DAEδALUS and dark matter detection

Among laboratory probes of dark matter, fixed-target neutrino experiments are particularly well suited to search for light weakly coupled dark sectors. In this paper, we show that the DAEδALUS source setup—an 800 MeV proton beam impinging on a target of graphite and copper—can improve the present LSND bound on dark photon models by an order of magnitude over much of the accessible parameter space for light dark matter when paired with a suitable neutrino detector such as LENA. Interestingly, both DAEδALUS and LSND are sensitive to dark matter produced from off-shell dark photons. We show for the first time that LSND can be competitive with searches for visible dark photon decays and that fixed-target experiments have sensitivity to a much larger range of heavy dark photon masses than previously thought. We review the mechanism for dark matter production and detection through a dark photon mediator, discuss the beam-off and beam-on backgrounds, and present the sensitivity in dark photon kinetic mixing for both the DAEδALUS/LENA setup and LSND in both the on- and off-shell regimes.

Figure 1

Left (a): schematic diagram of DM production in proton-carbon collisions, through on- or off-shell dark photons $A^{\prime }$ from exotic ${\pi }^0$ decays. Right (b): DM scattering at a detector through the same dark photon $A^{\prime }$. We focus on electron scattering in this paper, but the detector target may be protons or nuclei in alternative experimental setups.

Figure 2

Example DAEδALUS placements in the vicinity of the cylindrical LENA detector: midpoint (a), oblique (b), and on axis (c). The dotted lines show some representative paths of $\chi$ through the detector volume. The projected yields for each configuration are displayed in Fig. 5. Note that for our sensitivity projections we assume the DM incidence angle is always defined with respect to the incident proton direction.

Figure 3

Summary of DAEδALUS/LENA $3\sigma$ sensitivity to the kinetic mixing parameter ${\epsilon }^2$ assuming the on-axis configuration [see Fig. 2] and a full year of run time with $7.5\times {10}^{22}$ ${\pi }^0$ produced. We also display updated bounds from existing LSND data in both off-shell $A^{\prime }$ regimes. Left column: DAEδALUS sensitivity as a function of $m_{A^{\prime }}$ for fixed DM mass $m_{\chi }=1\mathrm{MeV}$ (a), 20 MeV (c), and 40 MeV (e). Right column: DAEδALUS sensitivity as a function of $m_{\chi }$ for fixed dark photon mass $m_{A^{\prime }}=10\mathrm{MeV}$ (b), 50 MeV (d), and 100 MeV (f). The thick green band is the region where $A^{\prime }$ could resolve the longstanding $(g-2{)}_{\mu }$ anomaly to within $\pm 2\sigma$ [20]; see Sec. 6 for information about the other projected sensitivities and constraints. Where applicable, the dashed vertical black line marks the transition between the on- and off-shell $A^{\prime }$ regimes for ${\pi }^0\to \gamma A^{\prime (*)}\to \gamma \chi \overline{\chi }$. In the lower off-shell regime, where we compare to visible $A^{\prime }\to e^{+}{e}^{-}$ searches, we emphasize that the LSND and DAEδALUS limits assume the existence of the off-shell process $A^{\prime }\to \chi \overline{\chi }$. Assuming such a $\chi$ exists, the dark gray region above the black LSND curve is excluded; this is the first demonstration that LSND can rule out a visibly decaying $A^{\prime }$ by searching for DM produced via an off-shell $A^{\prime }$.

Figure 4

Parameter space for the dark photon mass $m_{A^{\prime }}$ and dark coupling ${\alpha }_D$, taking $\epsilon$ to be the smallest value which resolves the $(g-2{)}_{\mu }$ anomaly for $m_{\chi }=1\mathrm{MeV}$. The DAEδALUS/LENA curve shows $3\sigma$ sensitivity. The solid black curve is the boundary where $\mathrm{Br}(A^{\prime }\to e^{+}{e}^{-})=\mathrm{Br}(A^{\prime }\to \overline{\chi }\chi )=50\%$. Note that for $\mathrm{Br}(A^{\prime }\to e^{+}{e}^{-})\simeq 100\%$ (just below the black curve) recent (preliminary) results from $\mathrm{NA}48/2$ [21] have ruled out the remaining parameter space for a visibly decaying $A^{\prime }$ that explains the discrepancy.

Figure 5

Sensitivity contours at DAEδALUS/LENA showing the effect of changing experimental geometries. All curves assume a $3\sigma$ signal-to-background sensitivity; see Secs. 5 and 4. Existing limits from the multiyear data set at LSND [10] are shown for comparison. The signal contours are computed by integrating the electron recoil profile over the interval that maximizes $S/\delta B$ for each value of $m_{A^{\prime }}$.

Figure 6

Left (a): Angular distributions for DM production and beam-on neutrinos produced at the DAEδALUS source. The neutrino distribution is roughly isotropic, while the signal is strongly peaked in the forward direction ($\cos \theta \simeq 1$). The slight excess of neutrino production in the backward direction is an artifact of the simplified target geometry used in the simulation; see the text for details. Above 106 MeV both the DM and neutrino distributions are strongly peaked in the forward direction; the relative normalizations of the curves with and without the cut show the reduction in signal and background due to this cut alone, though the actual signal is also determined by the geometric acceptance of LENA. For different DM masses, the normalization of the DM distribution changes, but not its shape. Although LENA cannot resolve electron-recoil angles for which $\cos \theta >0.9$, imposing a stronger angular cut of $\cos \theta >0.95$ would preserve an order-1 fraction of signal events and dramatically reduce both beam-off and beam-on backgrounds discussed in Secs. 4 and 5. To be conservative, we assume $\cos {\theta }_{\ell }>0.9$ for all of our sensitivity projections, but this is a potential avenue for improving new-physics searches in the electron scattering channel. Right (b): Electron energy spectra due to various DM signal points and principal beam-on backgrounds (unstacked histograms) assuming the on-axis DAEδALUS/LENA configuration. The color shaded region under each signal curve represents the signal window that maximizes $S/\delta B$ for each parameter point. The ${\nu }_{\mu }$ CCQE distribution shows the residual background after a 70% reduction from vetoing Michel electrons; the remaining muons are misidentified as electrons in LENA, and their kinetic energy spectrum is shown. The ${\nu }_e$ CCQE distribution was only simulated above 100 MeV where it begins to dominate. The ${\epsilon }^2$ values for each signal point are chosen to match the minimum value for which the DAEδALUS/LENA setup has the $3\sigma$ sensitivity displayed in Fig. 3.

Figure 7

Optimal electron recoil cuts $E_e^{\text{low}}$ (green curve) and $E_e^{\text{high}}$ (red curve), which optimize the signal-to-background sensitivity $S/\delta B$ as a function of $m_{\chi }$ for fixed $m_{A^{\prime }}=50\mathrm{MeV}$, assuming a minimum signal window width of 50 MeV. The shaded region between the red and green curves defines the optimal signal window for each mass point. Also shown is the maximum electron recoil energy $E_e^{\max }$. (black, dotted curve) for each $m_{\chi }$ assuming an initial proton energy of 800 MeV [see Eq. (12)]. The blue dashed lines at $E_e=106$, 147, and 250 MeV, respectively, denote the electron energies beyond which beam-on backgrounds from ${\mu }^{-}$ capture, ${\nu }_{\mu }$ CCQE (from ${\pi }^{+}$ DIF), and ${\nu }_{\mu }$ elastic scattering (from ${\pi }^{+}$ DIF) become irrelevant; these lines can be regarded as a heuristic estimate of $E_e^{\text{low}}(m_{\chi })$. Above 250 MeV, the only significant beam-on background is from the ${\nu }_e$ CCQE process (see Table 2).

Figure 8

Comparison of LSND sensitivities as computed using methods in the existing literature [9, 10] (magenta curve) and those obtained using the full three-body matrix element that includes DM production via an off-shell $A^{\prime }$.