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Title: Correct treatment of the stochastic dark-matter field amplitude in limits
Plain: 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: For a virialized ultralight bosonic field with velocity dispersion about $1e-3\,c$, the local amplitude is Rayleigh distributed when the measurement time $T$ is shorter than the coherence time $\tau_c \sim 1e6\,h/(m c^2)$. Determine the correct likelihood and the resulting correction factor to exclusion limits for $T < \tau_c$, including vector polarization and multi-sensor correlations.
Settled by: A derivation of the likelihood validated by simulation and adopted across clock, magnetometer and comagnetometer analyses.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: (empty)