Charting the fifth force landscape

Fifth forces arising from hidden sector scalar operator exchange, as probed in a variety of present and planned experiments, can be captured by general dispersion relation involving one real, positive, spectral density function. Previously considered fifth forces, tree-level to more exotic loop-level possibilities, are derived this formalism, without explicitly performing conventional loop calculations. A experimental observables commonly used force searches also presented the same allowing straightforward extraction limits on any specific model. The speculative possibility probing violations unitarity, causality, or locality, manifested breakdown positivity density, is discussed.