Correct treatment of the stochastic dark-matter field amplitude in limits
In plain words
A wave-like dark matter field is a sum of many waves with random phases, so its local strength fluctuates. Searches shorter than the field coherence time can be unlucky, and limits must account for this.
Precise statement
For a virialized ultralight bosonic field with velocity dispersion about $10^{-3}\,c$, the local amplitude is Rayleigh distributed when the measurement time $T$ is shorter than the coherence time $\tau_c \sim 10^{6}\,h/(m c^2)$. Determine the correct likelihood and the resulting correction factor to exclusion limits for $T < \tau_c$, including vector polarization and multi-sensor correlations.
What would settle it
A derivation of the likelihood validated by simulation and adopted across clock, magnetometer and comagnetometer analyses.
Status in the literature
Stochastic-amplitude corrections of up to an order of magnitude were derived for scalar fields around 2021; vector and multi-sensor cases remain incompletely treated.
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