Weinberg–Salam Model
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Weinberg–Salam Model

Electroweak Unification of Fundamental Forces

Introduction

The Weinberg–Salam model is a unified theory proposed independently by Sheldon Glashow, Abdus Salam, and Steven Weinberg. It unifies the electromagnetic and weak nuclear interactions into a single framework known as the Electroweak Theory. At very high energies, electromagnetic and weak forces behave as a single force, called the electroweak force.

Why Electroweak Unification?

  • Both forces act on leptons and quarks
  • Both are mediated by spin-1 gauge bosons
  • Weak interaction violates parity, electromagnetism does not
  • A unified description explains these differences naturally

Gauge Symmetry of the Model

The model is a non-Abelian gauge theory based on:

\( SU(2)_L \times U(1)_Y \)
  • \(SU(2)_L\): Weak isospin symmetry (acts on left-handed particles)
  • \(U(1)_Y\): Weak hypercharge symmetry

Gauge Bosons

Field Symbol Associated Force
Weak isospin fields \(W^1, W^2, W^3\) Weak interaction
Hypercharge field \(B\) Electroweak

After symmetry breaking, these combine to form physical particles.

Electroweak Symmetry Breaking

Initially all gauge bosons are massless. Mass generation occurs through the Higgs mechanism.

Higgs Field

  • A complex scalar doublet
  • Acquires a non-zero vacuum expectation value (VEV)
  • Spontaneously breaks \(SU(2)_L \times U(1)_Y\)
Gauge invariance is preserved while weak bosons acquire mass.

Physical Gauge Bosons

Particle Symbol Mass Interaction
Photon \(\gamma\) 0 Electromagnetic
W bosons \(W^\pm\) Heavy Weak (charged)
Z boson \(Z^0\) Heavy Weak (neutral)

Weinberg Angle (Weak Mixing Angle)

The mixing between \(W^3\) and \(B\) fields is described by the Weinberg angle \( \theta_W \).

\[ \begin{aligned} A_\mu &= B_\mu \cos\theta_W + W^3_\mu \sin\theta_W \\ Z_\mu &= -B_\mu \sin\theta_W + W^3_\mu \cos\theta_W \end{aligned} \]
  • \(A_\mu\): Photon field
  • \(Z_\mu\): Z boson field

Electric Charge Relation

Electric charge is related to weak isospin and hypercharge:

\( Q = T_3 + \dfrac{Y}{2} \)

This explains charge quantization in the Standard Model.

Successes of the Model

  • Predicted existence of \(W^\pm\) and \(Z^0\)
  • Correctly predicted their masses
  • Explains weak neutral currents
  • Forms electroweak part of Standard Model

Limitations

  • Does not include gravity
  • Does not explain fermion mass hierarchy
  • Parameters like \( \theta_W \) are experimentally determined

Summary

✔ Unifies electromagnetic and weak forces ✔ Based on \(SU(2)_L \times U(1)_Y\) symmetry ✔ Uses Higgs mechanism for mass generation ✔ Predicts W, Z bosons ✔ Cornerstone of the Standard Model

MCQs on Weinberg–Salam Electroweak Model

The Weinberg–Salam model unifies:




The gauge group of the electroweak theory is:




The electroweak mixing angle is called:




The photon (γ) arises from mixing of:




The weak charged current is mediated by:




The neutral weak current is mediated by:




The Higgs mechanism is responsible for:




After symmetry breaking, the photon is:




The W boson carries electric charge:




The Z⁰ boson is:




The electroweak symmetry is spontaneously broken by:




The Weinberg–Salam theory predicts existence of:




The discovery of W and Z bosons experimentally confirmed the model at:




The electromagnetic interaction after symmetry breaking is associated with:




The Weinberg–Salam model is part of: