Deriving Ultralight Dark Matter Limits with a Prototype Array of Mechanical Accelerometers

Motivated by the future prospects of the Windchime project, we show that even a small prototype array of 7 commercial accelerometers can be used to calculate dark matter limits for the well-known B − L coupled dark photon. As a member of the ultralight sector, the dark photon would be observed in high occupancy as a persistent plane wave characterized by de Broglie wavelength and coupling to the standard model via a hypothesized baryon minus lepton quantum number, g_B−L. Such an interaction can be probed by measuring the differential force or acceleration between two bodies of differing B −L charge-to-mass ratios. This is accomplished for a 7 sensor array of MEMS accelerometers by rigidly coupling all the sensors to a material of known B − L charge. Using a log-likelihood ratio test and Fourier transformed data from the prototype array, we are able to set a limit on g_B−L ∼ 10^−11 within a mass range of 10^{−13}−10^{−12}eV . Setting these noncompetitive limits with real data serves as a proof-of-principle demonstration of the limit-setting procedure used in Windchime future projections for B − L coupled ultralight dark matter. Additionally, this basic setup could be used for future studies on the properties of a detector array.