Electron-electron scattering into muon-muon state

Question

It is common in QED that electron positron pair can scatter into different lepton family such as muon and antimuon pair. Is it possible that two energetic electrons can scatter into two muons ? I have not been able to find any sources treating such a reaction. And I don't see any reason, such as a selection rule, that would prohibit such reaction.

Davide Morgante · Accepted Answer

The reaction $$e^-+e^-to mu^-+mu^-$$ is prohibited since it doesn't conserve lepton number. Every family of leptons has a specific lepton number $L_e, L_mu$ and $L_tau$. Leptons carry positive lepton number and anti-leptons carry negative lepton number. In the reaction you gave there's $2L_e$ on the left hand side and $2L_mu$ on the right hand side, and so it's not conserved.
A scattering like $$e^++e^-to mu^++mu^-$$ is not forbidden since on the LHS you have zero lepton number and on the RHS you have zero as well.

Cosmas Zachos · Answer

No, $eeto mumu$ is not likely. For charged leptons there is an approximately conserved lepton family number.
It is not strictly conserved, since neutrino mixing may induce violations in it, but it is freakishly small, with a BR bound for $muto egamma$ of less than 13 orders of magnitude.

Electron-electron scattering into muon-muon state

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