The neutrino and electroweak transformations

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SUMMARY

The neutrino is part of an SU(2) doublet in electroweak theory, specifically the left-handed neutrino and left-handed electron form an electroweak SU(2)xU(1) doublet. The right-handed electron is classified as an electroweak singlet, and the existence of a right-handed neutrino, if confirmed, would also categorize it as a singlet. The transformation properties of the neutrino can be discussed separately under SU(2) and U(1), with the neutrino transforming as part of a doublet under SU(2) and acquiring a phase related to its hypercharge under U(1).

PREREQUISITES
  • Understanding of electroweak theory
  • Familiarity with SU(2) and U(1) gauge groups
  • Knowledge of particle physics terminology
  • Basic concepts of particle transformation properties
NEXT STEPS
  • Research the role of SU(2) and U(1) in the Standard Model of particle physics
  • Study the implications of electroweak symmetry breaking
  • Explore the properties of left-handed and right-handed neutrinos
  • Investigate the significance of hypercharge in particle physics
USEFUL FOR

Physicists, students of particle physics, and anyone interested in the fundamentals of electroweak interactions and neutrino properties.

ryanwilk
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Hi, quick question.

"In electroweak theory, the neutrino belongs to an SU(2) doublet"

So, does the neutrino belong to an SU(2)xU(1) (electroweak) doublet or just SU(2)?
Thanks!
 
Last edited:
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The left-handed neutrino and left-handed electron form an electroweak SU(2)xU(1) doublet. The right-handed electron forms an electroweak singlet. The right-handed neutrino, if it exists, also forms a singlet.
 
ryanwilk said:
Hi, quick question.

"In electroweak theory, the neutrino belongs to an SU(2) doublet"

So, does the neutrino belong to an SU(2)xU(1) (electroweak) doublet or just SU(2)?

Thanks!

It's possible to speak of a particle's transformation properties under SU(2) and U(1) separately. Under SU(2) transformations the neutrino transforms as part of a doublet. Under U(1) transformations the neutrino picks up a phase proportional to its hypercharge. So I think it's most correct to say "SU(2)" double instead of "SU(2) x U(1)" doublet.
 

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