Figure 1

Schematic experimental setup. A high-intensity multi-GeV electron beam impinging on a beam dump produces a secondary beam of dark sector states. In the basic setup, a small detector is placed downstream so that muons and energetic neutrons are entirely ranged out. In the concrete example we consider, a scintillator detector is used to study quasielastic $\chi$-nucleon scattering at momentum transfers $\gtrsim 140\mathrm{MeV}$, well above radiological backgrounds, fast neutrons, and noise. Similar layouts with much smaller detectors or shorter target-detector distances than shown above are similarly sensitive. To improve sensitivity, additional shielding or vetoes can be used to actively reduce high-energy cosmogenic and other environmental backgrounds.Reuse & Permissions

Figure 2

(a) $\chi \overline{\chi }$ pair production in electron-nucleus collisions via the Cabibbo-Parisi radiative process (with $A^{\prime }$ on or off shell) and (b) $\chi$ scattering off a detector nucleus and liberating a constituent nucleon. For the momentum transfers of interest, the incoming $\chi$ resolves the nuclear substructure, so the typical reaction is quasielastic and nucleons will be ejected.Reuse & Permissions

Figure 3

The ${ϵ}^2$ sensitivity of electron beam fixed-target experiments plotted alongside existing constraints for benchmark values of $m_{\chi }$, $m_{A^{\prime }}$, and ${\alpha }_D$. The solid, dashed, and dot-dashed red curves mark the parameter space for which our basic setup—a 12 GeV beam impinging on an aluminum beam dump, with a $1{\mathrm{m}}^3$ mineral-oil detector placed 20 m downstream of the dump—respectively yields 40, ${10}^3$, and $2\times {10}^4$ $\chi$-nucleon quasielastic scattering events with $Q^2\gtrsim (140\mathrm{MeV}{)}^2$ per ${10}^{22}$ electrons on target (EOT). The orange curve shows the ten-event reach for an ILC style 125 GeV beam assuming the same detector and luminosity. Comparable sensitivity can be achieved with much smaller fiducial volumes than we consider, especially for detectors with active muon and neutron shielding and/or veto capabilities. The upper plots show the $ϵ$ sensitivity for ${\alpha }_D=0.1$ (left) and ${\alpha }_D=1$ (right). In these plots LSND may also have sensitivity to ${ϵ}^2\sim {10}^{-8}–{10}^{-6}$ via ${\pi }^0\to \gamma \chi \overline{\chi }$ decays for $2m_{\chi }<m_{A^{\prime }}<m_{\pi }$ [16]. The lower left plot shows the reach for $m_{\chi }=m_{{\pi }^0}/2\simeq 68\mathrm{MeV}$ where the production from pion decays is kinematically inaccessible and LSND has no significant sensitivity. The lower right plot recasts the ${ϵ}^2$ sensitivity for fixed $m_{A^{\prime }}$ and ${\alpha }_D$ as a (model-dependent) probe of the $\chi$-electron direct detection cross section ${\sigma }_{\chi e}$ and includes XENON 10 limits from 56. The black curve assumes ${\Omega }_{\chi }={\Omega }_{\mathrm{DM}}$; the direct detection constraint is weaker when $\chi$ is only a component of the total abundance. The light green band is the region in which an $A^{\prime }$ resolves the $(g-2{)}_{\mu }$ discrepancy to within $2\sigma$; the dark green curve is the boundary at which contributions to $(g-2{)}_{\mu }$ exceed the measured value by $5\sigma$ [64]. The bound from $e^{+}{e}^{-}\to \gamma +$ invisibles is introduced in detail in Sec. 3a. Other constraints in the literature arise from invisible $J/\psi$ decays [86], searches [62], rare kaon decays [63], and contributions to $(g-2{)}_e$ [65]; for a discussion see Sec. 3c.Reuse & Permissions

Figure 4

The “luminosity correction” factor $F(q_{\min }=m_{A^{\prime }}^2/(2E_{\mathrm{beam}}),q_{\max }=m_{A^{\prime }})$ defined in (15), for use in estimating $A^{\prime }$ yield. $F$ is proportional to the Weizsacker-Williams effective photon flux $\Phi (q_{\min },q_{\max })$, multiplied by a material-dependent luminosity factor. The red solid and blue dashed curves correspond to 12 GeV electron beams impinging on a thick aluminum or beryllium target (i.e. $q_{\max }=\sqrt{2·12·q_{\min }}$). For the $A^{\prime }$ mass ranges of interest, $F$ can depend sensitively on $q_{\min }$ but far less on $q_{\max }$, so that these curves remain approximately valid for other beam energies. For example, scaling beam energy and $m_{A^{\prime }}^2$ simultaneously by up to a factor of 10 (not shown), so that $q_{\min }$ is unchanged but $q_{\max }$ scales by $\sqrt{10}$, only affects $F$ at the $\sim 20\%$ level or smaller. The expression for $F$ shown here includes only coherent elastic nuclear scattering and quasielastic scattering off nucleons; neglecting inelastic contributions may underestimate the $F$’s for 1–2 GeV $A^{\prime }$ masses at the highest $q_{\min }$ shown by a factor of $\sim 5$.Reuse & Permissions

Figure 5

Same as Fig. 3 with overlays of curves for ${\alpha }_D=1$, 0.1. The gray region is excluded by the same curves shown in Fig. 3 and described in the caption.Reuse & Permissions

Figure 6

Same as Fig. 3 with overlays of different $m_{\chi }$ (top) and $m_{A^{\prime }}$ (bottom) parameters. The $m_{\chi }=m_{\pi }/2=68\mathrm{MeV}$ curve in the top in (a) shows our $ϵ$ reach in the regime where the dominant ${\pi }^0\to \chi \overline{\chi }$ process is kinematically forbidden at proton beam experiments. The dotted curve shows the BABAR $e^{+}{e}^{-}\to \gamma +$ invisibles for $m_{\chi }=10$ and 68 MeV. This constraint is identical for all $\chi$ produced in on-shell $A^{\prime }$ decays; for $m_{\chi }$ 250 MeV this bound shifts upward. Similarly, the kaon decay constraints are now dashed since both regions apply for $m_{\chi }=10\mathrm{MeV}$, but neither does at 250 MeV.Reuse & Permissions

Figure 7

Same as Fig. 3 (top) with red sensitivity curves for inelastic nuclear (thick, solid) and electron (dotted) signal yields.Reuse & Permissions