Nucleon vector strangeness form factors: multi-pion continuum and the OZI rule

We estimate the 3π continuum contribution to the nucleon strange quark vector current form factors, including the effect of 3π↔ρπ and 3π↔ω resonances. We find the magnitude of this contribution to be comparable to that the lightest strange intermediate states. We also study the isoscalar electromagnetic form factors, and find that the presence of a ρπ resonance in the multi-pion continuum may generate an appreciable contribution.