Understanding Neutron Star Formation Through Feynman Diagrams

[doggydan42]

Hello,

I recently watched a video as an introduction to Feynman diagrams for my own self-interest. The video gave a link to practice problems, and one of them was as follows:

In a neutron star gravitational collapse causes valence electrons to combine with protons. Draw a Feynman diagram representing this interaction.
$$p+e^{-} \rightarrow n + \nu_e
\\ uud+e^{-} \rightarrow udd + \nu_e$$

I understood most of the interaction and that there would be a W+ boson between the up quark and electron, though would the electron or up quark emit the boson, and why?

Thank you in advance

 

[PeterDonis]

would the electron or up quark emit the boson

Neither. The boson is exchanged between the electron/neutrino and the up quark/down quark, but neither one can be said to be the "emitter". You just have a Feynman diagram (at lowest order) with two interaction vertices.

 

[doggydan42]

Neither. The boson is exchanged between the electron/neutrino and the up quark/down quark, but neither one can be said to be the "emitter". You just have a Feynman diagram (at lowest order) with two interaction vertices.

So to the diagram, it does not matter if the curve drawn for the W boson is further left at the vertex with the electron, being that time increases to the right?

Or to rephrase the question, does it matter which particle, up quark or electron, decays first?

 

[PeterDonis]

to the diagram, it does not matter if the curve drawn for the W boson is further left at the vertex with the electron, being that time increases to the right?

The diagram does not tell you where in spacetime the two vertexes are; the fact that it seems to when you draw it is misleading. In the actual math, this diagram corresponds to an infinite number of terms, one for each possible pair of spacetime locations for the vertexes.

 

[doggydan42]

The diagram does not tell you where in spacetime the two vertexes are; the fact that it seems to when you draw it is misleading. In the actual math, this diagram corresponds to an infinite number of terms, one for each possible pair of spacetime locations for the vertexes.

Okay, thank you very much.