Higgs mechanism

Through the Higgs mechanism ( after the British physicist Peter Higgs, Englert and Brout - Higgs - Guralnik -Hagen - Kibble mechanism) describes how the fundamental property of " mass " at the level of elementary particles is established. As a central part of the standard model of particle physics explains the mechanism, why not have certain exchange particles (the " gauge bosons " of the weak interaction ), the mass is zero. Thus, they gain their mass through interaction with the so-called Higgs field, which is ubiquitous throughout the universe. The masses of all the other ( involving mass ) elementary particles like electrons and quarks are hereby declared as a result of interaction with the Higgs field. With this approach it was possible to interpret the weak and the electromagnetic interaction as two different aspects of a single strong fundamental electroweak interaction, which is one of the most important steps to prepare the Standard Model.

While the Higgs field is not directly measurable, another elementary particles must occur during its existence, the " Higgs boson ." This is the only particle of the Standard Model that has not yet been definitively proven. However, there is evidence suggesting that the material presented by the European nuclear research center CERN in July 2012 particle is a Higgs boson.

The mechanism was established in 1964 not only by Peter Higgs, but independently and almost simultaneously by two groups of researchers: François Englert and Robert Brout at the Université Libre de Bruxelles ( even slightly more filed ) and TWB Kibble and Carl R. Hagen Gerald Guralnik at Imperial College. However, Peter Higgs was the first person to predict the existence of a new particle, which is why it has finally been named after him. On October 8, 2013 François Englert and Peter Higgs was awarded for the development of the Higgs mechanism of the Nobel Prize for Physics.

History

Models in solid state theory

The elaboration of the theory of Higgs in 1964 based on a proposal from Philip W. Anderson from 1962, from solid state physics, ie of a non - relativistic environment. A similar mechanism has been developed by Ernst Stückelberg 1957.

Such a mechanism for the mathematically simpler abelian gauge symmetries, as in the case of the electromagnetic interaction, was originally proposed in solid state physics. The issued in 1950, Ginsburg - Landau theory fully describes how forced out by the Meissner effect, the magnetic fields of superconducting metals. As a phenomenological theory with far-reaching consequences not trivial, it is particularly suitable for translation into the high-energy physics.

The mentioned effect is the finite - and very small - penetration depth of the magnetic field in the superconductor. This phenomenon can be interpreted as if the magnetic field - in mathematical terms: a gauge field - get through the superconductivity instead of the ground zero a finite effective mass, according to the relation

Where is Planck's constant and c h denotes the speed of light. In normal line, however, is or.

The Ginzburg - Landau theory said in contrast to the microscopic BCS theory in 1957 not subject to the existence of Cooper pairs. Analogous to the experimental proof of the existence of the Higgs mechanism is expected to result in no microscopic explanation for the nature of the Higgs boson. Subsequently itself could be the Higgs boson, similar to the Cooper pairs of superconductivity, may prove " composed ", about two W bosons weakly bound to each other. In this case, the Higgs boson would have a mass of about 80 GeV twice, so have 160 GeV. Early 2010 could be excluded, the value range 150-160 GeV, so that only one mass 115-150 GeV was still under discussion. With the publication of the results of CERN on July 4, 2012 ( with a particle of mass 125 GeV ) seems to confirm this result, which is not excluded that it is a composite in a more complicated way particles.

Development of the standard model

The Higgs mechanism was originally formulated only for abelian gauge theories. After he was transferred in 1967 by TWB Kibble on non-Abelian gauge theories (Yang -Mills theories ), the mechanism could be applied to the weak interaction. This led to the prediction of the - experimentally confirmed in 1983 - the great mass of the responsible for the weak interaction Z0, W and W -.

1968 turned Abdus Salam to the Higgs mechanism to the electroweak theory of Sheldon Lee Glashow and Steven Weinberg, and thus created the Standard Model of particle physics, for which all three were awarded the 1979 Nobel Prize in Physics.

In the prediction of the Higgs boson, the phenomenon of spontaneous symmetry breaking of the Higgs field plays a role. In addition to physicists already mentioned this also Yoichiro Nambu in 1960 (Nobel Prize 2008) and Jeffrey Goldstone in 1961, have made ​​important contributions.

Description in field theory

After elementary particle physics all the forces are described by the exchange of so-called gauge bosons. These include, for example, the photons of quantum electrodynamics and the gluons of quantum chromodynamics. The photon and the gluons are massless. The exchange particles of the weak interaction, the W and Z bosons, have, however, compared to the electrons, protons and neutrons great masses of about 80 GeV / c ² and 91 GeV / c ². These help make sure that particles which decay according to the weak interaction, have relatively long lifetimes, so that radioactivity Although a widespread but relatively "weak " phenomenon is. Therefore, you have to insert into the equations of motion for these particles mass terms. Since the gauge fields with which the gauge bosons are described, but would then change in the gauge transformations so-called ( it involves local symmetries ), you can not. Because the properties of the fundamental forces are based precisely on the fact that the equations of motion do not change in gauge transformations; which is called " gauge invariance " of the equation of motion.

Without the Higgs mechanism ie mass terms would destroy the force of law for the gauge fields.

The Standard Model of elementary particle contains, inter alia, the electroweak interaction. In this coupled theory occur four gauge bosons, the photon, the Z boson and the two W bosons. Of these four gauge bosons get the latter three by the non-zero vacuum expectation value of the Higgs field their mass of 91 and 80 GeV/c2 and a longitudinal component. In contrast, the photon, which couples not to the Higgs field, massless and purely transverse remains.

Overall, the Higgs field, which generates the masses, a seemingly "surplus " contains complex variable that evaluates to the full longitudinal Higgs boson. The mass of the Higgs boson corresponds in the theory of superconductivity, the energy gap between the ground state and the excited states of the superconducting " condensate ".

Spontaneous symmetry breaking

It uses the difficult to be formulated principle of spontaneous symmetry breaking, on the one hand to obtain the power law and the other to give the gauge bosons mass. These leads are an additional Higgs field. This is massive and interacts in such a way with all the other fields and with themselves that this will also get the gauge boson mass. An example of such interactions is shown in the adjacent diagram.

The spontaneous symmetry breaking would have after the existence of massless Goldstone bosons Goldstonetheorem result. The Goldstonetheorem can, however, apply only to global symmetries.

The refractive local symmetries, however, is described by the Higgs mechanism, according to which at the W and Z gauge fields - be no Goldstone bosons - in the theory of superconductivity in the magnetic field. Instead, the Higgs field appears - in the theory of superconductivity, the " condensate " - as the longitudinal polarization degree of freedom with a non-zero vacuum expectation value ( see below). The gauge bosons - in superconductivity, the magnetic field - therefore are also massive. An analogy is the above mentioned finite penetration depth of the magnetic field into the superconductor, where the magnitude of the mass of the Higgs boson which should be about one and a half to be twice the mass of a Eichbosons.

In quantum electrodynamics ( QED), the "non- solid " and in which no Higgs field occurs, the relevant for the theory gauge boson, the photon, as a massless spin-1 particles only the two transverse polarization degrees of freedom. In contrast, the adjacent Feynman diagram in addition to the already mentioned magnitude of the masses involved suggests that the Higgs boson is longitudinally as it ( here the horizontal direction ) runs away in the direction of the limits established by the quark symmetry axis, and not transversely thereto.

Higgs potential ( with illustration )

The Lagrangian density of the Higgs field, with the ( directly visible ) self-interaction and the (only indirectly visible because contained only in the D operators ) coupling to gauge fields A, the partially massive by the interaction with the Higgs field interaction- are as follows:

Here and are positive real numbers and the so-called eichkovariante dissipation, which are the generators of the gauge group and the complex functions are the gauge fields.

At this Lagrangian density is not yet clear how the masses of the gauge fields come about. This requires a separate consideration of the potential of the Higgs field, helpful:

For a real field with only one component, the potential would describe a W-shaped parabolic fourth order. Since, however, is complex in all applications, one can imagine as a three-dimensional figure of rotation of this parabola whose shape with the bottom of a champagne bottle is comparable ( it is also called Mexican hat potentials ). When more than one complex component, you can make the shape of the potential only partly so simple descriptive as in the adjacent picture.

However, its most important feature is always the same: it has at least equivalent to a two-dimensional circle of such minima that are not at zero, but the deepest states of the bottle bottom. The minima of the potential are the lowest energy state for the field, because there has the lowest energy. It refers to the ground state as a " vacuum state". Thus, the Higgs field has many equivalent ground states, because the potential has many minima with the same energy. We therefore speak of a " degenerate ground state". The above-mentioned longitudinal degrees of freedom correspond to the ( not shown ) central axis of the champagne bottle potential and the Higgs boson, while the actual core of the Higgs mechanism relates to the transverse degrees of freedom, ie, essentially the " bottle bottom " corresponds.

The amount of the ground state is the so-called vacuum expectation value

The results by calculating the extreme points of the potential. One can now define the Higgs field so that as many components as you gauge fields, where one wants to give mass, starting from a zero point in the transverse direction does not leave the set of zeros. In a one-component complex field in which you can imagine the potential as a lower part of a champagne bottle, this component is thus an angular component, so that one comes out for each value in this component to a different place on the Minimakreises. These components, the transverse components, do not change the energy of the Higgs field; they correspond to global symmetries of the Goldstone modes and can be set in the case of gauge theories by selecting a calibration, so that the mass terms for the gauge bosons in the action function are obvious: the finite vacuum expectation value is calculated with the gauge field -terms of the covariant derivatives (ie with the kinetic energy, the first term of ) the mass terms for the gauge fields, namely contributions of the form, with

The remaining components, the so-called longitudinal components, change in contrast to the Goldstone modes of the Higgs field, the energy, ie correspond to massive excitations. They shall, at as Teilchenfelder, called Higgs bosons. The Higgs boson is not simply, as usual belonging to the Higgs field particles, but it is one of the newly defined "surplus" longitudinal components of the field. The Higgs mechanism - the actual associated with the Higgs field core of the Standard Model - the other hand, involves only the transverse field components.

Other effects

For other particles, such as quarks or other fermions, for the appearance of mass terms would not appear to interfere without coupling to the Eichteilchen the gauge invariance, these terms can be explained by the Higgs mechanism; mass terms arise - and by the Yukawa couplings of the fermions to the Higgs field with initially unknown coupling constants, which ( more precisely to the development of the Lagrangian to a ground state ) after the breaking of the gauge symmetry again - now explicitly gauge invariant. The Lagrangian for the interaction of a Fermionfeldes with the Higgs field ( and the gauge field ) is

Where the gauge field A is again only received, the Dirac matrices and the parameters of the Yukawa coupling with the Higgs field. Again, the mass production is done according to the same principle: the existence of a finite vacuum expectation value, whose training was described in the previous section, the reason for the presence of mass.

Relation to astrophysics

Since the Higgs field does not seem to massless light quanta ( " photons" ) couples and even " mass " produced, is close to a connection with the astrophysically interesting dark matter, because this matter is "visible" only through its gravity effect. In fact, Marco Taoso and staff from CERN have expected the end of 2009, that the Higgs field could indirectly be visible as a result of the annihilation of very heavy particles in the context of elementary reactions involving the dark matter.

Science and Interpretation ( "Alice, Bob and the party " )

As the everyday taken popular scientific illustration of the Higgs mechanism as a collective effect of the Higgs field is often found the emergence of a star, usually "Alice" called, at a party: Before "Alice" enters the hall, are the party guests evenly distributed in space. However, once it occurs, numerous guests run up to her, want autographs or small talk. As a result, "Alice" is in this crowd of party guests so much slower than it could actually, the interactions of the party guests with the star have so in view of the progress the same effect as additional body mass of the star. The effect of party guests on "Alice" is the same as would be obtained by a single, the female star itself fascinating male counterparts ( "Bob" ).

The party guests create in this illustration, the Higgs potential, "Alice" represents the Eichteilchen, gets the crowd. The Higgs field itself, together with " symmetry breaking ", is represented by the guests who bring closer to whisper about " Alice " and therefore hardly move as a group in the room. "Bob", which has the same effect as the whole of the party guests to " Alice", the Higgs boson represents. In "Bob" even the meeting of the party guests is attractive; that is in it "Alice", will be noted by him, but is basically secondary ( " it comes in the Lagrange density before "). He feels equally as " surplus " and is spaced accordingly, difficult to stimulate and even harder to find.

Another representation of the Higgs boson compares this with a rumor that shrinks also the party guests locally. Various other popular scientific interpretations are given in an online interview a noted television physicist.