B Can Leptons decay into mesons?

[Soffie]

I presume they cannot as they are fundamental particles? But then a meson can decay into a lepton?

 

[dukwon]

Only taus, since the other leptons are lighter than the lightest meson.
See here for a list of observed decays: http://pdglive.lbl.gov/Particle.action?node=S035&init=0

 

[Soffie]

Oh, so the rest mass of the lepton must be greater than the meson's rest mass? But what if the lepton is moving? Then its total energy will be greater (as it has Kinetic + rest mass energy) and this can be converted into a meson which may indeed be heavier when it decays

 

[dukwon]

What if you as an observer are moving very fast compared to the lepton? (What is the difference?) Do you think what it can decay into changes then?

 

[Soffie]

Oh I see, so if you were in the lepton's rest mass frame it would have K.E. 0, because energy and momentum are lorentz variant while the mass is not. So it isn't possible for the particle to decay into something with a greater rest mass. I think that's right?

 

[dukwon]

Correct! It might be useful to look up 'invariant mass', whose conservation follows from the conservation of energy and momentum.

There are also other conservation laws that determine possible decay products, such as angular momentum, baryon number, lepton number, lepton flavour, quark flavour (except in weak decays), parity (again, except in weak decays). Every tau decay, for example, must produce a tau neutrino to conserve lepton number and flavour.

 

[Orodruin]

Just to add that while it is more obvious in the rest frame of the decaying particle, it is also possible to do the kinematic analysis in any other inertial frame. You will then find that you cannot simultaneously satisfy both energy and momentum conservation if the sum of the decay product rest masses is larger than the mass of the decaying particle.

In addition, even if taus can have mesons in their decay products, there must also be at least one lepton as well for lepton number conservation to hold. If this is a neutrino it is typically not seen in the detector.

I presume they cannot as they are fundamental particles?

Note that being a fundamental particle has nothing to do with being able to decay or not. There are unstable fundamental particles and there are stable composite particles.

 

[mfb]

If this is a neutrino it is typically not seen in the detector.

If we neglect neutrino mixing in the decay, it has to be at least one tau neutrino.
There are decays without neutrino in the Standard Model plus neutrino mixing, but the predicted probability is something like 10^-50, they are completely negligible. New physics could increase this number significantly, therefore these decays are searched for.