Milli-Charged Particles (mCPs)

• Milli-charged particles (mCPs) are hypothetical particles defined by a fractional electric charge Q = εe (with ε ≪ 1) arising in various hidden-sector models.
• Their production mechanisms range from meson decays at colliders, atmospheric interactions, and dark matter decay, leading to diverse experimental signatures.
• Detection strategies employ scintillator arrays, drift chambers, neutrino detectors, and interferometric techniques to probe different mass and interaction regimes.

Millicharged particles (mCPs) are hypothetical states carrying an electric charge much smaller than the electron charge, conventionally written as $Q_\chi=\epsilon e$ with $\epsilon\ll 1$. In contemporary particle-physics and cosmology literature, the term encompasses several related possibilities: light MeV–GeV fermions produced in meson decays and collider annihilation, GeV–PeV states studied in atmospheric and ultrahigh-energy observatories, heavy Earth-bound dark matter candidates, and ultralight bosonic dark matter in the mass ranges $10^{-18}-3.5\times10^{-17}\,\text{eV}$ and $10^{-15}-10^{-14}\,\text{eV}$ (Adhikary et al., 13 May 2026, Magill et al., 2018, Arza et al., 24 Jan 2025). Their phenomenology is unified by the same parametric suppression of electromagnetic interactions, but the relevant production mechanisms, transport effects, and observables depend strongly on mass scale, environment, and whether the millicharge is fundamental or induced by kinetic mixing.

1. Definition and theoretical realizations

The standard parametrization takes an mCP $\chi$ to have charge

$Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$

Much of the literature treats $\chi$ as a Dirac fermion, although ultralight bosonic realizations are also studied. A representative hidden-sector construction introduces an extra gauge group $U(1)_D$ or $U(1)'$ with a massless or ultralight dark photon and kinetic mixing with the Standard Model photon. In one commonly used form,

$$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$

so that after diagonalization the effective visible coupling becomes

$\epsilon\ll 1$0

An alternative notation, used in reheating studies, writes the effective millicharge as $\epsilon\ll 1$1 in a kinetic-mixing model with a dark photon, while also distinguishing a “pure” mCP that carries tiny hypercharge but no accompanying dark photon (Adhikary et al., 13 May 2026, Xu, 2022, Gan et al., 2023).

These realizations motivate different theoretical interpretations. Hidden-sector models with kinetic mixing are standard in vector-portal phenomenology; they appear in dark-matter constructions, string compactifications, and discussions of charge quantization. The “pure” mCP scenario is conceptually distinct because it attributes the tiny charge directly to the particle rather than to a dark-photon sector. This distinction matters cosmologically: a kinetic-mixing mCP can populate a dark-radiation bath, whereas a pure mCP is constrained instead by relic overproduction and baryon scattering in the early universe (Gan et al., 2023).

Mass scales in the literature are correspondingly broad. Forward-LHC studies focus on light mCPs with $\epsilon\ll 1$2; neutrino-beam and collider studies emphasize the MeV–GeV regime; Earth-bound interferometric searches consider $\epsilon\ll 1$3 and up to $\epsilon\ll 1$4; geomagnetic searches target ultralight bosonic mCP dark matter; and decay scenarios at IceCube and Auger analyze relativistic mCPs produced by heavy or superheavy dark matter (Adhikary et al., 13 May 2026, Nugroho, 2024, Arza et al., 24 Jan 2025, Xu, 2024).

2. Production channels across environments

Production mechanisms for mCPs are unusually diverse. At $\epsilon\ll 1$5 colliders, the basic process is

$\epsilon\ll 1$6

with the standard invisible signature arising from

$\epsilon\ll 1$7

Near threshold, non-relativistic production becomes important because the ionization loss scales roughly as $\epsilon\ll 1$8, making direct tracker-based searches viable in a narrow mass window around $\epsilon\ll 1$9 (Liang et al., 2019, Gorbunov et al., 2022).

In hadronic environments, neutral-meson decays are central. Light-mass studies repeatedly use

$10^{-18}-3.5\times10^{-17}\,\text{eV}$0

while atmospheric and fixed-target analyses extend the meson set to $10^{-18}-3.5\times10^{-17}\,\text{eV}$1. For GeV-scale atmospheric mCPs, proton bremsstrahlung and Drell–Yan become necessary additions: one study finds that MCPs with masses below a GeV primarily arise from proton bremsstrahlung, while heavier MCPs predominantly originate from heavy meson decays and Drell–Yan (Adhikary et al., 13 May 2026, Magill et al., 2018, Plestid et al., 2020, Wu et al., 2024).

Forward-LHC production has acquired a second layer beyond interaction-point meson decays. A recent HL-LHC analysis identifies secondary production in hadronic and electromagnetic showers initiated by energetic neutral particles striking the TAXN absorber. In that framework, hadronic showers generate secondary $10^{-18}-3.5\times10^{-17}\,\text{eV}$2, while electromagnetic showers generate large $10^{-18}-3.5\times10^{-17}\,\text{eV}$3 populations that produce mCPs through annihilation on bound electrons,

$10^{-18}-3.5\times10^{-17}\,\text{eV}$4

and through bremsstrahlung on nuclei,

$10^{-18}-3.5\times10^{-17}\,\text{eV}$5

For the proposed FORMOSA detector, this secondary component enhances the expected signal yield by approximately $10^{-18}-3.5\times10^{-17}\,\text{eV}$6 for $10^{-18}-3.5\times10^{-17}\,\text{eV}$7, and becomes even more important for larger transverse acceptance (Adhikary et al., 13 May 2026).

Dark-matter decay provides another production class. In solar and terrestrial scenarios, heavy dark matter $10^{-18}-3.5\times10^{-17}\,\text{eV}$8 captured in the Sun or Earth decays through

$10^{-18}-3.5\times10^{-17}\,\text{eV}$9

yielding relativistic mCPs with $10^{-15}-10^{-14}\,\text{eV}$0. At much higher energies, superheavy dark matter with $10^{-15}-10^{-14}\,\text{eV}$1 mass can likewise decay to mCPs detectable at the Pierre Auger Observatory (Xu, 2022, Xu, 2024, Xu, 2024). A cosmological variant is the cosmic millicharge background produced from the Standard Model thermal bath during reheating; in that setting, the mCP abundance itself becomes a probe of reheating temperature (Gan et al., 2023).

3. Detection principles

Because mCP interactions scale with $10^{-15}-10^{-14}\,\text{eV}$2, detector concepts are organized around a common question: whether to exploit tiny ionization, rare scattering, coherent phase shifts, or macroscopic field effects. In scintillator-based far-forward detectors, the mean energy loss obeys a Bethe–Bloch-like scaling,

$10^{-15}-10^{-14}\,\text{eV}$3

and the signal is a few-photoelectron coincidence across multiple layers. For the benchmark FORMOSA geometry, the single-particle detection probability is modeled with independent Poisson statistics across four BC-408 scintillator layers (Adhikary et al., 13 May 2026).

Near-threshold $10^{-15}-10^{-14}\,\text{eV}$4 collider searches exploit the complementary regime in which small $10^{-15}-10^{-14}\,\text{eV}$5 compensates small $10^{-15}-10^{-14}\,\text{eV}$6. In a c–$10^{-15}-10^{-14}\,\text{eV}$7 factory drift chamber, the number of ionization events in a path length $10^{-15}-10^{-14}\,\text{eV}$8 scales as $10^{-15}-10^{-14}\,\text{eV}$9, and the search can be made effectively background-free by requiring at least $\chi$0 lit cells from an mCP pair. The resulting signature is direct observation of sparse but geometrically correlated hits rather than missing energy (Gorbunov et al., 2022).

Large neutrino detectors use scattering. For electron scattering in beam and atmospheric searches, the differential cross section behaves as

$\chi$1

so sensitivity is driven by low recoil thresholds. This is the basis of LSND, MiniBooNE, SBN, DUNE, Super-K, and JUNO reinterpretations, including multiple-scatter signatures in JUNO where one mCP can generate several correlated low-energy electron recoils during a single detector transit (Magill et al., 2018, Plestid et al., 2020, Wu et al., 2024).

IceCube and Auger instead use deep inelastic scattering on nuclei. In solar and Earth-core scenarios, relativistic mCPs produce cascade-like events in ice, analogous to neutrino-induced cascades but sourced by $\chi$2 electromagnetic DIS. At Auger, upward-going EeV mCPs traversing the Earth can interact in the atmosphere and produce fluorescence-detectable air showers (Xu, 2022, Xu, 2024, Xu, 2024).

A separate experimental branch searches for non-relativistic or Earth-bound mCPs. Precision optomechanical charge sensing with optically levitated SiO$\chi$3 spheres searches for stable mCPs electrostatically bound to nuclei inside bulk matter. Interferometric proposals use the phase shift of photons in a vertical arm passing through Earth-bound mCP populations, with one study proposing a single-arm unconventional interferometer and another a Mach–Zehnder interferometer. At the opposite extreme, ultralight bosonic mCP dark matter can induce a monochromatic quasi-static magnetic-field signal in the geomagnetic background with angular frequency twice the mCP mass (Afek et al., 2020, Nugroho, 2024, Chen et al., 2022, Arza et al., 24 Jan 2025).

4. Experimental landscape and representative exclusions

Collider limits cover several complementary regions. Monophoton searches at GeV-scale $\chi$4 colliders probe previously unexplored MeV–GeV parameter space: BaBar reaches $\chi$5 for $\chi$6, BESIII reaches $\chi$7 for $\chi$8, Belle II reaches $\chi$9 for $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$0, and STCF is projected to reach $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$1 for $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$2 (Liang et al., 2019). A distinct direct-observation strategy at c–$Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$3 factories can probe the charge down to $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$4 of the electron charge for MCP masses in an $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$5 MeV vicinity of each beam value where the factory collects $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$6 in one year; the same study states that this mass region is unreachable with single-photon missing-energy searches (Gorbunov et al., 2022).

Fixed-target and neutrino experiments dominate important MeV–GeV windows. Existing neutrino data provide new and leading constraints in $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$7 for LSND and $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$8 for MiniBooNE, while SBND and MicroBooNE are projected to provide leading bounds in the $Q_\chi=\epsilon e,\qquad \epsilon\ll 1.$9 range and DUNE and SHiP can probe $\chi$0 significantly beyond existing bounds (Magill et al., 2018). Reinterpreting cosmic-ray production, Super-K gives the best sensitivity reach for $\chi$1 and remains competitive with accelerator-based searches up to $\chi$2 (Plestid et al., 2020). For heavier atmospheric mCPs, JUNO multiple-scatter searches can be sensitive to milli-charges up to an order of magnitude beyond current constraints for MCP masses between $\chi$3 and $\chi$4 (Wu et al., 2024).

Neutrino telescopes and ultrahigh-energy observatories probe more model-specific but much higher-energy scenarios. In the solar IceCube study, the region

$\chi$5

is ruled out at $\chi$6 C.L. with six years of data (Xu, 2022). For Earth-core production from heavy dark matter, one analysis excludes

$\chi$7

while a later treatment with a running electromagnetic coupling excludes

$\chi$8

with 10 years of IceCube data (Xu, 2024, Xu, 24 Nov 2025). At still higher energies, Auger FD data exclude

$\chi$9

in a superheavy-dark-matter decay scenario (Xu, 2024).

Searches for Earth-bound or condensed-matter mCPs cover a qualitatively different domain. Optomechanical charge sensing improves sensitivity to the abundance of mCPs bound to matter by roughly two orders of magnitude relative to previous searches and reaches $U(1)_D$0 mCPs per nucleon for fractional charges $U(1)_D$1 (Afek et al., 2020). Interferometric proposals estimate sensitivity to $U(1)_D$2 as low as $U(1)_D$3 for $U(1)_D$4 when the number density is larger than $U(1)_D$5, and as low as $U(1)_D$6 to $U(1)_D$7 over $U(1)_D$8 to $U(1)_D$9 provided that the mCP number density is greater than $U(1)'$0 (Chen et al., 2022, Nugroho, 2024). For ultralight bosonic mCP dark matter, geomagnetic recasts of SuperMAG and SNIPE Hunt constrain the effective charge in the mass ranges $U(1)'$1 and $U(1)'$2, with bounds surpassing stellar cooling constraints by more than ten orders of magnitude and, for SuperMAG, by more than seventeen orders of magnitude (Arza et al., 24 Jan 2025).

5. Cosmology, dark matter, and terrestrial accumulation

mCP cosmology is strongly scenario-dependent. In reheating-based analyses, a “pure” mCP without an accompanying dark photon is constrained by overproduction and by mCP–baryon interactions, whereas a kinetic-mixing mCP with a massless dark photon is constrained by $U(1)'$3 generated through dark radiation. In both cases, the cosmic millicharge background produced from the Standard Model thermal bath during reheating can be used to identify regions where accelerator experiments probe reheating scenarios, and the resulting bounds can potentially set an upper bound on the reheating temperature down to $U(1)'$4 (Gan et al., 2023).

The abundance dependence of cosmological limits is not uniform across the literature. One bound-state study explicitly notes that cosmological constraints become much weaker for $U(1)'$5, while the solar IceCube scenario finds $U(1)'$6, comfortably below Planck’s bound $U(1)'$7 (Afek et al., 2020, Xu, 2022). This separation between abundance-dependent cosmological limits and abundance-independent laboratory production is central to current mCP phenomenology.

Terrestrial accumulation introduces another layer. Earth-bound mCP dark matter studies assume that captured particles can reach local underground densities

$U(1)'$8

much larger than the corresponding virial density, and then use optical phase shifts to search for them (Nugroho, 2024). A related Mach–Zehnder proposal emphasizes the same heavy-mass regime $U(1)'$9 and derives sensitivities from the phase shift of photons in one underground arm (Chen et al., 2022).

In matter-bound searches, the issue is not transit but electrostatic binding. For negatively charged mCPs bound to nuclei in SiO$$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$0, a hydrogenic approximation gives the ground-state binding energy

$$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$1

while screening becomes important when the orbit exceeds the atomic K-shell scale, leading to the condition

$$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$2

This defines the region in $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$3 space where stable bound states with matter are expected and can be sought experimentally (Afek et al., 2020).

6. Conceptual issues, misconceptions, and current directions

A recurring misconception is that mCP phenomenology is exhausted by one benchmark signature, usually monophoton plus missing energy. Recent work shows that this is too narrow. At $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$4 colliders, direct observation of sparse ionization in trackers becomes relevant for non-relativistic threshold production and covers a mass region inaccessible to missing-energy searches (Gorbunov et al., 2022). At the HL-LHC, forward sensitivity estimates that neglect secondary production in downstream absorbers can materially underestimate the mCP flux: the TAXN study argues that secondary production in downstream infrastructure is an essential ingredient for realistic sensitivity projections and new-physics searches (Adhikary et al., 13 May 2026).

A second misconception is that all strong mCP bounds are either purely cosmological or purely laboratory-driven. The literature instead exhibits a sharp division. Collider, beam-dump, forward, and cosmic-ray production searches are laboratory constraints independent of cosmological initial conditions, while relic-abundance, $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$5, and baryon-scattering limits depend on the early-universe history, on whether the mCP is accompanied by a dark photon, and on whether it constitutes a significant fraction of dark matter (Plestid et al., 2020, Gan et al., 2023). This suggests that experimental interpretation must remain model-explicit even when the charge parametrization $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$6 is identical.

A third issue is transport and environment modeling. Forward-LHC studies quantify generator dependence through EPOS-LHC, QGSJET-II, SIBYLL, and forward-tuned Pythia 8, and note that a full map of LHC magnetic fields would refine flux predictions (Adhikary et al., 13 May 2026). Atmospheric heavy-mCP analyses emphasize approximations in proton bremsstrahlung and detector-threshold modeling, while interferometric and Earth-bound proposals inherit uncertainties from capture, diffusion, and underground density profiles (Wu et al., 2024, Chen et al., 2022). A plausible implication is that progress in mCP searches will depend not only on increased exposure but also on more realistic environment-specific simulations.

The present direction of the field is therefore multipronged rather than convergent on a single optimal strategy. Far-forward detectors, neutrino experiments, dedicated scintillator arrays, optomechanical charge sensors, interferometers, and global magnetometer networks are probing different regions of $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$7 and, in some cases, different theoretical notions of what an mCP is. The topic is unified by the simple parameter $$\mathcal{L}\supset -\frac14 F'_{\mu\nu}F'^{\mu\nu}-\frac{\kappa}{2}F'_{\mu\nu}F^{\mu\nu}-g_DA'_\mu\bar\chi\gamma^\mu\chi,$$8, but its modern research program is defined by the fact that the same small charge can manifest through ionization, electron scattering, deep inelastic cascades, coherent optical phase shifts, bound-state chemistry, or geomagnetic conversion, depending on the environment and on the ultraviolet origin of the millicharge.