Lepton Flavors: Beyond e-, μ-, τ-?

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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.

Incnis Mrsi
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TL;DR
Are they mass eigenstates by definition?
Do three mass eigenstates of the charged lepton define the flavor eigenstates e, μ, τ ? Ī̲ know that—for neutrinos—mass eigenstates do not correspond to νe, νμ, ντ .

Can we define reasonable flavor states for leptons in any way other than the abovementioned two bases?
 
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Sure, you could define them as orthogonal; linear combinations. But why would you want to?
 
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Incnis Mrsi said:
Do three mass eigenstates of the charged lepton define the flavor eigenstates e−, μ−, τ− ?
Yes.
 
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Vanadium 50 said:
But why would you want to?
Ī̲’m no expert, but this may be related to decay of W and Z, for example.
 
Vanadium 50 said:
Sure, you could define them as orthogonal; linear combinations. But why would you want to?
Yes, I believe it is a choice: you can either have the electron 'flavours' defined as mass eigenstates or the neutrino flavours as mass eigenstates, but not both.
 
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Michael Price said:
Yes, I believe it is a choice: you can either have the electron 'flavours' defined as mass eigenstates or the neutrino flavours as mass eigenstates, but not both.
The situation is completely analogous to the quark sector, where we indeed define the quark flavours as the mass eigenstates. With these definitions the W couplings become off diagonal. The reason we usually work with neutrino states that give flavour diagonal W couplings and call them ”flavour eigenstates” is the low neutrino mass leading to approximate flavour conservation in experiments with short enough baselines not to be affected by neutrino oscillations (and the fact that neutrino masses are so small that we typically cannot tell them apart based on kinematics alone).
 
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Orodruin said:
The reason we usually work with neutrino states that give flavour diagonal W couplings and call them ”flavour eigenstates”…
This looks exactly the thing I was interested in. The W boson governs interconversion between charged lepton and neutrino. Quantitatively, it defines an operator, but which namely are its eigenvalues and eigenvectors (in terms of e, μ, τ)? It seems to be related to so named ”Yukawa couplings/interaction/matrix”, but it’s hard to me to understand these things as explained in flavor-physics papers.
 

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