Wake forces in a background of quadratically coupled mediators

Two particles can exert forces on each other when embedded in a sea of weakly-coupled particles. These "wake forces'' occur whenever the source and target particles have quadratic interactions with the mediating particles; they are proportional to the ambient energy density, and typically have a range of order the characteristic de Broglie wavelength of the background. The effect can be understood as source particles causing a disturbance in the background waves -- a wake -- which subsequently interacts with the target particles. Wake forces can be mediated by bosons or fermions, can have spin dependence, may be attractive or repulsive, and have a generally anisotropic spatial profile and range that depends on the phase-space distribution of the ambient particles. In this work, I investigate the application of wake forces to dark matter searches, recast existing limits on short-range forces into leading constraints on dark matter with quadratic couplings, and sketch out potential experimental modifications to optimize sensitivity. Wake forces occur in the Standard Model: the presence of the cosmic neutrino background induces a millimeter-range force about 22 orders of magnitude weaker than gravity. Wake forces may also be relevant in condensed-matter and atomic physics.