Constraints on millicharged particles from nuclear gamma-decays

This paper establishes the strongest current constraints on millicharged particles with masses between 0.7 and 2 MeV by identifying overlooked $\gamma$-cascade sources in nuclear reactors and deriving new limits from electron recoil data, while also assessing sensitivity from solar production in low-threshold dark matter experiments.

The Gist

Imagine the Standard Model of physics as a perfectly tuned orchestra playing a symphony we can hear and understand. But physicists suspect there's a "dark sector"—a hidden orchestra playing in a different key, with instruments we can't see. One of the most intriguing hypothetical instruments in this hidden orchestra is the Millicharged Particle (MCP). Think of an MCP as a ghostly electron: it has a tiny, almost invisible electric charge, far weaker than a normal electron's, making it incredibly hard to catch.

This paper is like a detective story where the authors go back to a crime scene they thought they had already solved: nuclear reactors.

The Old Theory: A Leaky Faucet

Previously, scientists thought nuclear reactors produced these ghostly particles mostly through a process like a "leaky faucet." When high-energy photons (light particles) bounce off electrons, they might occasionally leak out a pair of MCPs. However, this method has a limit. If the MCPs are too heavy (like trying to push a heavy boulder through a small hole), the faucet stops dripping. This meant previous studies could only rule out very light MCPs.

The New Discovery: A Firehose

The authors of this paper realized they missed a massive source of these particles. They looked at what happens inside a reactor when a neutron gets captured by an atomic nucleus.

Imagine a nucleus as a excited child jumping up and down. When it finally calms down (de-excites), it usually releases a burst of energy as a gamma ray (a high-energy photon). The authors realized that every time this happens, there's a chance the nucleus could "spit out" a pair of MCPs instead of, or in addition to, the photon.

This is a game-changer. It's like realizing that while the faucet was leaking a little water, there was actually a firehose spraying water right next to it. Specifically, they focused on a specific type of nuclear reaction involving Uranium-239. This reaction produces gamma rays with enough energy to create much heavier MCPs than previously thought possible.

The Hunt: Catching the Ghosts

So, how do you catch a ghost that barely interacts with anything? You look for the "kick."

When an MCP flies through a detector (like a tank of liquid or a crystal), it might bump into an electron inside an atom. Because the MCP has a tiny charge, it gives the electron a gentle nudge, knocking it loose. This creates a tiny electrical signal.

• The Analogy: Imagine trying to hear a whisper in a noisy room. If you know exactly when the whisper should happen (near the reactor) and you have a super-sensitive microphone (a low-threshold detector), you might hear it.
• The Result: By recalculating how many MCPs are being produced by this "firehose" (the nuclear de-excitation) and comparing it to the silence in the detectors (specifically the TEXONO experiment), the authors set new, stricter rules. They effectively said, "If these particles exist with a mass between 0.7 and 2 MeV, their charge must be even smaller than we thought." They found the strongest limits to date in this specific weight range.

Other Sources: The Sun and the Earth

The paper also looked at other places where these particles might be hiding:

1. The Earth's Crust: Just like the reactor, the Earth has natural radioactive elements (like Uranium and Thorium) that act as tiny, natural reactors. However, because the Earth is thick, these particles lose energy as they travel through rock, making them harder to detect far away.
2. The Sun: The Sun is a giant nuclear furnace. It produces a massive flood of these particles. However, the Sun is also a thick soup of matter. If the particles have even a tiny bit of charge, the Sun's material acts like a thick fog, slowing them down and trapping them. The authors calculated that only the very lightest, fastest particles might escape the Sun to reach Earth, offering a potential signal for future, ultra-sensitive dark matter detectors.

The "Dark Photon" Cousin

Finally, the authors looked at a related character called the Dark Photon. Think of this as a heavy, unstable cousin of the MCP. If the reactor produces a heavy dark photon, it might travel a short distance and then explode into an electron and a positron (a pair of matter and antimatter). The authors checked if existing detectors near reactors could spot these "explosions." While they didn't find new, stronger limits than what already exists, they confirmed that reactors are a valid place to look for these heavy particles.

The Bottom Line

This paper is a reminder that in physics, you never stop looking at the data. By realizing that nuclear reactors produce a much higher "flux" (flow) of these ghostly particles than previously calculated, the authors have tightened the net. They haven't found the particles yet, but they have successfully narrowed down the hiding spots, telling us exactly where not to look next.

Technical Summary

Technical Summary: Constraints on Millicharged Particles from Nuclear $\gamma$-Decays

Problem Statement
Millicharged particles (MCPs), denoted as $\chi$, are hypothetical fermions with an electric charge $Q_\chi = \epsilon e \ll e$. While existing searches for MCPs have utilized electron beam dumps and cosmic-ray interactions, previous constraints on MCPs in the mass range of $\sim 0.7 - 2$ MeV derived from nuclear reactor environments were limited. Specifically, prior analyses (e.g., TEXONO, CONNIE) primarily considered the production mechanism $e + \gamma \to e + \bar{\chi} + \chi$ (bremsstrahlung-like pair production). This mechanism results in a sharp drop in the MCP flux for masses $m_\chi > 0.5$ MeV due to kinematic constraints on electron recoil. The authors identify a gap in the literature: the potential for nuclear de-excitation processes, particularly those involving neutron capture, to emit $\gamma$-rays with energies extending into the several MeV range, thereby allowing for the production of heavier MCP pairs ($2m_\chi < \omega$) that were previously overlooked.

Methodology
The authors develop a comprehensive framework to calculate the flux of MCPs produced in nuclear reactors and natural environments, focusing on the following mechanisms:

1. Reactor Production via Nuclear De-excitation:

   • The study revisits the production of MCP pairs in nuclear reactors, specifically focusing on $\gamma$ cascades from $^{239}\text{U}$ (formed via $^{238}\text{U}(n, \gamma)$) and $^{2}\text{H}$ (from $p(n, \gamma)$).
   • Instead of relying solely on electron-photon scattering, the authors calculate the ratio of the cross-section for off-shell photon emission decaying into an MCP pair ($\gamma^* \to \chi\bar{\chi}$) versus on-shell photon emission ($\gamma$).
   • Using a multipole expansion of nuclear matrix elements, they derive differential ratios for Electric Dipole (E1) and Magnetic Dipole (M1) transitions. The calculation assumes recoil-less processes and utilizes the Photo Absorption Ionization (PAI) model for the detection cross-section, which is more accurate than the Free Electron Approximation (FEA) for low-energy transfers.
   • Key transitions analyzed include the 3.297 MeV and 4.060 MeV E1 transitions from $^{239}\text{U}$ and the 2.223 MeV M1 transition from deuterium.

2. Detection via Atomic Ionization:

   • The detection signal is modeled as the ionization of atomic electrons by incoming MCPs.
   • The differential count rate is calculated by convolving the derived MCP flux with the atomic ionization cross-section (using the PAI model) and the detector mass.
   • Constraints are derived by comparing the predicted signal rate against the background and experimental limits established by the TEXONO collaboration (using a PCGe detector with a 300 eV threshold).

3. Natural and Solar Sources:

   • Geo-background: The authors estimate the MCP flux from natural radioactivity ($^{238}\text{U}$, $^{232}\text{Th}$, $^{40}\text{K}$) in the Earth's crust. They account for energy loss (slow-down) of MCPs as they traverse the Earth, concluding that only MCPs produced within the "Local Crust" (within $\sim 300$ km) are relevant for deep-underground detectors like XENONnT and Borexino.
   • Solar Production: The paper calculates the MCP flux generated in the Sun via various nuclear reactions (e.g., $e^+e^-$ annihilation, $D+p$ fusion, CNO cycle). They analyze the thermalization and slow-down of MCPs within the solar interior, noting that for $\epsilon \gtrsim 10^{-6}$, MCPs may be trapped or thermalized, whereas for $\epsilon < 10^{-7}$, they escape with high energy.

4. Dark Photon Constraints:

   • The formalism is extended to massive dark photons ($A'$) produced in nuclear de-excitations. The authors calculate the production rates for $A'$ and their subsequent decay into $e^+e^-$ pairs, deriving constraints for detectors near reactors and deep underground (e.g., KamLAND).

Key Contributions and Results

• Revised Reactor Flux: The inclusion of nuclear de-excitation channels (specifically $(n, \gamma)$ reactions) significantly increases the predicted MCP flux compared to previous studies that only considered $e+\gamma$ scattering. This opens up the kinematic window for producing MCPs with masses up to $\sim 2$ MeV.
• New Exclusion Limits: By applying the revised flux estimates to TEXONO data, the authors derive the strongest current limits on the millicharge parameter $\epsilon$ in the mass range $0.7 - 2$ MeV. These limits surpass previous constraints from TEXONO, CONNIE, Atucha-II, and SLAC E137 in this specific mass interval.
• Solar and Geo-Flux Estimates:
  • For natural radioactivity, the authors find that while the flux is lower than in reactors, the low-background environment of deep detectors is advantageous. However, energy loss in the crust limits the sensitivity, yielding a tentative bound of $\epsilon \lesssim 10^{-4}$ at $m_\chi \sim 1$ MeV, though this is not a solid independent bound due to uncertainties in crustal composition and energy loss.
  • For solar MCPs, the flux is dominated by positron annihilation for $m_\chi < m_e$ and $D+p$ fusion for higher masses. The paper suggests that future low-threshold experiments (e.g., Oscura, DAMIC-M) could probe $\epsilon \sim 10^{-6}$ or lower, provided the thermalization effects in the Sun are better understood.
• Dark Photon Limits: The study provides the first constraints on visibly decaying dark photons ($A' \to e^+e^-$) derived specifically from near-reactor experiments in the MeV mass range ($1.1 - 4$ MeV). While these limits do not currently exceed existing bounds (e.g., from SLAC or supernova cooling), they offer an independent confirmation. The authors note that far-detector constraints (e.g., KamLAND, JUNO) are currently less stringent but could improve with better energy resolution and background analysis.

Significance and Claims
The paper claims that the primary significance of this work lies in the identification of nuclear $\gamma$-decays (specifically from neutron capture) as a powerful, previously overlooked source of millicharged particles. By incorporating these channels, the authors extend the kinematic reach of reactor-based searches to higher masses ($m_\chi \sim 2$ MeV), establishing the most stringent constraints in this regime to date.

The authors modestly frame their findings regarding natural and solar sources, noting that while the fluxes are calculable, the constraints derived from them are currently limited by uncertainties in energy loss mechanisms (thermalization in the Sun and crust) and detector thresholds. They emphasize that the reactor-based limits are the most robust result of this study. Furthermore, they highlight that the improved energy reach via $(n, \gamma)$ reactions also enables the on-shell production of massive dark photons, providing a new avenue for constraining dark sector models in the MeV scale.

The paper concludes that while these results address the EDGES anomaly parameter space (sub-100 MeV MCPs), the lightest MCPs remain problematic for Big Bang Nucleosynthesis (BBN) predictions, suggesting that additional dark sector physics may be required to reconcile such models with early universe cosmology.