McLight: Probing MCPs & Dark Photon Portals

• McLight is a set of experimental methodologies that search for millicharged particles and light dark matter using beam-dump, fixed-target, and LSW setups, reinterpreting the SLAC mQ experiment.
• It leverages kinetic mixing between the standard photon and a dark photon to generate effective small charges, enabling detection channels beyond traditional neutrino and direct detection experiments.
• Future upgrades—such as increased electron exposure, refined detector acceptance, and enhanced background rejection—promise to extend exclusion limits and fully probe parameter space linked to dark photon models and the (g-2)μ anomaly.

McLight refers both to experimental programs and to methodologies in the search for millicharged particles (MCPs) and sub-GeV dark matter through beam-dump, fixed-target, and related laboratory probes. The term is historically associated with the reinterpretation and potential upgrading of the SLAC mQ beam-dump experiment for MCP and light dark matter searches, and more broadly applies to new in situ probes exploiting electromagnetic interactions suppressed by small effective charges. McLight methodologies are pivotal for exploring parameter space inaccessible to neutrino detectors, direct detection, or astrophysical bounds, especially for kinetically mixed dark photon scenarios and their associated millicharged relics (Diamond et al., 2013, Berlin et al., 2023, Fung et al., 2023).

1. Theoretical Framework: Millicharges and Dark Photons

The central models in McLight studies involve extensions of the Standard Model (SM) by an additional gauge boson $A'_\mu$ associated with a hidden U(1)$_D$ gauge symmetry. Kinetic mixing between $A'_\mu$ and the SM photon $A_\mu$ is parametrized by a small dimensionless mixing parameter $\varepsilon$. The relevant Lagrangian terms (in the gauge basis) are

$$\mathcal{L} \supset -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} - \frac{1}{4}F'_{\mu\nu}F'^{\mu\nu} - \frac{\varepsilon}{2}F_{\mu\nu}F'^{\mu\nu} + \frac{m_{A'}^2}{2}A'_\mu A'^\mu + e_D A'_\mu \bar\chi\gamma^\mu\chi$$

where $F_{\mu\nu}$ and $F'_{\mu\nu}$ are the field strengths of the photon and dark photon, $e_D$ is the dark charge, $\chi$ is a Dirac fermion (the dark matter candidate), and $m_{A'}$ is the dark photon mass. After basis rotation and normalization, the dark photon $A'$ acquires couplings $\varepsilon e$ to the electromagnetic current $J_{\rm EM}^\mu$, and $e_D$ to the dark current $\bar\chi\gamma^\mu\chi$.

This setup generates effective SM charges for the dark fermion: $\epsilon_{\rm eff} = \varepsilon e_D/e$. In massless $A'$ scenarios, this leads to MCPs under the visible photon; for $A'$ massive (dark photon portal), new production and detection channels become available. These theoretical constructs underpin all McLight experimental sensitivities (Diamond et al., 2013, Berlin et al., 2023).

2. The SLAC mQ/“McLight” Beam-Dump Program

The SLAC mQ experiment (“McLight”) was initially designed for direct MCP searches, but has been reinterpreted as an incisive probe of sub-GeV dark matter produced via dark photon portals. In this approach, a high-energy electron beam (29.5 GeV, $1.35$ C, $\sim8.4\times10^{18}$ electrons) is dumped on tungsten, producing dark photons by radiative processes analogous to bremsstrahlung: $e^-(E_0) + N(Z) \to e^- + N + A'$ The differential cross section (Weizsäcker–Williams approximation) is

$$\frac{d\sigma}{dx} \approx \frac{8 Z^2 \alpha_{\rm EM}^3 \varepsilon^2}{3 m_{A'}^2} x \left[3 + \frac{x^2}{1-x}\right] \log[\mathcal{O}(10)]$$

with $x = E_{A'}/E_0$. For $2m_\chi < m_{A'}$, $A'$ decays dominantly to $\chi\bar\chi$, which propagate through shielding and are detected via coherent scattering on carbon nuclei in a scintillator. The elastic $\chi$-nucleus cross-section is

$$\frac{d\sigma}{dT} \approx \frac{8\pi \alpha_{\rm EM} \alpha_D \varepsilon^2 Z^2 M}{(m_{A'}^2 + 2 M T)^2}$$

where $M$ is the nuclear mass and $T$ the recoil energy. The experimental background and single-photon sensitivity limit the statistical relevance; 2$\sigma$ exclusion curves are produced by comparing predicted signal rates with background (Diamond et al., 2013).

3. Parameter Space Constraints and Sensitivity Enhancement

The McLight reinterpretation yields competitive exclusion limits on $\varepsilon$ for $m_{A'}$ in the 30–200 MeV range. Without background suppression, $\varepsilon \gtrsim {\rm few} \times 10^{-3}$ is excluded, and pulse-height cuts refine the sensitivity to $\varepsilon \gtrsim 10^{-3}$–${\rm few} \times 10^{-4}$ over 30–160 MeV.

Enhancements suggested for future McLight-like efforts include:

• Increasing total electron exposure (e.g., $10^{22}$ e$^-$ on target), linearly improving production probability.
• Expanding detector solid angle and acceptance, mitigating cosmic and beam-related backgrounds.
• Pulse-height discrimination and neutron vetoing, lowering noise floor by 10–100$\times$.
• Optimizing dump geometry and materials.

Such improvements would permit testing of virtually the entire parameter space favored by the $(g-2)_\mu$ anomaly in dark photon models (Diamond et al., 2013).

4. Complementarity with Astrophysical and Laboratory Probes

Astrophysical bounds on MCPs, notably from stellar evolution, impose strong constraints for low-mass MCPs. The most stringent such limit currently derives from modeling the tip of the red giant branch (TRGB) luminosity:

• For $m_\chi \ll \omega_{p, {\rm core}}$ (core plasma frequency, $\sim$keV), the constraint is $q < 6.3 \times 10^{-15}$.
• Limits weaken exponentially for higher $m_\chi$ due to phase-space closing and Boltzmann suppression.

These bounds are robust due to the insensitivity of TRGB luminosity to standard stellar modeling uncertainties. The McLight approach tests regions not accessible to stellar cooling, especially for higher $m_\chi$ and moderate $\varepsilon$ (Fung et al., 2023).

Laboratory-based direct detection limits (e.g., XENON10) for light $\chi$ are improved upon by McLight by up to an order of magnitude for $m_\chi \lesssim 20$ MeV. Future direct-deflection proposals and light-shining-through-wall (LSW) experiments (see below) complement McLight by probing both lower and higher mass/charge regimes (Berlin et al., 2023).

5. Light-Shining-Through-Wall Sensitivity to MCPs

McLight's scope includes new LSW-type setups, in which a background of MCP dark matter enables electromagnetic signals to “shine through” a conducting barrier between high-Q radiofrequency cavities. The key observables are:

• Induced currents/resonant excitation in the receiver cavity, calculated from the MCP number density $n_\chi$, mass $m_\chi$, and effective charge $\epsilon_{\rm eff}$.
• Signal power in the receiver, $$P_{\rm sig} \propto (\epsilon_{\rm eff} e e' n_\chi / m_\chi)^4$$ for both TM$_{010}$ and TE$_{011}$ modes.

A salient feature is the terrestrial enhancement of $n_\chi$: For $$\epsilon_{\rm eff} \gtrsim 10^{-7} (m_\chi/1\,{\rm GeV})^{1/2}$$, MCPs thermalize and accumulate in the Earth’s crust, yielding $n_\chi \gg n_{\rm gal}$. Sensitivities can therefore surpass those from astrophysical and collider searches, with projected bounds reaching $\epsilon_{\rm eff} \lesssim 10^{-6}$–$10^{-7}$ for $n_\chi \gtrsim 10^3\,{\rm cm}^{-3}$ and $m_\chi \sim$ MeV–GeV (Berlin et al., 2023).

6. Implications and Experimental Outlook

McLight methodologies, by expanding fixed-target, beam-dump, and resonance-cavity probes to sub-GeV MCP and dark photon models, systematically advance the exploration of weakly-coupled hidden sectors. Key findings include:

• The TRGB luminosity constraint $q < 6 \times 10^{-15}$ for $m_\chi \lesssim 100$ eV is the leading stellar bound (Fung et al., 2023).
• SLAC mQ/McLight beam-dump data exclude a significant portion of the $(g-2)_\mu$ motivated region, with future upgrades covering essentially all simple dark photon scenarios in the 30–200 MeV $m_{A'}$ domain (Diamond et al., 2013).
• LSW experiments exploiting collective plasma responses of terrestrial MCP backgrounds access parameter regions denied to standard recoil searches and cosmic/astrophysical analyses (Berlin et al., 2023).

A plausible implication is that modest improvements to McLight-like experimental setups—including higher luminosity, refined background rejection, and advanced cavity techniques—could close much of the viable parameter space for minimal dark photon portals and MCPs underpinning proposed extensions of the Standard Model.