[tex]R = \frac{\sigma(e^+ P^+ \rightarrow C)}{\sigma(e^+ P^+ \rightarrow \bar{\nu}_e)}[/tex]

We know the proton composition is UUD and the reaction is a scattering and not a decay. So the positron has to scatter off one of the constituent quarks in the proton to produce either a charm quark or a neutrino. We know that lepton number and presumably quark number have to be preserved at each vertex as well.

A Feynman diagram (dunno how to draw here) would be one of those vertical...