Electroweak theory

introduction

• Glashow-Weinberg-Salam model
  
• doublets of leptons and quarks => SU(2) symmetry
  

• W-boson mass causes some trouble
  
• Goldston boson
  
• Higgs mechanism

 

 

recipe

• start with the local gauge symmetric SU(2) Lagrangian with massless gauge fields
  
• introduce the Higgs field
  
• break the local gauge symmetry in such a way by a new interaction between the Higgs field and gauge fields so as to generate terms in the Lagrangian that look like mass terms for gauge fields
  

 

 

adjoining U(1) symmetry

\(\begin{pmatrix}\gamma \\Z^0 \end{pmatrix} = \begin{pmatrix}\cos \theta_W & \sin \theta_W \\-\sin \theta_W & \cos \theta_W \end{pmatrix} \begin{pmatrix}B^0 \\W^0 \end{pmatrix} \)

 

 

 

weak interactions

• massive gauge bosons 
  
  • W and Z bosons
    

 

 

consequences

• neutral currents
  
• new mesons
  
• parity violating effects
  
• W and Z bosons
  

 

 

W-boson

• massive charged spin 1 boson
  

 

 

Z-boson

• massive neutral spin 1 boson
  

 

 

weak force

• neutron beta decay
  
• muon decay
  
• high-energy neutrino collisions with matter
  

 

 

three classes of weak interactions

• leptonic reactions
  
• semi-leptonic reactions
  
• hadronic weak reactions
  

 

 

Higgs mechanism

• Higges field
  
  • pervasive universal background field that modifies the simple electroweak gauge theory as the gravitational field caused by mass
    
• two initial charged massless weak field W, W^{+}
  
  • mix with Higgs fields H^{+}, H^{-}
    
  • W fields get mass
    
• two electrically neutral massless fields W^0, G^0
  
  • mix with neutral Higgs field H^0
    
  • Z-field massive neutral weak field
    
• resulting bosons
  
  • W - massive charged spin 1
    
  • Z- massive neutral spin 1 boson
    
  • photon - massless spin 1
    
  • Higgs - massive neutral scalar spin 0
    

 

 

 

 

encyclopedia

• http://en.wikipedia.org/wiki/Electroweak_interaction
• http://en.wikipedia.org/wiki/Quantum_electrodynamics
• http://en.wikipedia.org/wiki/Beta_decay
• http://en.wikipedia.org/wiki/weak_force

 

expositions

• Kibble, T. W. B. ‘History of Electroweak Symmetry Breaking’. arXiv:1502.06276 [hep-Ex, Physics:hep-Ph, Physics:hep-Th, Physics:physics], 22 February 2015. http://arxiv.org/abs/1502.06276.

articles

• Hitoshi Murayama Why do we want a linear collider, 1996