Mechanical Sensors for Ultraheavy Dark Matter Searches via Long-range Forces

TL;DR

This work proposes metre-scale arrays of mechanical impulse sensors to search for ultraheavy dark matter that couples to Standard Model matter via long-range forces. It develops a track-based detection framework using template matching in a 6D track-parameter space, accounts for the Look-elsewhere Effect, and provides semi-analytical sensitivity projections for magnetic-levitation and MEMS-based realizations. The study finds that pure gravitational coupling to Planck-scale DM is extremely challenging, requiring unrealistically large quantum-noise reductions, but a broad class of non-gravitational long-range interactions is accessible with near-term technology, enabling substantial exploration of new DM parameter space. The results suggest a practical path forward for experimental tests beyond conventional direct-detection strategies, with significant potential impact for understanding heavy dark matter and long-range forces. The work also clarifies the data-analysis challenges and provides a framework for scaling to larger sensor arrays in future research.

Abstract

Dark matter candidates with masses around the Planck-scale are theoretically well-motivated, and it has been suggested that it might be possible to search for dark matter solely via gravitational interactions in this mass range. In this work, we explore the pathway towards searching for dark matter candidates with masses around the Planck-scale using mechanical sensors while considering realistic experimental constraints, and develop analysis techniques needed to conduct such searches. These dark matter particles are expected to leave tracks as their signature in mechanical sensor arrays, and we show that we can effectively search for such tracks using statistical approaches to track-finding. We analyze a range of possible experimental setups and compute sensitivity projections for searches for ultraheavy dark matter coupling to the Standard Model via long-range forces. We find that while a search for Planck-scale dark matter purely via gravitational couplings would be exceedingly difficult, requiring $\sim 80\,\mathrm{dB}$ of quantum noise reduction with a $100^3$ array of devices, there is a wide range of currently unexplored dark matter candidates which can be searched for with already existing or near-term experimental platforms.

Figures (7)

• Figure 1: Schematic of a 3D sensor array, where sensors are represented by coloured circles, with the colour indicating the strength of an acceleration signal. A dark matter track going through the array is shown in green. A zoomed-in schematic showing the impact parameter vector $\boldsymbol{b}$, the position vector $\boldsymbol{r}(t)$, and the dark matter velocity vector $\boldsymbol{v}$ is displayed on the top left.
• Figure 2: 2D slices of the template matching significance map. The signal-to-noise ratio (SNR) is shown by the colormap, and the truth values are shown by the red crosses. $\phi_0$ and $\cos \theta_0$ refer to the spherical coordinates of the entry point of the dark matter track. It can be seen that a clear peak around the truth parameter values of the track is clearly visible. These 2D slices are produced by setting all other parameters to the simulation truth values.
• Figure 3: A corner plot showing the posterior distribution of the temporal and geometric parameters and the signal strength produced using nested sampling, with the truth parameters indicated by the red crosses. The signal strength parameter is defined as \ref{['eq:signal_strength_prior']}. $t$ and $v$ refer to the entry time and speed of the track, respectively. The geometric parameters are parameterised using the spherical coordinates of the entry and exit points of the track, as $(\cos \theta_0, \phi_0)$ and $(\cos \theta_1, \phi_1)$. It can be seen that the a posterior consistent with the truth value can be obtained in a full 6-dimensional search. The 6-dimensional 1, 2, 3 and 4$\sigma$ contours are shown. In 2D histograms as shown here, these correspond to $39\,\%,\: 86\,\%,\: 99\,\%$ and $99.97\,\%$, because the probability content of $\sigma$-levels depend on dimensionality of the parameter space Workman:2022ynf. Illustration made with cornercorner.
• Figure 4: Dark matter sensitivity of the different sensor configurations shown in \ref{['tab:parameters_windchime_arrays']}. These sensitivity curves represent $90\,\%$ exclusion limits in the signal-free scenario, where there is no detectable dark matter for the given configurations. These sensitivity curves are shown alongside recast XENON1T and LZ limits XENON:2023ikuLZ:2024psa; details of the recasting procedure can be found in \ref{['sec:cross_section_alpha_conversion']}. The value of $\alpha$ corresponding to the gravitational coupling is shown in the dark green dashed line. Two lines are shown due to material dependence of the equivalent gravitational coupling strength, this can be seen from \ref{['eq:force']}, as the force is defined as a function of the number of nuclei instead of mass. The dotted and dashed lines for Near-future MEMS represent the detector sensitivity when the laser intensity is constrained by cooling power, with and without $10\, \mathrm{dB}$ of quantum noise reduction, respectively.
• Figure 5: The coupling strength $(\alpha)$ where the probability of a dark matter track above threshold exceeds $90\,\%$, as a function of the amount of quantum noise reduction $(\xi)$. The strength of the gravitational coupling for lead is indicated by the dark green dashed line. In addition, the expected scaling when quantum noise dominates is shown by the maroon dotted line. This corresponds to $\alpha\propto1/\sqrt{\xi}$, as can be seen from the second term in \ref{['eq:impulse_noise']}. Above $\sim 90\, \mathrm{dB}$, we can see that the sensitivity is flat because thermal noise becomes dominant. The amount of quantum noise reduction needed to reach this thermally-limited regime from Carney:2019pza is shown by the vertical dot-dashed lines; the discrepancy is discussed in the text.