:::info Authors:
(1) Dorian W. P. Amaral, Department of Physics and Astronomy, Rice University and These authors contributed approximately equally to this work;
(2) Mudit Jain, Department of Physics and Astronomy, Rice University, Theoretical Particle Physics and Cosmology, King’s College London and These authors contributed approximately equally to this work;
(3) Mustafa A. Amin, Department of Physics and Astronomy, Rice University;
(4) Christopher Tunnell, Department of Physics and Astronomy, Rice University.
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Table of Links2 Calculating the Stochastic Wave Vector Dark Matter Signal
3 Statistical Analysis and 3.1 Signal Likelihood
4 Application to Accelerometer Studies
4.1 Recasting Generalised Limits onto B − L Dark Matter
6 Conclusions, Acknowledgments, and References
\ A Equipartition between Longitudinal and Transverse Modes
B Derivation of Marginal Likelihood with Stochastic Field Amplitude
D The Case of the Gradient of a Scalar
6 ConclusionsWe have provided an analysis strategy for inferring the properties of ultralight vector dark matter from terrestrial experiments, taking into account the stochastic and vector nature of the field (see Fig. 1). Our main results are suited for observation times that are longer than a sidereal day, but shorter than the coherence time. They are as follows:
\ • We focused on the signal in Fourier space, deriving the power spectral density that such dark matter is expected to leave on an axial sensor that is sensitive to its oscillatory signal. Accounting for the rotation of the Earth, we found that the signal manifests as three peaks at definite frequencies but with random amplitudes (see Fig. 2).
\ • We derived the likelihoods in each of the signal-containing bins in Fourier space. We did this by considering the marginal likelihood after integrating out the six random variables exhibited by the ULDM signal in the coherent regime: the three Rayleigh amplitudes and the three uniformly distributed DM phases (see Eq. (3.2) and Fig. 3). We found that the general elliptical motion of the vector field afforded us a significantly simpler analysis in Fourier space than the linear polarization assumption since, in the former, all peaks become statistically uncorrelated.
\ • We drew exclusion limits on a generalised, dimensionless parameter that can be reinterpreted in the context of a concrete sensor setup and dark matter model. We did this via a series of log-likelihood ratio tests following a hybrid frequentist-Bayesian approach. Crucially, we found that, unlike analyses focusing on only a single peak, our approach retains constraining power for experimental setups at all latitudes. This is because we make use of the entire DM signal, which is distributed across all three peaks, instead of constraining ourselves to the signal in any one peak, which is dependent on the latitude of the experiment (see Fig. 4).
\ • We considered a specific sensor technology (the optomechanical light cavity) and dark matter model (ultralight dark matter stemming from a new gauged U(1)B−L symmetry) as a concrete application of our analysis strategy. We recast our general limit onto one on the gauge coupling of this model, gB−L, finding that long-exposure cavities can rule out previously unexplored regions of the B −L parameter space (see Fig. 5).
\ In this work, we have established a framework for future experimental efforts in the detection of ultralight vector dark matter. Novel direct-detection probes require an understanding of how the signal of ultralight vector dark matter behaves in our local neighborhood and manifests itself in a sensor. We hope that our work aids in (i) designing search strategies using emerging detector technologies that are not traditionally used for dark matter searches, and (ii) in understanding how well a given model can be tested in the context of calls for Big Science projects using quantum sensing [62].
AcknowledgmentsWe would like to thank Andrew Long for insightful discussions throughout this work, as well as John Carlton, Daniel Carney, Zhen Liu, and Yue Zhao for their valuable feedback. DA would like to thank Yunan Gao and Juehang Qin for helpful discussions regarding our statistical treatment. CT & DA are supported by the National Science Foundation under award 2046549. MA & MJ were partly supported by DOE grant DE-SC0021619, and MJ is currently supported by a Leverhulme Trust Research Project (RPG-2022-145).
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