Probing millicharged particles with NA64$μ$ and LDMX

TL;DR

This work investigates millicharged particles (MCPs) with charge $Q_\chi = e \epsilon$, leveraging kinetic-mixing realizations with a dark photon to map constraints in the $(\epsilon, m_\chi)$ plane. It develops exact-tree-level cross sections for MCP production in lepton-nucleus interactions using CalcHEP and applies them to two fixed-target facilities, NA64$\mu$ and LDMX, via bremsstrahlung-like processes $l N \to l N \gamma^*(\to \chi \bar\chi)$ and vector-meson decays $V \to \chi \bar\chi$. The results show NA64$\mu$ can probe $10~\mathrm{MeV} \lesssim m_\chi \lesssim 150~\mathrm{MeV}$ with $10^{-4} \lesssim \epsilon \lesssim 7\times 10^{-4}$, while LDMX can reach $250~\mathrm{MeV} \lesssim m_\chi \lesssim 400~\mathrm{MeV}$ and $10^{-3} \lesssim \epsilon \lesssim 1.5\times 10^{-3}$ via an invisible $\rho$ decay channel and bremsstrahlung-like production, benefiting from high electron-on-target statistics. These complementary probes extend MCP constraints in a region relevant for dark sector phenomenology and illustrate the importance of background control (down to $b \lesssim 1$) in lepton missing-momentum searches.

Abstract

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$μ$ and LDMX, to the parameter space of millicharged particles. For the NA64$μ$ experiment, with an anticipated muon flux of $\mbox{MOT}\lesssim 10^{14}$, our analysis reveals a detectable mass window of $10~\mbox{MeV} \lesssim m_χ\lesssim 150~\mbox{MeV}$ and charge parameter range $10^{-4} \lesssim ε\lesssim 7\times 10^{-4}$. This sensitivity arises from the bremsstrahlung-like missing energy signature $μN \to μN γ^{*}( \to χ\barχ)$. 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 $250~\mbox{MeV} \lesssim m_χ\lesssim 400 ~\mbox{MeV}$, with sensitivities reaching $10^{-3} \lesssim ε\lesssim 1.5 \times 10^{-3}$. This parametric window can be accessible through the distinctive invisible decay channel $ρ\to χ\barχ$, where $ρ$-meson photo-production $γN \to N ρ$ plays a pivotal role.

Figures (5)

• Figure 1: Feynman diagrams describing bremsstrahlung-like signature for the MCPs pair production $l N \to l N \gamma^* (\to \chi \bar{\chi})$.
• Figure 2: The differential cross sections of the process $l N \to l N \gamma^* (\to \chi \bar{\chi})$ as function of the missing energy $E_{\rm miss}=E_{\chi}+E_{\bar{\chi}}$ for the set of MCP masses. Left panel shows the typical spectra for LDMX experiment with electron beam energy of $E_{\rm e} \simeq 8~\hbox{GeV}$. Right panel is the differential cross section for the NA64$\mu$ experiment, with muon beam energy of $E_\mu \simeq 160~\hbox{GeV}$. We set $\epsilon=1$.
• Figure 3: The plot shows the total number of mCPs produced versus their mass for both NA64$\mu$ and LDMX, with the charge fraction chosen to be $\epsilon=1$. The MCPs are produced in bremsstrahlung-like reactions and various meson decays. At the NA64$\mu$ facility, the dominant production mechanism is virtual photon emission $\gamma^* \to \chi \bar{\chi}$ (red solid line). At the LDMX experiments, the MCPs are produced through the bremsstrahlung-like channel $\gamma^*\to \chi \bar{\chi}$ (dark green), rho meson $\rho \to \chi \bar{\chi}$ (brown solid line), omega meson $\omega \to \chi \bar{\chi}$ (yellow solid line), and phi meson decay $\phi \to \chi \bar{\chi}$ (violet solid line). The resulted number of MCPs produced at the LDMX is also shown (blue solid line).
• Figure 4: Total cross section of MCPs production as a function of $m_{\chi}$ for both the lepton missing momentum experiments, implying that $\epsilon=1$. We integrate the cross sections over the experimental cut range $x_{\rm th} \lesssim x \lesssim x_{\rm max}$. Red solid line is the cross section for the NA64$\mu$ experiment, blue solid line corresponds to the LDMX fixed target facility,
• Figure 5: The expected experimental reach of the NA64$\mu$ (red solid lines) and LDMX (blue solid lines) fixed target facilities in the $(\epsilon, m_\chi)$ plane. For the LDMX experiment, we take into account invisible decays of vector mesons to MCPs, $V\to \chi \bar{\chi}$, and MCP production by energetic beam electrons via the bremsstrahlung-like channel $\gamma^*\to \chi \bar{\chi}$. The projected limits, for an ultimate prospect statistics of $\hbox{EOT}=2\times 10^{16}$ and $10^{16}$ in the MCP mass range $10~\hbox{MeV}\lesssim m_{\chi} \lesssim 1~\hbox{GeV}$, correspond to backgrounds of $b\simeq 1$ and $b=0$, respectively. We also show the expected reach of NA64$\mu$ for prospect statistics of $\hbox{MOT}= 10^{14}$ and $5\times 10^{13}$, implying the virtual photon dominated channel of MCP production, $\gamma^* \to \chi \bar{\chi}$. Both of these scenarios imply a finite background of $b\simeq 1$ for the NA64$\mu$. The limits based on data of LSND LSND:2001akn, SLAC Prinz:1998ua, BEBC Marocco:2020dqu, and SENSEI SENSEI:2023gie are shown by grey shaded region (these bounds don't imply the MCP to be a DM or its fraction). All constraints are set at 95% CL. The shaded brown region is excluded by present direct detection experiments as shown in Ref. Emken:2019tni (see text). The green solid lines correspond to the millicharged dark matter explaining the EDGES anomaly Ref. Liu:2019knx. We emphasize, that our sensitivity of LDMX for bremsstrahlung like channel $e N \to e N \gamma^* (\to \chi \bar{\chi})$ is in a reasonable agreement with previous study of the authors Ref. Berlin:2018bsc.