Cavendish Tests of Millicharged Particles

Abstract

A terrestrial population of room-temperature millicharged particles can arise if they make up a dark matter subcomponent or if they are light enough to be produced in cosmic ray air showers. In a companion paper, we showed that a simple electrified shell acts as an efficient accumulator for such particles, parametrically enhancing their local density by many orders of magnitude. Here we demonstrate that Cavendish tests of Coulomb's Law, performed since the late 18th century, function as both quasistatic accumulators and detectors for this overdensity. Reinterpretations of these past Cavendish tests thus provide some of the strongest bounds on a terrestrial millicharge population. We also propose surrounding a Cavendish test with an additional charged shell, which significantly improves the sensitivity and can even enable detection of the irreducible density of millicharged particles generated from cosmic rays. Using decades-old technology, this can outperform future accelerator searches for sub-GeV masses.

Figures (5)

• Figure 1: New limits (blue) on the terrestrial density $n_\chi$ of room-temperature millicharged particles (regardless of their origin), recast from past Cavendish experiments Plimpton:1936ontBartlett:1970js. Also shown are previous limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso (gray). Above the solid gray line, millicharged dark matter quickly sheds its kinetic energy in Earth's atmosphere before reaching surface-level and underground direct detection experiments. Below this line, direct detection experiments are sensitive to a millicharged dark matter population, provided that these particles make up a sufficiently large fraction of the dark matter density, $f_{_\text{DM}} \gtrsim 10^{-8}$Pospelov:2020ktu. Above the dashed black line, millicharged dark matter is able to efficiently thermalize as it passes through Earth, which leads to large terrestrial overdensities (see Ref. forthcoming). A comparison to recent limits derived from ion trap experiments Budker:2021quh is shown in Fig. \ref{['fig:ion']}.
• Figure 2: The projected sensitivity of a dedicated Cavendish test enclosed in an electric trap to the irreducible terrestrial density of millicharged particles produced by cosmic rays. We take the millicharged particles to efficiently ($E_\oplus \neq 0$) or not efficiently ($E_\oplus = 0$) couple to the atmospheric electric field, which can substantially enhance the local density of particles near and below the crust. We show both possibilities for clarity, but as discussed in Ref. forthcoming, ignoring the effect of $E_\oplus$ is unrealistic, and thus a detailed modeling is likely to yield results much closer to our $E_\oplus \neq 0$ projections. This cosmic ray population is irreducible and solely a function of the charge and mass, such that testing this local density is equivalent to testing the model itself. We consider setups placed inside a room of radius $R_\text{room} = 10 \ \text{m}$ or placed outdoors. Also shown as the dashed orange line is a collection of projections for proposed future accelerator searches, taken from Refs. Berlin:2018bscPBC:2025sny.
• Figure S1: Limits recast from the past Cavendish experiments of PL Plimpton:1936ont and BGP Bartlett:1970js on a room-temperature terrestrial population of millicharged particles (solid red, orange, and blue lines), as a function of the particle's mass $m_\chi$ and charge $q_\chi$ and fixing the ambient density to $n_\chi = 10^4 \ \text{cm}^{-3}$. Also shown are previous limits from accelerator probes Davidson:2000hfHaas:2014ddaPrinz:1998uaArgoNeuT:2019ckqmilliQan:2021lneArguellesDelgado:2021lekPBC:2025snyCMS:2024eyxAlcott:2025rxn and SN1987A Chang:2018rso (gray). In regions of parameter space labeled "$t_\text{diff} > t_\text{osc}$," the time for mCPs to diffuse into the experiment is longer than the voltage oscillation time, suppressing the signal exponentially. The point at which $q_\chi = 3 T_\chi / (e \phi_0)$ is labeled as "strong coupling," since millicharged particles are able to efficiently electrically bind to the shell for couplings larger than this value.
• Figure S2: As in Fig. \ref{['fig:recast']}, new limits (blue) on millicharged particles, recast from past Cavendish experiments Plimpton:1936ontBartlett:1970js, but now including previous limits derived from ion trap experiments Budker:2021quh. These are shown for the same choices of the terrestrial density $n_\chi$ as in Fig. \ref{['fig:recast']}, except for $n_\chi = 0.1 \ \text{cm}^{-3}$ since ion traps are not sensitive to $n_\chi < 1 \ \text{cm}^{-3}$.
• Figure S3: Analogous to Fig. \ref{['fig:recast']}, but the projected sensitivity to the terrestrial density $n_\chi$ of millicharged particles, for a modified Cavendish test that includes an additional shell fixed at high voltage ($\text{MV}$) and whose interior is operated at high vacuum ($10^{-6} \ \text{atm}$). This additional shell functions as a trap for millicharged particles, enhancing the sensitivity to much smaller ambient densities. Aside from this trap, the experimental setup, including noise levels, is taken to be similar to the previous Cavendish experiment of Ref. Bartlett:1970js.