Introduction
In modern particle physics, symmetry principles play a central role
in formulating fundamental interactions. However, nature often exhibits
situations where the underlying laws are symmetric but the observed state is not.
This phenomenon is known as Spontaneous Symmetry Breaking (SSB).
Spontaneous symmetry breaking explains how particles acquire mass
without destroying gauge symmetry.
What is Spontaneous Symmetry Breaking?
A system undergoes spontaneous symmetry breaking when:
- The laws (Lagrangian) are symmetric
- The ground state (vacuum) is not symmetric
Classical Analogy
A ball placed at the top of a symmetric hill rolls down in one direction,
choosing a particular minimum. Although the hill is symmetric,
the final state is not.
SSB in Quantum Field Theory
Consider a scalar field with potential:
\[
V(\phi) = \mu^2 \phi^2 + \lambda \phi^4 \quad (\lambda > 0)
\]
- If \( \mu^2 > 0 \): single minimum → symmetry preserved
- If \( \mu^2 < 0 \): degenerate minima → symmetry broken
The vacuum expectation value (VEV) becomes non-zero:
\( \langle \phi \rangle = v \neq 0 \)
The Higgs Mechanism
In gauge theories, direct mass terms violate gauge invariance.
The Higgs mechanism resolves this by:
- Introducing a scalar Higgs field
- Allowing spontaneous symmetry breaking
- Giving mass to gauge bosons
Gauge symmetry remains hidden, not destroyed.
Role of Higgs Boson in the Standard Model
In electroweak theory, a complex Higgs doublet breaks:
\( SU(2)_L \times U(1)_Y \rightarrow U(1)_{EM} \)
Mass Generation
| Particle |
Mass Origin |
| \(W^\pm\), \(Z^0\) |
Interaction with Higgs field |
| Photon |
Remains massless |
| Fermions |
Yukawa coupling with Higgs |
Prediction of the Higgs Boson
The Higgs boson is a scalar particle arising as a quantum excitation
around the Higgs field vacuum.
- Predicted in 1964 by Higgs, Englert, Brout, Guralnik, Hagen, and Kibble
- Spin-0, electrically neutral
- Mass not predicted by theory
The Higgs boson was essential to validate the Standard Model.
Large Hadron Collider (LHC)
The LHC at CERN is the world’s most powerful particle accelerator.
- Proton–proton collisions
- Center-of-mass energy up to 13–14 TeV
- Main detectors: ATLAS and CMS
Detection of Higgs Boson at LHC
The Higgs boson was discovered in 2012 by:
- ATLAS experiment
- CMS experiment
Important Decay Channels
| Decay Mode |
Signature |
| \(H \rightarrow \gamma\gamma\) |
Clean electromagnetic signal |
| \(H \rightarrow ZZ^* \rightarrow 4\ell\) |
Four-lepton final state |
| \(H \rightarrow WW^*\) |
Leptons + missing energy |
Experimental Confirmation
The observed Higgs boson has:
- Mass ≈ 125 GeV
- Spin-0
- Couplings consistent with Standard Model predictions
This discovery confirmed spontaneous symmetry breaking
as the origin of mass.
Significance and Limitations
Significance
- Completion of the Standard Model
- Nobel Prize in Physics 2013
- Foundation for Beyond Standard Model physics
Limitations
- Does not explain dark matter
- Hierarchy problem remains
- Does not include gravity
Summary
✔ Explains origin of mass via Higgs mechanism
✔ Based on spontaneous symmetry breaking
✔ Higgs boson discovered in 2012
✔ Confirms electroweak theory
✔ Opens path to new physics
