# Feynman diagram for Muon decaying into electron and photon

I'm trying to draw a Feynman Diagram for a muon decaying into an electron and photon. I'm not sure if this is correct.

Is it even possible that a particle will stay around waiting for another particle which will get created later, so that they may interact? Wouldn't the neutrino speed away before the anti-neutrino is created?

(Feynman Diagram and standard model rookie here. I just started teaching myself with the help of Internet)

• Just for reference the Particle Physics Booklet (I've got the 2008 ed at home) puts a limit on the branching ratio for this mode at $< 1.2 \times 10^{-11}$ and I don't believe it has ever been unambiguously observed. – dmckee Oct 14 '16 at 3:10
• This is wrong, violates muon number conservation, google "feynman diagram for muon decay, there has to be muon number conservation too, so a nu_mu is necessry – anna v Oct 14 '16 at 5:42
• @annav it is possible he is trying to do a non-standard model diagram though. – Suzu Hirose Oct 14 '16 at 5:52
• @SuzuHirose that is why I quoted the " rookie " – anna v Oct 14 '16 at 6:28

Feynman Diagram and standard model rookie here

In drawing Feynman diagrams one has to be within a model, for the standard model there exists conservation laws that cannot be violated in the Feynman diagrams. Lepton flavor conservation gives a nu_mu coming from conserving muon lepton number. So the correct diagram for muon decay to an electron to first order is

Any loop corrections have to obey lepton flavor conservation. What you have drawn is a forbidden decay within the standard model .

Extending the standard model to include the experimental observation that neutrinos have mass, will allow the diagram in the question due to oscillations but the specific extension of the SM has to be decided before a meaning can be given to the diagram.

In the Standard Model, leptonic family numbers (LF numbers) would be preserved if neutrinos were massless. Since neutrino oscillations have been observed, neutrinos do have a tiny nonzero mass and conservation laws for LF numbers are therefore only approximate. This means the conservation laws are violated, although because of the smallness of the neutrino mass they still hold to a very large degree for interactions containing charged leptons. However, the (total) lepton number conservation law must still hold (under the Standard Model). Thus, it is possible to see rare muon decays such as µ → eγ or µN→eN:

Searches for these decays have come up negative, just giving limits. Feynman diagrams for neutrino oscillation effects can be drawn .

Is it even possible that a particle will stay around waiting for another particle which will get created later, so that they may interact? Wouldn't the neutrino speed away before the anti-neutrino is created?

Feynman diagrams are iconal representations for planning the mathematical intergrals necessary to get a value for the decay rate ( in this case). Within the diagram the "particles" are virtual, i.e. not on mass shell because they will be integrated over the limits of the problem given. It has no meaning to think of "waiting", everything happens within the limits of integration.