Generation number conservation

[bsaucer]

Why is "generation number" or "family number" conserved among leptons, but not among quarks? Why does a positive kaon decay into an antimuon and a muon neutrino? Why doesn't it decay into an antimuon and an electron neutrino? The anti-strange (generation 2) flavor then becomes anti-muon flavor, while the up flavor (generation 1) becomes electron (neutrino) flavor. Has the neutrino flavor ever been tested in kaon decays?

What would the Feynman diagram look like? I'd imagine that the quark and antiquark become a W+, which then decays into the lepton-antilepton pair. Somehow the W+ must carry a "generation" quantum number...

"Does the strangeness lose its flavor (on the bedpost overnight...)"

 

[mfb]

Why doesn't it decay into an antimuon and an electron neutrino?

It is a possible process via neutrino mixing, it is just incredibly unlikely.

Both for neutrinos and quarks, the eigenstates of the weak interaction are not the mass eigenstates. The mathematical details are a bit different, and processes that involve different quark families are much more common, but family numbers are not a strict conservation law in either case.

The anti-strange (generation 2) flavor then becomes anti-muon flavor, while the up flavor (generation 1) becomes electron (neutrino) flavor.

That's not how it works at all. Even with the common decay to muon+muonneutrino, you cannot say "this quark becomes that lepton".

Has the neutrino flavor ever been tested in kaon decays?

I'm not sure about kaon decays, but for pion decays I would expect that. Neutrinos from pion decays occur as side-product in the production of neutrino beams from muon decays. (edit: that was wrong)
pion decays are the main source of neutrinos for neutrino beams, and their flavor has been measured. Some muon decays produce their own neutrinos as side-effect.

Somehow the W+ must carry a "generation" quantum number...

It does not.

 

[Orodruin]

Why is "generation number" or "family number" conserved among leptons

It isnt.

It is a possible process via neutrino mixing, it is just incredibly unlikely.

I would disagree with this statement. Decays go into the mass eigenstates. Whether oscillations occur or not depends on the coherence of the different possible decays.

Neutrinos from pion decays occur as side-product in the production of neutrino beams from muon decays.

Current neutrino beams are not produced from muon decays. However, muon decays are of importance for atmospheric neutrinos. Pion decays are the main neutrino source for experiments such as NOvA.

 

[mfb]

I would disagree with this statement. Decays go into the mass eigenstates. Whether oscillations occur or not depends on the coherence of the different possible decays.

That gets a matter of definition. If you measure the decay products with a detector, you can detect a muon plus an electron neutrino - I think we can agree on that. You'll rarely see that unless your detector is far away.

Current neutrino beams are not produced from muon decays. However, muon decays are of importance for atmospheric neutrinos. Pion decays are the main neutrino source for experiments such as NOvA.

Oh, good point. The tunnels are not long enough to have many muon decays. Didn't realize that.

 

[Orodruin]

If you measure the decay products with a detector, you can detect a muon plus an electron neutrino - I think we can agree on that. You'll rarely see that unless your detector is far away.

What you measure really is not the neutrino, what you measure is the charged lepton created by the neutrino interaction and you use that to assert the flavour of the detected neutrino. In the same way you use the flavour of the charged lepton at the decay to assert the flavour of the created neutrino. By definition, the electron neutrino is the linear combination of mass eigenstates that interacts with the electron. Also, if the detector is far away, the chance is not necessarily very small either.

I would say that the main (essentially the only) difference between the lepton and quark sectors is that the neutrino masses are so close that coherence among the neutrino states can be maintained for long enough to maintain interference over macroscopic distances. When it comes to the quarks, you would have the same type of oscillations if the quarks were very close in mass.

Oh, good point. The tunnels are not long enough to have many muon decays. Didn't realize that.

There are some ideas about creating a muon decay based neutrino beam - the most ambitious one being the neutrino factory. It shares several problems with the idea of building a muon collider. Most conventional neutrino beams use pion decays and look for $\nu_\mu \to \nu_e$ oscillations.

 

[mfb]

When it comes to the quarks, you would have the same type of oscillations if the quarks were very close in mass.

Neutral meson oscillations are interesting in that aspect. The mass eigenstates have a very small mass difference and we can see the oscillations (indirectly, via observing the decays).

I know about the muon accelerator idea. We'll have to see what MICE can achieve in terms of cooling.

 

[Orodruin]

Neutral meson oscillations are interesting in that aspect. The mass eigenstates have a very small mass difference and we can see the oscillations (indirectly, via observing the decays).

Indeed, experimentally they also predate the discovery of neutrino oscillations.