Weak interaction

The weak interaction (also called weak nuclear force, sometimes also β - interaction) is one of the four fundamental forces of physics. However, in contrast to the known from the everyday interactions of gravitation and electromagnetism, it acts only at very small distances. They may, as with other forces for energy and momentum exchange, but particularly effective for decays or conversions of the participating particles, such as the beta decay of certain radioactive nuclei. Due to the weak interaction are no bound states can be formed, what makes them different from the other three interactions.

Decisive significance of the weak interaction through their role in the fusion of hydrogen into helium in the Sun ( proton-proton reaction), because only by doing it the conversion of protons into neutrons is possible. The result of four protons ( the hydrogen nuclei ) through several intermediate steps of the stable helium nucleus with two protons and two neutrons. From this process the sun gets its energy. Due to the low strength of the weak interaction, this process is so slow that the sun lit stable for many billions of years and it is expected to do so again as long.

  • 7.1 Electromagnetic interaction
  • 7.2 Weak interaction 7.2.1 Charged currents
  • 7.2.2 Neutral currents

Overview

The weak interaction can be in charged currents and currents differ uncharged. Charged currents interact between all ( left-handed ) quarks and ( left-handed ) leptons, and the ( right-handed ) quarks and ( right-handed ) anti - leptons. Uncharged currents act between the same particles that interact by charged currents, but also between all charged ( anti) quarks and (anti) leptons regardless of their chirality.

The electromagnetic is about 1011 times, the strong interaction of about 1013 times stronger than the weak interaction. As the strong and the electromagnetic interaction is described by the exchange of gauge bosons. These exchange particles of the weak interaction are the neutral Z boson and the two positively or negatively charged W bosons. Since these are massive, the weak force is of short range (less than an atomic nucleus radius).

The weak interaction is most easily observed in decays of quarks or leptons. In scattering experiments, however, this is more difficult to access, since it is superimposed on the charged leptons or hadrons by the strong and electromagnetic interactions. Particles which are uncharged leptons, ie the neutrinos, but in scattering experiments have very small cross sections, neither the strong nor the electromagnetic interaction subject ( no color charge and carry no electrical charge ).

The weak interaction violates parity conservation, as detected in the Wu experiment. It also violates the CP- conservation about the decay of the uncharged K0 mesons ( kaons ).

A quantum field theory describing the weak interaction with the electromagnetic interaction, the Glashow -Weinberg -Salam model. One speaks in this formulation by two aspects of the electroweak interaction, which are unified by the Higgs mechanism.

Exchange particles

The following table gives an overview of the properties of the exchange particles (mass and resonance width according to the Particle Data Group, lifetime on the energy-time uncertainty relation calculated).

Reach can be roughly estimated by assuming that the particles during their lifetime ( at rest system of the particle ) with 71% of the speed of light in the laboratory system move ( Lorentz factor). This results in a lifetime of 3:10 -25 s a range of about 0.09 femtometer - the smallest atomic nucleus, the proton, has a diameter of about one femtometer.

The mass ratio of W and Z bosons predicted by the electroweak theory with the Weinberg angle:

The experimentally determined mass ratio is about 0.882.

As a consequence of the vineyard mixture shows that the coupling strength of the Z bosons not with that of the W bosons is identical. The coupling strength of the W boson to a left-handed fermion is given by

The coupling strength of a fermion is to contrast

The charge of the fermion is in units of the elementary charge. denotes the weak isospin ( third component), for left-handed neutrinos applies, for example.

The coupling strengths are weak and electromagnetic interaction, which is the weak charge and the electric charge are related by:

Reactions, crossing symmetry, reaction probability

For the description of a weak process is usually used the spelling of a reaction equation as

The particles A and B are thus converted in the process to the particle C, and D. Once this process is possible, as all the others are also possible after Vertauschungsregel of cruising ( engl. crossing ) arise. A particle can thus be written to the other side of the reaction equation by its corresponding antiparticle there is noted:

In addition, the reverse processes are possible.

Whether these processes are actually observed in nature (ie, their probability, which can differ by many orders of magnitude ), depends not only on the strength of the weak interaction, but also inter alia energy, rest mass and momentum of the particles involved.

The known sets of conservation of energy, conservation of momentum and conservation of angular momentum, which are connected in space according to the theorem of Noether with the invariance with respect to spatial and temporal translation and rotations apply to each reaction.

Are the sums of the rest masses of the particles involved on the right side than on the left, so it is an endothermic reaction, which is only possible if the particle on the left carry enough kinetic energy. If on the left side only stand a particle, then the reaction is forbidden in this case, because there is always a reference system in which this particle is at rest (ie, that mass out of nowhere would have to be generated, which is not possible ).

Are the rest masses of the incoming particles larger than the rest masses of the particles produced, the reaction is exothermic, and the difference between the rest masses can be found as kinetic energy of the particles produced again.

Processes

A distinction is weak processes both on whether leptons and / or quarks are involved in them, as well as according to whether the process through an electrically charged or boson ( charged currents and charged currents: CC ) or the neutral boson ( neutral currents or. neutral currents NC ) was mediated. The terms weak processes are as follows:

All reactions involving neutrinos are involved, extend only through the weak interaction ( gravity neglected). Conversely, there are also weak reactions without the participation of neutrinos.

Similar to the photon and in contrast to the W bosons Z boson mediates an interaction between the particles, without the particle (or more precisely: flavor ) to change it. While the photon but gives only forces between electrically charged particles interact, the Z boson with the uncharged neutrinos. For neutral fermions processes involved remain unchanged (no change of mass or charge ). The Z0 boson affects all left-handed fermions and by the vineyard mixture on the right-hand portions of charged fermions. It's not like the W bosons maximum parity- violating, as it contains a portion of the B0- boson (see: Electroweak interaction).

Examples of neutral processes are: the scattering of two electrons to each other (but superimposed for low energies by the stronger electromagnetic interaction and only at high energies the interactions are comparable in strength ). The scattering of muon neutrinos on electrons ( no competing processes, the first experimental evidence of the neutral currents at CERN in 1973 ).

Leptonic process

An elementary charged leptonic decay process is a process of a lepton L in a lepton L ' with the participation of their respective neutrinos or antineutrinos ():

As an example, the decay of muons may serve:

As well as the associated scattering processes

Semileptonischer process

In an elementary charged semileptonic process next leptons and quarks or antiquarks ( ) are involved:

An example of a semileptonic process is the aforementioned β - decay of the neutron, in which converts a down quark of the neutron in an up- quark:

This is a neutron n = udd UUD to a proton p =:

A down - and an up quark are uninvolved. They are called "spectator quarks " (English spectator quarks ).

This process is mediated by a Boson, wherein the negatively charged down curd is converted to a positively charged up curd - the negative charge is " carried off 'by a boson. and therefore must be quarks, whose charge difference is even.

Other examples of semi-leptonic processes are:

Hadronic process

In an elementary charged hadronic (or nichtleptonischen ) process only quarks and antiquarks are involved:

The kaon decay is a good example of a hadronic process

Quark representation:

Hadron representation:

Where the particles involved are structured as follows: and and. In this process, the up- quark of the kaon is a bystander again. The positive charge of the Strange antiquarks is carried away by a boson. Through this exchange the quark changes its flavor to an anti -up quark.

Other examples of hadronic processes are two decay channels of the Λ - baryon:

Particle transformations

For charged currents of the weak interaction only particles of the same doublet can interconvert:

It involves only left-handed fermions. These have a weak isospin, with third component of the weak isospin for the upper particle and is the lower. The weak hypercharge, ie twice the difference of electric charge and third weak Isospinkomponente is constant within a doublet. It is for the Leptonendupletts and for Quarkdupletts.

Right-handed fermions do not couple to W bosons and therefore carry no weak isospin. Furthermore, it is found that neutrinos in nature only handed occur ( Goldhaber experiment). Thus, right-handed fermions are described as singlets. Since the charged currents couple only to the left-handed doublets, there occurs a maximum violation of parity in these processes. This has been experimentally investigated in the Wu experiment and explained by the VA theory.

In the curd, (t, b ' ), the doublet (u, d'), (C, s') eigenstates of the interaction, and not ( U, D), (C, S ), ( T, B ). The states of the coated particles in each case a linear combination of three states. The crossed- quark states are rotated with respect to the quark states:

This is the so-called CKM matrix. This is unitary and has four independent parameters. The specified matrix indicates the amounts of the elements whose square is proportional to the transition probability between the quarks.

The transitions within the same family quark (u, d ), ( c, s ), ( t, b ) take place most frequently, since the diagonal elements show the largest transition probabilities. It is less likely to change the way also the flavor. This behavior is caused by the mass eigenstates not correspond to the so-called interaction eigenstates.

The decay of quarks or leptons by neutral currents, eg the transitions c → u or d or s → μ → e have not been observed.

Neutrino oscillations

The neutrino eigenstates of the weak interaction, (flavor states are eigenstates of the weakly interacting part of the Hamiltonian ) are not identical to the eigenstates of the mass operator, ( eigenstates of the kinetic part of the Hamiltonian ). In analogy to the CKM matrix can introduce the so-called Pontecorvo - Maki - Nakagawa- Sakata ( PMNS ) matrix here

Current values ​​are:

The matrix has large values ​​outside the diagonal. This differs from the CKM matrix and results in a strong mixing of the neutrino families with time.

If a neutrino originally created with a specific of these three flavors, then a subsequent quantum measurement a different flavor arise ( conservation of Leptonenfamilienzahlen is injured). Since the probabilities for each flavor change periodically with the propagation of neutrinos, one speaks of neutrino oscillations.

The decay of a ( left-handed ) lepton by the weak interaction changes during the interaction is not the flavor ( conservation of Leptonenfamilienzahl in each interaction vertex ), but in the further time evolution, resulting neutrinos can transform into each other, thus changing the flavor and thus violate the Leptonenfamilienzahl - preservation. The lepton number is, however, always obtained in this oscillation.

Had the neutrinos no mass, then each Flavor state would also be an eigenstate of the mass operator. Consequently, you might observe no flavor oscillations.

Lagrangian density

In the following the interaction between fermions and gauge bosons shares are analyzed for the Lagrangian density of the weak interaction.

In order to assess the description of the weak interaction better, the electromagnetic interaction is described first. All of the following provided with Greek indices sizes represent four-vectors

Electromagnetic interaction

In quantum electrodynamics, the interaction energy is the coupling of ( four ) streams of charged particles to photons, represented by the electromagnetic ( four ) potential, given by:

The coupling constant is the elementary charge. The current density is given by

Wherein the charge quantum number (the electric charge of the particles in terms of the elementary charge ), the Dirac matrices. is the field of the incoming fermion (or expiring Antifermions ) with ( four ) pulse and that of the outgoing fermion (or the incoming Antifermions ) with pulse. In a Feynman diagram describing the spinors and the outer solid lines.

The scattering of two charged particles is described in the Born approximation (lowest order perturbation theory ) by the adjacent Feynman diagram. The corresponding scattering amplitude is

At each vertex of a charge factor must be multiplied. Applies at the vertex because of the energy-momentum conservation for the four-vector of the photon.

Interior lines of the Feynman diagram are the so-called propagators, here the photon propagator, where the ( four - ) momentum transfer and the metric tensor of special relativity is.

Weak interaction

In the weak interaction describe ( neutral current ) and (charged current) the summands of the Lagrangian density containing the interaction between fermions and gauge bosons to.

Charged currents

The weak charged currents are described by the following interaction contribution:

The bosons couple with the same coupling constant to all the left-handed leptons and quarks.

In the description of the individual currents in each of the Chiralitätsoperator occurs ( this transforms a polar in an axial vector). For massive particles this Teilchenspinoren positive helicity transforms into Antiteilchenspinoren negative helicity and vice versa ( ). From this, construct the Linkshändigkeitsoperator:

This operator applied to a spinor, projected on the left-hand portion:

Because of the occurrence of this operator, the weak interaction is a chiral theory. The left-handed current

Is the (half ) difference from vector current and axial current, so V minus A (see: VA- theory).

Weak left-handed charged quark currents with, ,, is the CKM mixing matrix:

Weak left-handed charged with Leptonenströme, :

To a vertex of the following factor must be multiplied:

The propagator for massive ( mass) of spin-1 particles, as are the W and Z bosons is:

As is true for most cases, the Propatator can be approached. In contrast to the photon propagator of the propagator for small momentum transfers is constant.

For small values ​​of the weak interaction is much weaker than the electromagnetic. This is not due to the coupling constant of the weak interaction, since the fragile payload is in the same magnitude as the electrical charge. The reason for the weakness of the interaction is in the form of the propagator of the exchange particle, since the huge Bosonenmasse in the denominator and thus reduces the interaction term.

Mediated by a W boson scattering of two leptons, has a scattering amplitude ( in lowest order ) by:

In the approximate form

The scattering amplitude is described by the coupling of two left-handed currents by means of a coupling constant. This has been described by Enrico Fermi by the Fermi - interaction, as an interaction of four participating particles to a space-time point. The Fermi constant has the value.

Neutral currents

The weak neutral currents are described by the following interaction contribution:

The bosons couple with the coupling constant of neutral currents, which are composed of isospin currents and electromagnetic currents.

Considered separately, this means that the bosons couple with the coupling constant of isospin currents ( is the weak isospin of the fermions: 1/2 for and, -1 / 2 for and, and 0 for all right-handed particles ), so all left-handed fermions

And with the coupling constant of electromagnetic currents (the electric charge of fermions )

Thus couple charged fermions ( and, but not ) regardless of their handedness to Z bosons.

The dispersion of two charged fermions can thus not only electromagnetic interaction so photon exchange, but also by a neutral weak interaction, that is Z- exchange take place. For low particle energies former process, however, is much more likely.

To a vertex always the factor and in addition, depending on the type of particle involved several factors must be multiplied:

  • Neutrinos:
  • Charged leptons:
  • Quarks with 2/3 charge
  • Quarks with -1 / 3 charge

In the latter three occur summands on without the Linkshändigkeits operator. This Z- couplings thus have a beneficial effect on left - right-handed fermions and on.

Combination of electromagnetic and neutral currents

In the electroweak theory can be combined electromagnetic and weak neutral currents. Instead electromagnetic currents of photons and weak neutral currents at Z bosons

Now couple to the isospin currents and hyper -charge currents to bosons:

Where a hypercharge current was introduced based on the hypercharge of the fermion:

The relation of the bosons is given over and and the relation of the coupling constants over.

History of Research

The Z- boson and thus the weak process was demonstrated in 1973 with the Gargamelle experiment at CERN for the first time. Significant contributions to the study were made by Henry Primakoff in the course of his work for later named after him Primakoff effect.

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