# Electroweak interaction

Beta decay in the electroweak interaction

The electroweak interaction forms the basis of a unified theory of quantum electrodynamics and weak interaction within the framework of the Standard Model . It was introduced in the 1960s by physicists Sheldon Glashow , Steven Weinberg and Abdus Salam to summarize the electromagnetic and weak interaction in one theory. They received the 1979 Nobel Prize in Physics for this , after the theory had been experimentally confirmed in the 1970s.

While in quantum electrodynamics the interaction is described by the exchange of a massless photon and is the quantum field theoretical version of classical electrodynamics , the unified theory explains the short range of the weak interaction , which acts, for example, in neutrino physics and during beta decay, with the fact that here much heavier particles are exchanged: the charged W boson and the neutral Z boson with masses in the order of magnitude of gigas - electron volts (GeV). The electroweak theory is also an example of a gauge field theory with a gauge group that corresponds to the product , where stands for the two-dimensional special unitary group and for the one-dimensional unitary group . The two-dimensional matrix character is an expression of the fact that the proportion of the weak interaction in the electroweak interaction converts various elementary particles into one another. In contrast, only corresponds to a phase factor (multiplication by a complex number) in front of the wave function. The easiest way to visualize the effect of the electroweak interaction is through Feynman diagrams . For example, when the neutron beta decays, a proton, an electron and an antineutrino are generated, which can be described by the exchange of a negatively charged W boson, which converts a d quark into a u quark in the nucleon and at the other the leptons an antineutrino into an electron (see figure on the right). ${\ displaystyle 10 ^ {2}}$ ${\ displaystyle SU (2) \ times U (1)}$${\ displaystyle SU (2)}$${\ displaystyle U (1)}$${\ displaystyle U (1)}$

## Physics of the weak and electroweak interaction

For the physical description it is necessary to combine the leptons or quarks of a generation (or family) to a doublet for left-chiral particles and to singlets for right-chiral particles . The electroweak interaction acts on the following particle doublets and singlets from fermions :

Doublets ( weak isospin T = ½)
Leptons Electric
charge

Q
Weak
hypercharge

Y w
3rd component of the
weak isospin
T z
${\ displaystyle {\ nu _ {e} \ choose e} _ {L}}$ ${\ displaystyle {\ nu _ {\ mu} \ choose \ mu} _ {L}}$ ${\ displaystyle {\ nu _ {\ tau} \ choose \ tau} _ {L}}$ ${\ displaystyle {0} \ choose {-1}}$ ${\ displaystyle {-1} \ choose {-1}}$ ${\ displaystyle {+1/2} \ choose {-1/2}}$
Quarks
${\ displaystyle {u \ choose d '} _ {L}}$ ${\ displaystyle {c \ choose s'} _ {L}}$ ${\ displaystyle {t \ choose b '} _ {L}}$ ${\ displaystyle {2/3} \ choose {-1/3}}$ ${\ displaystyle {1/3} \ choose {1/3}}$ ${\ displaystyle {+1/2} \ choose {-1/2}}$

The up-like fermions are each listed above. Their electrical charge is 1 greater than that of the corresponding down-like particles listed below.

Singlets (weak isospin T = 0)
1 2 3 Electric
charge

Q
weak
hypercharge
Y w
${\ displaystyle e_ {R} ^ {-}}$ ${\ displaystyle \ mu _ {R} ^ {-}}$ ${\ displaystyle \ tau _ {R} ^ {-}}$ ${\ displaystyle -1}$ ${\ displaystyle -2}$
${\ displaystyle u_ {R}}$ ${\ displaystyle c_ {R}}$ ${\ displaystyle t_ {R}}$ ${\ displaystyle + {\ frac {2} {3}}}$ ${\ displaystyle + {\ frac {4} {3}}}$
${\ displaystyle d_ {R}}$ ${\ displaystyle s_ {R}}$ ${\ displaystyle b_ {R}}$ ${\ displaystyle - {\ frac {1} {3}}}$ ${\ displaystyle - {\ frac {2} {3}}}$

The electrical charge is understood in units of the elementary charge e. The dash at d, s and b quarks indicates that these are the states of weak interaction and not the observable mass eigenstates. This difference leads to the CKM mixing of quarks.

The electroweak interaction also acts on the associated antiparticles and systems composed of these particles. In addition to the electric charge Q , the above enumerated particles carry a charge faint Hyper Y W . The electric charge associated with this and the third component of the weak isospin in context , the following applies: . ${\ displaystyle Q = Y_ {W} / 2 + T_ {z}}$

## Calibration bosons

As with all quantum field theoretical gauge theories , the interactions in the electroweak theory are mediated by gauge bosons . In the electroweak theory, four massless gauge bosons appear mathematically:

• a B 0 boson (weak isospin singlet with coupling strength g 'to the weak hypercharge ),${\ displaystyle T = T_ {z} = 0}$${\ displaystyle Y_ {w}}$
• three W bosons W 0 , W 1 , W 2 (weak isospin triplet and with coupling strength g an ).${\ displaystyle T = 1}$${\ displaystyle T_ {z} = 0, \ pm 1}$${\ displaystyle T_ {z}}$

After a spontaneous symmetry break , there is a mass matrix for the four bosons that is not diagonal. A diagonalization to the mass eigenstates ultimately leads to three massive gauge bosons and one massless one:

• the photon , massless, not electrically charged${\ displaystyle \ gamma}$
• the Z 0 boson, mass 91.1879 (21) GeV, not electrically charged
• two W bosons W ± , mass 80.385 (15) GeV, electrical charge ± 1.

The linear combinations with which these bosons are described are:

${\ displaystyle \ vert \ gamma \ rangle = \ cos \ theta _ {\ mathrm {W}} \ vert B ^ {0} \ rangle + \ sin \ theta _ {\ mathrm {W}} \ vert W ^ {0 } \ rangle}$
${\ displaystyle \ vert Z ^ {0} \ rangle = - \ sin \ theta _ {\ mathrm {W}} \ vert B ^ {0} \ rangle + \ cos \ theta _ {\ mathrm {W}} \ vert W ^ {0} \ rangle}$
${\ displaystyle \ vert W ^ {\ pm} \ rangle = {\ frac {1} {\ sqrt {2}}} \ left (\ vert W ^ {1} \ rangle \ mp i \ vert W ^ {2} \ rangle \ right)}$

Unlike the W ± bosons, the Z 0 boson does not violate parity as much as possible, since it contains a portion of the calculated B 0 boson. It is said that the states of the photon and the Z 0 boson are rotated around the Weinberg angle . ${\ displaystyle \ theta _ {\ mathrm {W}}}$

The photon behaves as described in the context of the QED .

## Z and W bosons

The uncharged calibration boson Z 0 acts on all of the left-handed parts listed in the table above and, due to the Weinberg mixture, to a certain extent also on the right-handed parts . Since the Z boson has no electrical charge, these processes are also referred to as neutral currents (English neutral currents , NC), see Figure 1. In both processes, parity is sometimes violated .

In contrast to the Z boson, the W ± bosons carry an electrical charge. The associated Teilchenprozesse refers therefore also to as "charged current" (English charged currents , CC), see Figure 2. Since these two charged streams couple only to the left-handed doublets, occurs in two operations, a maximum violation of the parity.

### CKM mixture in quarks

In the case of quarks, the CKM mixture (named after Nicola Cabibbo , Makoto Kobayashi and Toshihide Maskawa ) must also be observed in connection with the two W bosons . For example, a u-quark can be converted by a W - not just to a d-quark. There is also less chance of getting an s-quark or b-quark. The W bosons can also change the flavor . This behavior is caused by the fact that the mass eigenstates do not match the interaction eigenstates.

### Naming

The W bosons are named after the weak force (English: w eak force) (an alternative designation was and is an intermediate vector boson), the Z boson after its electrical neutrality (English: z ero charge).
The abbreviations W and Z can be found in the original work by Weinberg from 1967, Salam used in his original work published in 1968 for the charged vector bosons and X for the Z boson (a mixture of the and components), Glashow used in his work from 1961 for all four exchange particles have the abbreviation Z. ${\ displaystyle W _ {\ pm}}$${\ displaystyle W_ {0}}$${\ displaystyle W_ {3}}$

The term weakons is not only found in popular scientific media, although not very often, mostly for the two W bosons and the Z boson, more rarely only for the W bosons. Apart from the different usage, the term is problematic because it does not denote a complete, self-contained group - the photon is missing. The term does not appear in official publications such as CERN or the Particle Data Group (as of 2009).

## Interaction and mass

In quantum field theory, gauge bosons with mass can only be described with the help of a scalar field , which gives mass to the gauge bosons involved. In the electroweak theory, this field is the Higgs field (named after Peter Higgs ). It is assumed that the scalar Higgs field had only a minimum in the early universe .

The continuous cooling resulted in a spontaneous break in symmetry and the Higgs field fell into a new minimum. The gauge bosons of the electroweak interaction receive finite masses due to the coupling to the Higgs field. On July 4, 2012, CERN announced the discovery of a boson with a mass of about 125 GeV / c², which is very likely the Higgs particle.

## Extensions

Attempts are made to combine the electroweak interaction with other interactions. The obvious solution is to add the strong interaction ( QCD ) to a GOOD . Extensions of the calibration groups z. B. Right-handed have been suggested. Depending on the exact model, these extensions predict Z- and / or W-like bosons, after which u. a. at the Large Hadron Collider . So far, such Z 'or W' bosons have not been observed. ${\ displaystyle SU (2) _ {R}}$

## Nobel Prizes

The quantization of the electromagnetic radiation is ultimately to the explanation of blackbody radiation by Max Planck in 1900 back ( Planck's law ). Albert Einstein received the Nobel Prize in Physics in 1921 for the interpretation of the photoelectric effect in the form of the light quantum hypothesis in 1905 . These light quanta were later found as photons in quantum physics. The photon is the best known exchange boson of the electroweak interaction.

In 1957, in the Wu experiment named after her (carried out at the National Bureau of Standards ) , Chien-Shiung Wu succeeded in demonstrating parity violations in weak interactions and thus providing empirical evidence for the hypothesis of Tsung-Dao Lee and Chen Ning Yang . In 1956 they published the theory that in elementary particle physics an exchange of right and left can make a difference, i.e. H. In the case of a spatial mirroring, the original and the mirror image do not always have to be indistinguishable (parity violation).

When Lee and Yang received the Nobel Prize in Physics that same year , many experts believed that Chien-Shiung Wu had wrongly received nothing. The reason was seen in the traditional disregard for experimental versus theoretical physics.

The unification of the electromagnetic with the weak interaction was first described theoretically by Sheldon Glashow , Abdus Salam and Steven Weinberg in 1967 ( GWS theory ), experimentally the theory was indirectly established in 1973 through the discovery of the neutral currents and in 1983 directly through the detection of the W ± and Z 0 - calibration bosons (exchange bosons) confirmed. A special feature is the violation of parity due to the electroweak interaction . For their theory, the above-mentioned received the 1979 Nobel Prize in Physics .

As spokesman for the international research team at the UA1 detector and the particle accelerator SPS at CERN , Carlo Rubbia and, as chief developer of stochastic cooling, Simon van der Meer received the Nobel Prize in Physics in 1984 , “for their significant contributions to the major project that led to the discovery of the Field particle W and Z , mediators of weak interaction , has led ”.

In 2013, François Englert and Peter Higgs received the Nobel Prize in Physics for their significant participation in the development of a theoretical description of the mass generation in gauge theories . The theory was confirmed by the discovery of the associated field quantum, the Higgs boson , at the Large Hadron Collider .

## Classification of the electroweak interaction

 Fundamental interactions and their descriptions Strong interaction Electromagnetic interaction Weak interaction Gravity classic Electrostatics & magnetostatics , electrodynamics Newton's law of gravitation , general relativity quantum theory Quantum ( standard model ) Quantum electrodynamics Fermi theory Quantum gravity  ? Electroweak Interaction ( Standard Model ) Big Unified Theory  ? World formula ("theory of everything")? Theories at an early stage of development are grayed out.

## Individual evidence

1. Sheldon Glashow, Partial-Symmetries of Weak Interactions , Nuclear Physics B, Volume 22, 1961, p. 579
2. Steven Weinberg, A model of leptons , Phys. Rev. Lett., Vol. 19, 1967, pp. 1264-1266
3. Salam gives as the last step on the electroweak theory (simultaneously with Weinberg) his contribution Weak and Electromagnetic Interaction to N. Svartholm (ed.), Elementary Particle Theory, Proc. 8th Nobel Symposium, Almqvist and Wiksell, Stockholm 1968. See Salam, Gauge unification of fundamental forces, Reviews of Modern Physics, Volume 52, 1980, p. 529
4. Walter Greiner , Berndt Müller : Calibration theory of weak interaction . 2nd edition, Harri Deutsch, 1995, p. 184, ISBN 3-8171-1427-3
5. a b c K.A. Olive et al. (PDG): 'Review of Particle Physics'. Chin.Phys. C, 38, 2014.
6. Chris Quigg , Elementary particles and forces , Scientific American, April 1985, p. 91
7. Wolfgang Bauer, Gary Westfall, Walter Benenson: Fundamentalkrätze , in: Universität Frankfurt, cliXX Physik, Chapter 28: Nuclear Physics and Elementary Particles; harri german electronic science (hades)
8. Christoph Heimann: Introduction of elementary particles and their fundamental interactions within the framework of nuclear physics lessons in the 10th grade of a grammar school , written term paper according to §58 OVP for the teaching post for the secondary level I + II in the subject physics, Cologne in August 2002, p. 9 ; as well as elementary particles - the building blocks of nature - particle physics. Appendices , p. XII; on: teilchenphysik.de German Electron Synchrotron DESY, 2016
9. Paul Hemetsberger: Weakonen , dict.cc German-English dictionary, 2002–2018
10. Andreas Müller: Weakonen , Lexikon der Astronomie, 2007-2014; Astro-Lexikon , p. 6; on: Spektrum.de
11. Erich Übelacker, Arno Kolb: Modern Physics . WHAT IS WHAT, band 79 . Tessloff Verlag, 2018, ISBN 978-3-7886-0419-6 , pp. 48 . Here: Page 33 in Google Book Search, Page 48 .
12. Frank Wilczek : A Beautiful Question: Finding Nature's Deep Design . Penguin, 2015, ISBN 978-0-698-19562-2 , pp. 400 ( limited preview in Google Book Search).
13. Excursus: Of Quarks and Higgs Bosons - The Standard Model in the 'Nutshell' , on: scinexx.de Dossier of April 13, 2007
14. CERN experiments observe particle consistent with long-sought Higgs boson . Press release from CERN. July 4, 2012. Retrieved July 6, 2012.
15. G. Senjanovic and RN Mohapatra, Phys. Rev. D 12, 1502
16. ^ Nobel Prize in Physics 2013 . The Nobel Foundation. Retrieved August 23, 2016.