# Charged and neutral current in Feynman diagrams

I am stuck on finding the 'right' mediator in weak interactions. Consider the following reactions.

1:

$$\mu^+\rightarrow \bar{\nu}_\mu + e^+ +\nu_e$$

This is mediated by the vector boson $$W^+$$.

2:

$$\pi^-\rightarrow \bar{\nu}_\mu+\mu^-$$

This is mediated by the vector boson $$W^-$$.

3:

$$\nu_\mu +e^- \rightarrow \nu_\mu + e^-$$

This is mediated by the neutral current $$Z^0$$.

My question is: is there a systematic way of finding the vector boson or mediator in weak interactions? It might be very trivial but I do not see it. I want to understand this since I want to draw Feynman diagrams well.

• it has to do with charge conservation, if the mediator is chargeless, it is the Z. – anna v Nov 9 '18 at 14:34

The s-channel diagram, (c), would be a $$W^-$$ in order to conserve charge, while the u-channel diagram, (b), there isn't really a direction associated with the exchange boson. It's a $$W^-$$ if it's going "up" from the incoming to outgoing electron, and it's a $$W^+$$ if it's going "down" from the incoming neutrino to the outgoing neutrino. The diagram includes both.