Charting the Fifth Force Landscape

TL;DR

This paper introduces a general dispersion relation framework for scalar fifth forces, enabling analysis of experimental data and theoretical constraints without complex loop calculations, and explores fundamental principles like unitarity and causality.

Contribution

It develops a unified formalism for scalar fifth forces using dispersion relations, simplifying analysis and connecting experimental limits with fundamental theoretical principles.

Findings

Derived scalar fifth force models within the dispersion relation framework

Presented experimental observables for fifth force searches in a unified formalism

Discussed implications of spectral density positivity and potential violations

Abstract

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.