriers of the above-mentioned BCS theory of superconductivity, the Higgs field could finally turn out to consist of two weakly bound W-particles. This would lead to a rough mass estimate of 2x80=160 GeV.
General Discussion
The problem with
spontaneous symmetry breaking models in particle physics is that, according to
Goldstone's theorem, they come with massless scalar particles. If a symmetry is broken by a condensate, acting with a symmetry generator on the condensate gives a second state with the same energy. So certain oscillations don't have any energy, and in
quantum field theory the particles associated with these oscillations have zero mass.
The only observed particles which could be interpreted as Goldstone bosons were the
pions. Since the symmetry is approximate, the pions are not exactly massless. Yoichiro Nambu, writing before Goldstone, suggested that the pions were the bosons associated with
chiral symmetry breaking. This explained their
pseudoscalar nature, the reason they couple to nucleons through
derivative couplings, and the
Goldberger-Treiman relation. Aside from the pions, no other Goldstone particle was observed.
A similar problem arises in
Yang-Mills theory, also known as
nonabelian gauge theory. These theories predict massless spin 1 gauge bosons, which (apart from the
photon) are also not observed. It was Higgs' insight that when you combine a gauge theory with a spontaneous symmetry-breaking model the (unobserved) massless bosons acquire a mass, which we observe, solving the problem.
Higgs' original article presenting the model was rejected by
Physical Review Letters when first submitted, apparently because it didn't predict any new detectable effects. So he added a sentence at the end, mentioning that it implies the existence of one or more new, massive scalar bosons, which don't form complete
representations of the symmetry. These are the
Higgs bosons.
The Higgs mechanism was incorporated into modern particle physics by
Steven Weinberg and is an essential part of the
Standard Model.
In the standard model, at temperatures high enough so that the symmetry is unbroken, all elementary particles except the scalar Higgs boson are massless. At a critical temperature, the Higgs field spontaneously slides from the point of maximum energy in a randomly chosen direction, like a pencil standing on end that falls. Once the symmetry is broken, the gauge boson particles — such as the
leptons,
quarks,
W boson, and
Z boson — get a mass. The mass can be interpreted to be a result of the interactions of the particles with the "Higgs ocean".
Superconductivity
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 is due to currents in a thin surface layer, whose thickness, the
London penetration depth, can be calculated from a simple model.
This simple model, due to
Lev Landau and
Vitaly Ginzburg, treats superconductivity as a charged
Bose-Einstein condensate. Suppose that a superconductor contains bosons with charge
. The wavefunction of the bosons can be described by introducing a
quantum field,
, which obeys the
Schrödinger equation as a field equation (in units where
, the Planck quantum divided by
, is replaced by 1):
» .
Further Information
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