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
