Discussion Overview
The discussion revolves around the definition of lepton flavor eigenstates, specifically in relation to charged leptons (e−, μ−, τ−) and their mass eigenstates. Participants explore whether alternative definitions of flavor states exist beyond the conventional bases and the implications of these definitions in particle interactions, particularly in the context of W and Z boson decays.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- Some participants question whether the three mass eigenstates of charged leptons define the flavor eigenstates e−, μ−, τ−, noting that this is not the case for neutrinos.
- Others suggest that flavor states could be defined as orthogonal linear combinations, but express skepticism about the necessity of such definitions.
- One participant asserts that it is a choice to define either the electron flavors or the neutrino flavors as mass eigenstates, but not both simultaneously.
- Another participant draws an analogy to the quark sector, stating that quark flavors are defined as mass eigenstates, which leads to off-diagonal W couplings.
- There is a discussion about the implications of using flavor diagonal W couplings for neutrinos, with some participants noting that this is related to the low mass of neutrinos and their approximate flavor conservation in certain experimental conditions.
- A later reply raises a question about the specific eigenvalues and eigenvectors related to the W boson and its role in the interconversion between charged leptons and neutrinos, referencing Yukawa couplings and expressing difficulty in understanding these concepts.
Areas of Agreement / Disagreement
Participants express differing views on the definitions of flavor eigenstates and whether they can be defined in multiple ways. There is no consensus on the necessity or implications of alternative definitions, and the discussion remains unresolved regarding the best approach to defining lepton flavors.
Contextual Notes
Some limitations include the dependence on definitions of flavor and mass eigenstates, as well as unresolved questions about the mathematical framework surrounding Yukawa couplings and their implications in flavor physics.