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The Feynman diagram you'd naively draw for a beta decay such as [itex]p\rightarrow n + e^++\bar{\nu}[/itex] would have four lines joined at a vertex, but in reality there's a virtual W or Z involved, which makes it into two 3-vertices.

Is there any fundamental reason why all the vertices in a field theory *must* be 3-line vertices, and not 4 or more? If we'd known about the general structure of field theory before the discovery of the neutrino, could we have inferred that there must be some intermediate particle such as the W or Z?

[EDIT] Googling on "charged scalar field," I get, e.g., a statement that in such a theory, "the number of arrows flowing into a vertex equals the number flowing out" (Sterman, p. 110). So I guess maybe there is no reason we can't have 4 or more lines at a vertex, and maybe my question should really be whether such things exist in the standard model, or if not, whether there is any known reason why the universe has to be this way.

Is there any fundamental reason why all the vertices in a field theory *must* be 3-line vertices, and not 4 or more? If we'd known about the general structure of field theory before the discovery of the neutrino, could we have inferred that there must be some intermediate particle such as the W or Z?

[EDIT] Googling on "charged scalar field," I get, e.g., a statement that in such a theory, "the number of arrows flowing into a vertex equals the number flowing out" (Sterman, p. 110). So I guess maybe there is no reason we can't have 4 or more lines at a vertex, and maybe my question should really be whether such things exist in the standard model, or if not, whether there is any known reason why the universe has to be this way.

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