# A Flavor of leptons

#### Incnis Mrsi

Summary
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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Staff Emeritus
Sure, you could define them as orthogonal; linear combinations. But why would you want to?

#### Orodruin

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Do three mass eigenstates of the charged lepton define the flavor eigenstates e−, μ−, τ− ?
Yes.

#### Incnis Mrsi

But why would you want to?
Ī̲’m no expert, but this may be related to decay of W and Z, for example.

#### Michael Price

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.

#### Orodruin

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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).

#### Incnis Mrsi

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.

"Flavor of leptons"

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