Electroweak interaction

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In particle physics, the electroweak interaction is the unified description of two of the four fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 102 GeV, they would merge into a single electroweak force. Thus if it is hot enough (approximately 1015 K, a temperature reached early in the Big Bang) then the electromagnetic force and weak force will merge into a combined electroweak force.

For contributions to the unification of the weak and electromagnetic interaction between elementary particles Abdus Salam, Sheldon Glashow and Steven Weinberg were awarded the Nobel Prize in Physics in 1979.[1] The existence of the electroweak interactions was experimentally established in two stages: the first being the discovery of neutral currents in neutrino scattering by the Gargamelle collaboration in 1973, and the second in 1983 by the UA1 and the UA2 collaborations that involved the discovery of the W and Z gauge bosons in proton-antiproton collisions at the converted Super Proton Synchrotron.

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[edit] Formulation

Mathematically, the unification is accomplished under an SU(2) × U(1) gauge group. The corresponding gauge bosons are the photon of electromagnetism and the W and Z bosons of the weak force. In the Standard Model, the weak gauge bosons get their mass from the spontaneous symmetry breaking of the electroweak symmetry from SU(2) × U(1)Y to U(1)em, caused by the Higgs mechanism (see also Higgs boson). The subscripts are used to indicate that these are different copies of U(1); the generator of U(1)em is given by Q = Y/2 + I3, where Y is the generator of U(1)Y (called the weak hypercharge), and I3 is one of the SU(2) generators (a component of weak isospin). The distinction between electromagnetism and the weak force arises because there is a (nontrivial) linear combination of Y and I3 that vanishes for the Higgs boson (it is an eigenstate of both Y and I3, so the coefficients may be taken as −I3 and Y): U(1)em is defined to be the group generated by this linear combination, and is unbroken because it doesn't interact with the Higgs.

[edit] Lagrangian

[edit] Before Electroweak Symmetry Breaking

The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking

\mathcal{L}_{E-W} = \mathcal{L}_g + \mathcal{L}_f + \mathcal{L}_H + \mathcal{L}_y

The g term describes the interaction between the three W particles and the B particle.

\mathcal{L}_g = -\frac{1}{4g^2}W_a^{\mu\nu}W_{\mu\nu}^a - \frac{1}{4g'{}^2}B^{\mu\nu}B_{\mu\nu}

The f term gives the kinetic term for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the covariant derivative.

\mathcal{L}_f = \overline{q}_i iD\!\!\!\!/\; q_i+ \overline{u}_i^c iD\!\!\!\!/\; u^c_i+ \overline{d}_i^c iD\!\!\!\!/\; d^c_i+ \overline{l}_i iD\!\!\!\!/\; l_i+ \overline{e}^c_i iD\!\!\!\!/\; e^c_i

The H term describes the Higgs field F.

\mathcal{L}_H = |D_\mu h|^2 + \frac{1}{4} \lambda (|h|^2 - v^2)^2

The y term gives the Yukawa interaction that generates after the Higgs acquires a vacuum expectation value.

\mathcal{L}_y = y_{u\, ij} \,h\, q_i u_j^c + y_{d\, ij}\, h^\dagger\, q_i d^c_j + y_{e\,ij} \,h^\dagger\, l_i e^c_j

[edit] After Electroweak Symmetry Breaking

The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value.

[edit] See also

[edit] References

  1. ^ Sander Bais (2005), The Equations. Icons of knowledge ISBN 0-674-01967-9 p 84

[edit] Textbooks

  • Gordon L. Kane (1987). Modern Elementary Particle Physics. Perseus Books. ISBN 0-201-11749-5. 

[edit] Journal Articles

  • S.F. Novaes, Standard Model: An Introduction, hep-ph/0001283
  • D.P. Roy, Basic Constituents of Matter and their Interactions — A Progress Report, hep-ph/9912523
  • Y. Hayato et al., Search for Proton Decay through p → νK+ in a Large Water Cherenkov Detector. Phys. Rev. Lett. 83, 1529 (1999).
  • Ernest S. Abers and Benjamin W. Lee, Gauge theories. Physics Reports (Elsevier) C9, 1-141 (1973).
  • J. Hucks, Global structure of the standard model, anomalies, and charge quantization, Phys. Rev. D 43, 2709–2717 (1991). [1]
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