Why is this interaction forbidden? $$\nu_e+\bar{\nu}_e\rightarrow K^+ + K^-$$ Lepton number is conserved, charge is conserved, baryon number is irrelevant since these are mesons. Energy is conserved since we could collide these two neutrinos (and anti) at any energy required to produce the two mesons. Neutrinos only interact via the weak force so if it were possible it would be a weak decay. Parity needn't be conserved since this would be a weak interaction. The only thing that is bugging me is that quark flavour (and strangeness) is not conserved but I thought this was allowed via a weak interaction. Maybe it is momentum?
EDIT
I think this process is allowed and here is my attempt at the lowest order Feynman diagram, does this look correct?
EDIT
Second attempt at a Feynman diagram, following comments made.