Probing millicharged particles with NA64$\mu$ and LDMX

Millicharged particles emerge as compelling candidates in numerous theoretically well-motivated extensions of the Standard Model. These hypothetical particles, characterized by an electric charge that is a small fraction of the elementary charge, have attracted significant attention in contemporary experimental physics. Their potential existence motivates dedicated search strategies across multiple experimental platforms, leveraging their distinctive electromagnetic interactions while evading conventional detection methods. In the present paper we estimated the projected sensitivity of fixed-target experiments, specifically NA64$\mu$ and LDMX, to the parameter space of millicharged particles. For the NA64$\mu$ experiment, with an anticipated muon flux of $\mbox{MOT}\lesssim 10^{14}$, our analysis reveals a detectable mass window of $10~\mbox{MeV} \lesssim m_\chi \lesssim 150~\mbox{MeV}$ and charge parameter range $10^{-4} \lesssim \epsilon \lesssim 7\times 10^{-4}$. This sensitivity arises from the bremsstrahlung-like missing energy signature $\mu N \to \mu N \gamma^{*}( \to \chi \bar{\chi})$. Furthermore, we evaluate the discovery potential of the LDMX facility, considering its projected electron beam statistics, $\mbox{EOT}\lesssim 2\times 10^{16}$, and energy, $E_{\rm e}\simeq 8~\mbox{GeV}$. Our results demonstrate that LDMX can probe heavier MCPs in the mass range $250~\mbox{MeV} \lesssim m_\chi \lesssim 400 ~\mbox{MeV}$, with sensitivities reaching $10^{-3} \lesssim \epsilon \lesssim 1.5 \times 10^{-3}$. This parametric window can be accessible through the distinctive invisible decay channel $\rho \to \chi \bar{\chi}$, where $\rho$-meson photo-production $\gamma N \to N \rho$ plays a pivotal role.