Missing energy signatures of inelastic magnetic dipole DM at NA64e

Abstract

Some extensions of the Standard Model consider inelastic dark matter (iDM) as an attractive candidate for sub-GeV DM of thermal origin that could be detected at modern accelerators. In the present paper, we calculate the production rate of iDM pairs $χ_{1} \barχ_0$ interacting with the ordinary photon via dipole magnetic moment in the reaction of high-energy electron scattering on nuclei, $e^- N \to e^- N χ_{1} \barχ_0$, in the NA64e experiment at the CERN SPS. We derive the projected sensitivity of NA64e to such particles assuming of $\simeq10^{13}$ 100 GeV electrons on target. We also show, that incorporating heavy vector meson decays, $γ^* N \to N V (\to χ_1 \barχ_0)$, alongside bremsstrahlung-like emission of inelastic dark matter pairs, $e^- N \to e^- N γ^* (\to χ_1 \barχ_0)$, will allow NA64e to probe previously unexplored regions of the iDM parameter space, in particular for modest mass splittings, $Δ\simeq 5 \times 10^{-2}$, and relatively light masses, $m_{χ_0} \lesssim 100~\mbox{MeV}$.

Figures (5)

• Figure 1: Feynman diagrams illustrating the production iDM pairs in electron-nucleus scattering for two channels: (a) bremsstrahlung like emission $e N \to e N \gamma^*(\to \chi_1 \bar{\chi}_0)$; (b) reaction of vector meson photoproduction $\gamma^* N \to N V$ followed by its radiative decay $V \to \gamma^* \to \chi_1 \bar{\chi}_0$Barducci:2023hzoJodlowski:2023ohnDienes:2023uve.
• Figure 2: Feynman diagram describing two-body radiative decay of excited iDM state, $\chi_1$, into SM photon, $\gamma$, and lightest mode $\chi_0$.
• Figure 3: A schematic view of a missing energy signature $V/\gamma^* \to \chi_1 \bar{\chi}_0 (\chi_1 \to \chi_0 \gamma)$ produced after a 100 GeV $e^-$ scatters off in the active dump, $e^- N \to e^- N+ E_{\rm miss.}$. The $\chi_1$ particle decays within HCAL 1-3 into soft undetectable photon $\gamma$ ($E_{\gamma} \lesssim 100~\hbox{MeV}$) and lightest sterile iDM state $\chi_0$. This sketch illustrates the NA64e setup to search for missing energy events NA64:2016owwNA64:2025nqqNA64:2025ddkAndreev:2021fzdNA64:2021xzoBanerjee:2019pdsNA64:2023wbi.
• Figure 4: Left panel: the differential cross sections of the process $e^- N \to e^- N \gamma^* (\to \chi_1 \bar{\chi}_0)$ as function of the missing energy $E_{\rm miss}=E_{\chi_1}+E_{\bar{\chi}_0}$ for the set of iDM masses in the range $10~\hbox{MeV} \lesssim m_{\chi_0} \lesssim 700~\hbox{MeV}$. The electron beam energy is $E_e \simeq 100~\hbox{GeV}$, we also set $\Lambda_{\rm M} =1~\hbox{GeV}$. Right panel: the plot shows the number of $\chi_1 \bar{\chi}_0$ pairs produced versus $\chi_0$ mass for NA64e ($5\times 10^{12}$ EOT), with the splitting parameter chosen to be $\Delta=10^{-3}$. The hidden particles are produced through the bremsstrahlung-like emission $\gamma^*\to \chi_1 \bar{\chi}_0$ (red line), J-psi meson $J/\psi\to \chi_1 \bar{\chi}_0$ (black line), rho meson $\rho \to \chi_1 \bar{\chi}_0$ (brown line), omega meson $\omega \to \chi_1 \bar{\chi}_0$ (orange line), and phi meson decay $\phi \to \chi_1 \bar{\chi}_0$ (green line). The resulted number of $\chi_1 \bar{\chi}_0$ pairs produced at the NA64e is shown by blue line.
• Figure 5: Left panel: the expected limits at $90~\%~\hbox{CL}$ on $1/\Lambda_{\rm M}$ coupling for the NA64e fixed-target experiments as a function of the lightest iDM mass $m_{\chi_0}$, implying mass splitting $\Delta=10^{-3}$. Current limits of NA64e NA64:2023wbi are shown by red solid line and imply the typical statistics of $\hbox{EOT}\simeq 10^{12}$, these bounds have been ruled out by LEP L3:2003yonFortin:2011hv and CHARM II CHARM:1985anbCHARM:1983ayi experiments (shaded gray region). Blue solid line is the projected sensitivity for NA64e experiment for $\hbox{EOT}\simeq 5\times 10^{12}$ and background free case, $b=0$. The expected reaches of the NA64e ($\hbox{EOT}\simeq 10^{13}$) for background free, $b=0$, and finite background case, $b=1$, are shown by brown and green solid lines, respectively. The iDM thermal target curve is shown by black dashed line, it was adapted from Ref. Jodlowski:2023ohn. Right panel: the same as for the left panel, but for the benchmark mass splitting chosen to be as $\Delta = 0.05$. The grey shaded region is ruled out from the BaBar Izaguirre:2015zva, NuCal Blumlein:1990ayBlumlein:2011mv, and LEP L3:2003yonFortin:2011hv data, adapted from Jodlowski:2023ohn.