English

Adjective

1. Describing the combination of the electromagnetic and weak nuclear forces

Translations

• Italian: elettrodebole

Related terms

• electrostrong

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

See also

• Fundamental forces
• Formulation of the standard model

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