  A method is proposed to streamline the computation of hidden particle
production rates by factorizing them into i) a model-independent SM
contribution, and ii) a observable-independent hidden sector contribution. The
Standard Model (SM) contribution can be computed once for each observable and
re-used for a wide array of hidden sector models, while the hidden sector
contribution can be computed once for each model, and re-used for a wide array
of observables. The SM contribution also facilitates extracting model
independent constraints on hidden particle production. The method is compatible
with effective field theory (EFT) and simplified model approaches. It is
illustrated by factorizing the rate of charged kaon decays into a charged
lepton and a number of hidden particles, and a single form factor $F_{\ell}$ is
found to parametrize the impact of general hidden sectors. We derive
model-independent constraints on the form factor $F_e$ that governs decays into
positrons and hidden particles.
