# User Contributed Dictionary

### Adjective

- Describing the combination of the electromagnetic and weak nuclear forces

# Extensive Definition

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 the universe is hot enough
(approximately 1015 K, a temperature
reached shortly after 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. 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.

## 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.## Lagrangian

### Before Electroweak Symmetry Breaking

The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking- \mathcal_ = \mathcal_g + \mathcal_f + \mathcal_h + \mathcal_y

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

- \mathcal_g = -\fracW_a^W_^a - \fracB^B_

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_f = \overline_i iD\!\!\!\!/\; Q_i+ \overline_i^c iD\!\!\!\!/\; u^c_i+ \overline_i^c iD\!\!\!\!/\; d^c_i+ \overline_i iD\!\!\!\!/\; L_i+ \overline^c_i iD\!\!\!\!/\; e^c_i

The h term describes the Higgs field F.

- \mathcal_h = |D_\mu h|^2 - \lambda \left(|h|^2 - \frac\right)^2

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

- \mathcal_y = - y_ \epsilon^ \,h_b^\dagger\, \overline_ u_j^c - y_\, h\, \overline_i d^c_j - y_ \,h\, \overline_i e^c_j + h.c.

### After Electroweak Symmetry Breaking

The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value. Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.- \mathcal_ = \mathcal_K + \mathcal_N + \mathcal_C + \mathcal_H + \mathcal_ + \mathcal_ + \mathcal_ + \mathcal_Y

The kinetic term \mathcal_K contains all the
quadratic terms of the Lagrangian, which include the dynamic terms
(the partial derivatives) and the mass terms (conspicuosly absent
from the Lagrangian before symmetry breaking)

- \mathcal_K = \sum_f \overline(i\partial\!\!\!/\!\;-m_f)f-\frac14A_A^-\frac12W^+_W^+m_W^2W^+_\mu W^-\frac14Z_Z^+\frac12m_Z^2Z_\mu Z^\mu+\frac12(\partial^\mu H)(\partial_\mu H)-\frac12m_H^2H^2

where the sum runs over all the fermions of the
theory (quarks and leptons), and the fields A_^, Z_^, W^-_, and
W^+_\equiv(W^-_)^\dagger are given as

- X_=\partial_\mu X_\nu - \partial_\nu X_\mu + g f^X^_X^_, (replace X by the relevant field, and f^(abc) with the structure constants for the gauge group).

The neutral current \mathcal_N and charged
current \mathcal_C components of the Lagrangian contain the
interactions between the fermions and gauge bosons.

- \mathcal_ = e J_\mu^ A^\mu + \frac g(J_\mu^3-\sin^2\theta_WJ_\mu^)Z^\mu,

where the electromagnetic current J_\mu^ and the
neutral weak current J_\mu^3 are

- J_\mu^ = \sum_f q_f\overline\gamma_\mu f,

and

- J_\mu^3 = \sum_f I^3_f\overline\gamma_\mu f

q_f^ and I_f^3 are the fermions electric charges
and weak isospin.

The charged current part of the Lagrangian is
given by

- \mathcal_C=-\frac g\left[\overline u_i\gamma^\mu\frac2M^_d_j+\overline\nu_i\gamma^\mu\frac2e_i\right]W_\mu^++h.c.

\mathcal_H contains the Higgs three-point and
four-point self interaction terms.

\mathcal_H=-\fracH^3-\fracH^4

\mathcal_ contains the Higgs interactions with
gauge vector bosons.

\mathcal_=\left(gm_WH+\frac4H^2\right)\left(W_\mu^+W^+\frac1Z_\mu
Z^\mu\right)

\mathcal_ contains the gauge three-point self
interactions.

\mathcal_=-ig[(W_^+W^-W^W_^-)(A^\nu\sin\theta_W-Z^\nu\cos\theta_W)+W_\nu^-W_\mu^+(A^\sin\theta_W-Z^\cos\theta_W)]

\mathcal_ contains the gauge four-point self
interactions

\mathcal_ = -\frac4 \left\

and \mathcal_Y contains the Yukawa interactions
between the fermions and the Higgs field.

\mathcal_Y = -\sum_f \frac\overline ffH

## References

### Textbooks

- Introduction to Elementary Particles

- Gauge Theory of Weak Interactions

- Modern Elementary Particle Physics

### 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). http://prola.aps.org/abstract/PRD/v43/i8/p2709_1

electroweak in Catalan: Interacció
electrodèbil

electroweak in Danish: Elektrosvag kraft

electroweak in German: Elektroschwache
Wechselwirkung

electroweak in Spanish: Modelo
electrodébil

electroweak in French: Interaction
électrofaible

electroweak in Korean: 약전자기력

electroweak in Italian: Interazione
elettrodebole

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electroweak in Hungarian: Elektrogyenge
kölcsönhatás

electroweak in Dutch: Elektro-zwakke
interactie

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electroweak in Polish: Teoria oddziaływań
elektrosłabych

electroweak in Portuguese: Força
eletrofraca

electroweak in Russian: Электрослабое
взаимодействие

electroweak in Slovenian: Elektrošibka
interakcija

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vuorovaikutus

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växelverkan

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kuvvet