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