Feynman rules for electroweak multiplets

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SUMMARY

The discussion focuses on the Feynman rules for electroweak interactions involving SU(2) multiplets of weak isospin n and weak hypercharge Y. The interaction term in the standard model Lagrangian is specified as Lγμ(i∂μ - g/2 τ·Wμ - g'/2 Y Bμ)L + Rγμ(i∂μ - g'/2 Y Bμ)R, where L and R represent left- and right-handed fermions. The user seeks guidance on extending the standard rules for SU(2) doublets to higher isospin multiplets, specifically by substituting the Pauli matrices with the appropriate SU(2) matrices for isospin n.

PREREQUISITES
  • Understanding of SU(2) gauge theory
  • Familiarity with electroweak interactions
  • Knowledge of the standard model Lagrangian
  • Proficiency in using Pauli matrices in quantum mechanics
NEXT STEPS
  • Research the derivation of Feynman rules for SU(2) multiplets
  • Study the implications of weak hypercharge Y in electroweak theory
  • Learn about the role of gauge bosons in electroweak interactions
  • Explore advanced applications of the standard model Lagrangian
USEFUL FOR

This discussion is beneficial for theoretical physicists, particle physicists, and graduate students studying electroweak interactions and the standard model of particle physics.

Rocky Raccoon
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Can someone refer me to Feynman rules for electroweak interactions in the general case of SU(2) multiplets of weak isospin n and weak hypercharge Y interacting with EW gauge bosons?

I can only find the standard rules for SU(2) doublet electron - neutrino.

Thanks!
 
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The interaction term in the standard model Lagrangian is

Lγμ(i∂μ - g/2 τ·Wμ - g'/2 Y Bμ)L + Rγμ(i∂μ - g'/2 Y Bμ)R

where L and R are left- and right-handed fermions and τ are the three Pauli matrices. So all you would have to do for an isospin n fermion is to replace τ by the three SU(2) matrices for isospin n, which are given by

τ±|n m> = √(n∓m)(n±m+1) |n m±1>
τ3|n m> = m |n m>
 

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