Factorizing Hidden Particle Production Rates

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.