Underground Production of Electromagnetic Dark States by MeV-scale Electron Beams and Detection with CCDs

TL;DR

This work addresses the detection of new light dark-sector fermions χ with millicharge or EM form factor couplings using underground MeV-scale electron beams and silicon CCD detectors. It combines analytic four-body phase-space treatment and numerical cross sections for χ production via electron-electron bremsstrahlung with a detailed bound-electron detection framework that incorporates dielectric screening, plasmon effects, and electron-hole yield in silicon. The authors derive projections for millicharged particles, identifying an unconstrained parameter window near $m_χ\sim$ keV–MeV that could be probed with $N_{\mathrm{EOT}}$ up to $10^{22}$ and a DAMIC-M–like CCD setup, while EM form-factor signals yield smaller rates at $E_2=100$ MeV; MDM/EDM could become observable with higher beam energy or exposure, whereas AM/CR remain challenging. A key methodological contribution is the analytic treatment of the four-body phase space for bremsstrahlung-induced χ pair production, enabling precise predictions for underground accelerator–CCD experiments and providing a complementary approach to higher-energy searches.

Abstract

In this work we explore the possibility of new light fermionic particles with millicharge or electromagnetic form factor interactions and their underground production via an electron beam in the 100 MeV range and their subsequent detection using a CCD-sensor. We evaluate the S-matrix elements and the phase spaces for production analytically, and then calculate the corresponding cross sections numerically. For millicharged fermions this set-up could be able to probe a window in parameter space, yet unconstrained by direct detection experiments. The electric or magnetic dipole moment of a light fermion could feasibly be probed with enough beam time or an increased beam energy.

Figures (12)

• Figure 1: Production of $\chi\bar{\chi}$ pairs from a photon emitted by an outgoing electron. The $k_{\gamma,n}$ and $k_{e,n}$, with ${n\in\{a,b,c,d\}}$, represent the momenta for each diagram indexed by $n$.
• Figure 2: Total cross section for $\chi\bar{\chi}$ pair production from $e^- e^-$ scattering for all interactions considered, relative to the a reference cross section $\hat{\sigma}_{\text{tot}}$ of the same interaction type. The left panel shows the mass dependence of the production cross section at an energy of the incoming electron of $E_2 = 100$ MeV relative to a reference value $\hat{\sigma}_{\text{tot}}(m_{\chi,\text{ref}})$ at $m_{\chi,\text{ref}}=1$ keV. The weakening sensitivity to mass with the increasing order of the operators can be seen. The right panel shows the dependence of the production cross section on the energy of the incoming electron $E_2$ of a particle with mass $m_{\chi}=1$ MeV relative to a reference value $\hat{\sigma}_{\text{tot}}(E_{2,\text{ref}})$ at $E_{2,\rm ref}=1$ GeV. It shows that with increasing operator dimension, the energy scaling becomes more pronounced. Additionally, the operators containing $\gamma^5$ display a steeper fall-off at low input energies. See Tab. \ref{['tab:ref']} for the values of the reference cross sections.
• Figure 3: Differential cross section for the creation of two to seven charges with respect to the recoil energy deposited into electrons by millicharged $\chi$ of energy $E_{\chi}=5$ MeV and mass $m_{\chi}=1$ keV. The left panel shows the values for free electron-$\chi$ scattering and its sum given by the black solid line. The right panel shows the results using an ab-initio electron-loss function of silicon Dreyer:2023ovn. The black line there is the (Gaussian-smoothed) sum of bins. Noticeable is the peak at the plasmon resonance frequency for 4 to 5 electron events and the overall larger cross section on the right side compared to the simpler, free-electron case; the latter is shown for better comparison by the dashed grey line.
• Figure 4: Heat map of the normalised production cross section $\sigma_{\rm prod}^{-1} d^2\sigma_{\rm prod}/dE_\chi d\cos\theta_\chi$ in units of $\rm MeV^{-1}$ shown as a function of the final state $\chi$-energy $E_\chi$ and production angle $\theta_\chi$ for a millicharged particle of mass $m_\chi = 1~{\rm MeV}$; the beam energy is $E_2=100$ MeV. Note that the y-scale is displayed in degrees for the ease of readability and that the distribution is symmetric for negative values $\theta<0$. The dominant angular region is between $0^\circ$ to $2^\circ$ and peaks at energies of around 50 MeV. This is expected for highly relativistic processes, since the particles are boosted into the beam line. The thick red-dashed lines indicate the kinematically forbidden regions.
• Figure 5: Projected constraints using the set-up described here for a millicharged particle in the 1 keV to 1 MeV range for a 100 MeV beam. The red line shows the exclusion limits for $10^{20}$ electrons on target, the blue one for $10^{22}$ electrons on target. The dashed lines describe the background-free case. The open parameter window of millicharge is taken from An:2021qdl. The indirect constraints are from red giants (RG) Vogel:2013raa, SN1987A Chang:2018rso and ortho-positronium decay (OPOS) Badertscher:2006fm. The direct detection constraints are from SLAC Prinz:1998ua, as well as SENSEI SENSEI:2020dpa and DAMIC DAMIC:2019dcn, which disappear above $\varepsilon\sim10^{-5}$ as indicated by the hatching Emken:2019tniAn:2021qdl.