Discussion Overview
The discussion revolves around the properties and implications of ##SU(2)## doublets and Majorana fermions in the context of their coupling to the Higgs field via Yukawa interactions. Participants explore the significance of various terms in the Lagrangian, gauge invariance, and the mathematical structure of fermion fields.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants inquire about the difference between ##L## and ##L^{c}##, suggesting that the superscript ##c## signifies charge conjugation.
- One participant claims that the term ##LL^{c}## breaks ##SU(2)## gauge invariance, prompting questions about how this occurs.
- Another participant points out that the term ##\bar{L}L^{c}## is not a hypercharge singlet due to both fields having the same hypercharge, raising concerns about the correct formulation of the mass terms.
- There is a discussion about the necessity of including the bar in the expression for Lorentz invariance, with one participant referencing an article that omits it.
- Participants debate the validity of using the mass term ##M_{0}\bar{L}L## instead of ##M_{0}\bar{L}L^{c}##, with one asserting that the former cannot involve two left-handed fields and the latter violates gauge invariance.
- Questions arise regarding the terminology of ##M_0## as a vector mass rather than simply a mass, indicating a need for clarification on this distinction.
Areas of Agreement / Disagreement
Participants express differing views on the implications of the terms in the Lagrangian, particularly regarding gauge invariance and the necessity of certain field configurations. No consensus is reached on the correct formulation or interpretation of these terms.
Contextual Notes
There are unresolved questions regarding the assumptions made about gauge invariance and the definitions of the fermion fields. The discussion reflects a variety of perspectives on the mathematical formalism involved.
Who May Find This Useful
This discussion may be of interest to those studying particle physics, particularly in the context of electroweak interactions and the role of Higgs couplings in fermion mass generation.