Search for Boosted Dark Matter at ProtoDUNE

We propose the first experimental test of the inelastic boosted dark matter hypothesis, capitalizing on the new physics potential with the imminent data taking of the ProtoDUNE detectors. More specifically, we explore various experimental signatures at the cosmic frontier, arising in boosted dark matter scenarios, i.e., relativistic, inelastic scattering of boosted dark matter often created by the annihilation of its heavier component which usually comprises of the dominant relic abundance. Although features are unique enough to isolate signal events from potential backgrounds, vetoing a vast amount of cosmic background is rather challenging as the detectors are located on the ground. We argue, with a careful estimate, that such backgrounds nevertheless can be well under control by performing dedicated analyses after data acquisition. We then discuss some phenomenological studies which can be achieved with ProtoDUNE, employing a dark photon scenario as our benchmark dark-sector model.


I. INTRODUCTION
The Deep Underground Neutrino Experiment (DUNE) [1] is projected to be in operation in 2024 and it will cover a broad physics program including precision measurements of neutrino oscillations, CP phase measurement in the lepton sector, and possibly explorations of new physics at both the intensity and cosmic frontiers, thanks to high intensity proton beams and the large mass detectors located about 1.5 km underground at the Sanford Underground Research Facility in South Dakota, USA. There will be a total of four 10 kt fiducial mass far-detector modules based on liquid Argon time projection chamber (LArTPC) technology with two initially and extending to four within a few years and a near-detector [1].
For the successful operation of the DUNE experiment with kiloton-scale LArTPC detectors, a prototype of DUNE called ProtoDUNE [2,3] was planned and is under construction at CERN, anticipating the initial operation from September 2018. The two ProtoDUNE detectors use different technologies, single-phase (SP) [2] and dualphase (DP) [3] LArTPCs, both of which may be adopted as the DUNE far-detector, and will test the long-term stability and operation of these detectors, act as an engineering proof-of-principle for scalability, and calibrate beam and cosmic-ray responses.
While these tasks take the highest priority for the detectors, we ask whether there are physics opportunities at ProtoDUNE, in particular, considering a large active volume of 720 tons (420 tons for SP and 300 tons for DP) [2,3] and high-performance LArTPC detectors proven at Argon Neutrino Test (ArgoNeuT) [4], Imaging Cosmic And Rare Underground Signals (ICARUS) [5], and Micro Booster Neutrino Experiment (MicroBooNE) [6]. However, cosmic backgrounds will be formidable because the ProtoDUNE detectors are installed on the Earth's surface, and as a result, any signals of interest could be buried in such backgrounds.
In this paper, after performing a careful estimation, we argue that the cosmic backgrounds can be well controlled by dedicated event selections at the analysis stage and possibly, but less crucially, the addition of an efficient cosmic ray tagging apparatus. This opens up the unexpected potential for cosmic frontier physics opportunities at ProtoDUNE and thus for DUNE. Such a potential is indeed further advocated, as the ProtoDUNE detectors are now planned to take data for cosmic-origin signal searches. We remark that the DUNE far-detector will start taking data 1−2 years earlier than the neutrino beam becomes available and collect signals of cosmic and solar origin, thus our physics studies at ProtoDUNE will provide valuable physics input and potentially a realistic guideline for new physics searches at the DUNE fardetector.

II. BENCHMARK PHYSICS SCENARIO
An exciting physics opportunity with ProtoDUNE is the search for dark matter (DM). Unfortunately, the conventional DM search via its non-relativistic scattering is arXiv:1803.03264v2 [hep-ph] 14 Feb 2019 not accessible because the expected threshold energy for electron/nucleon recoil (∼ 30 MeV) [7] is far beyond the typical energy deposit resulting from the ordinary DM scattering. By contrast, typical energy deposits in association with a relativistic scattering of boosted DM readily surpass such a threshold, which renders ProtoDUNE as an ideal detector in the search for boosted DM with its relativistic scattering signatures.
A possible mechanism to create relativistic DM in the current universe is the boosted dark matter (BDM) scenario [8] which hypothesizes two stable DM species: the heavier χ 0 and the lighter χ 1 . Their overall relic abundance is determined by the "assisted freeze-out" mechanism [9], and in typical cases the heavier (lighter) becomes the dominant (negligible) relic as it has indirect coupling to the Standard Model particles through the lighter component. Therefore, in the current universe, a pair of χ 0 annihilate into a pair of χ 1 in the galactic halo.
The mass gap between the two species allows χ 1 to acquire a large boost factor and induce relativistic scattering signatures in terrestrial detectors. FIG. 1 shows two such possible processes. The process on the left corresponds to the ordinary elastic scattering with a visible target recoil [8,[10][11][12] (henceforth called eBDM). The process on the right assumes a non-minimal darksector scenario allowing the transition to a heavier unstable state (χ 2 ) which subsequently disintegrates back to χ 1 together with possibly visible secondary particles in addition to the primary target recoil [13,14] (henceforth called iBDM). We define the masses of the dark-sector particles χ i as m i for i = (0, 1, 2).
To investigate signal detection prospects at any given experiment, it is crucial to estimate the total flux of the incoming boosted χ 1 , which is given by [8] where the reference value for σv 0→1 , the velocityaveraged annihilation cross section of χ 0 χ 0 → χ 1 χ 1 , corresponds to an observed DM thermal relic density [8,9] assuming χ 0 andχ 0 are distinguishable. Considering the fiducial volume of the ProtoDUNE detectors and assuming 2-year data collection at 50% duty factor (i.e., 3 × 10 7 s), we find that ProtoDUNE is capable of probing models with m 0 in the range O(30 MeV) − O(10 GeV). While numerous DM models conceiving the aforementioned signatures are available, we employ the following dark photon scenario throughout this paper for illustration: The first term describes the usual kinetic mixing between the field strength tensors F µν for the ordinary Standard Model photon and X µν for the dark photon X by the amount . The second (third) operator describes the flavor-conserving (flavor-changing) neutral current responsible for elastic (inelastic) scattering. Given this scenario, we expect three types of signal events in association with electron recoil, that is, Here we divide the iBDM case into two subcategories, whether or not the secondary e + e − pair comes from the decay of a long-lived particle X (prompt) or χ 2 (displaced). Searches for similar signatures can be done at fixed target experiments, with active production of relativistic dark matter. An ample amount of literature has been focusing on the elastic scattering channel, e.g. see Refs. [15,16]. By contrast, phenomenological consideration to the inelastic scattering channel is being increasingly made [17][18][19].

III. BACKGROUND CONSIDERATION
We are now in the position to discuss potential backgrounds to iBDM signals. In general, it is hard for conventional cosmic-origin events to mimic the signal due to several distinguishing features. Nevertheless, we consider plausible scenarios that could give rise to potential background events since both SP and DP detectors are placed on the ground and exposed to a high cosmic-ray rate, followed by discussions on useful background rejection strategies.
Firstly, let us estimate the cosmic background anticipated at the ProtoDUNE detectors, separating it into low-energy cosmic rays (30 MeV E 400 MeV) and high-energy ones (E 400 MeV). As we will see shortly, we expect that the majority of low-energy cosmic background is suppressed, considering the (partially covered) outermost steel exoskeleton, the insulator region, and the LAr volume outside the active volume. We further take out 35 cm inward from the boundary of the active volumes as per DUNE conceptual design report (CDR) Vol. IV [1]. For the DP, we additionally cut away 1 m from the top surface of LAr to offset the passive volume existing in the other sides. These considerations reduce the fiducial volumes of the SP and DP to 300 t and 170 t, respectively.
Highly energetic cosmic particles such as muons, however, are not sufficiently removed even with the abovedefined fiducial volumes. Indeed, the integral intensity of vertical muons above 1 GeV at the altitude of the actual site (∼ 400 m) is about 70 m −2 s −1 sr −1 (which negligibly differs from that at sea level [20]), and the muon energy spectrum below 1 GeV is almost flat [20]. We find that muons above ∼ 400 MeV may reach the fiducial volume for both SP and DP detectors, taking into account the energy-dependent stopping power for muons in LAr (1 m from the passive volume + 35 cm by fiducialization) [20,21].
Considering the flatness of the muon energy spectrum below 1 GeV and the muon flux at 1 GeV [20], we estimate ∼ 24 m −2 s −1 sr −1 in-between 400 MeV and 1 GeV. Hence, we conclude that ∼ 60 cosmic-ray muons per detector will enter the active volume within the 5 ms trigger-window [2] allowing for a 2.25 ms electron drift time [2], with a range of π steradians included. This is within the ProtoDUNE data-recording capacity.
For the data analysis, most of the cosmic-muons will be easily recognized since they leave identifiable tracks in the detectors. However, one may argue that a significant number of muons could still mimic signal despite small rates of missed tracks, particle misidentification, and other cases described below, purely due to the fact that the total number of muons with energies above 400 MeV is as large as ∼ 4 × 10 11 per year in each detector. One plausible scenario to fake an iBDM signal is that a muon i) enters the fiducial volume without leaving a track, i.e., "sneaks-in", ii) emits a hard photon which converts into an e + e − pair, and iii) starts to leave a visible track resulting in a signal-like event shape, iv) which appears electron-like. While a more thorough and dedicated study on "sneaking-in" muons under the Pro-toDUNE environment is highly desired, we can estimate the effect from a study of the muon reconstruction efficiency at the MicroBooNE detector [22]. They reported that 0.09% of cosmic muons are reconstructed such that tracks appear only inside the fiducial volume, with the more advanced selection scheme. We take this as the upper limit of the "sneaking-in" muon probability, thus conservatively estimate the probability to be 0.1%. 1 The second condition can be given by a phase-space suppression factor, α/π ≈ 2 × 10 −3 , with α being the fine structure constant. For the rate of electron-like muon tracks, a dedicated analysis is again needed, but here we simply take a very conservative suppression factor of 10 −2 based on the study reported in Ref. [24] with the LArTPC detector of the ArgoNeuT Collaboration. The remaining criterion iii), where the momentum direction of the e + e − pair intersects at most with the beginning point associated with the e-like outgoing µ track, is hard to estimate. But we see that if ∼ 0.6% of suppression power is achieved, it should be possible to have fewer than ∼ 100 muon-induced background events per year in the two ProtoDUNE detectors. Note, however, that this estimation is based on very conservative probabilities written in criteria i), iii), and iv). In reality, a dedicated analysis should easily decrease these rare possibilities by a few orders of magnitude. Nevertheless, we show the experimental sensitivities assuming 100 background events per year in order to clarify that ProtoDUNE can probe the iBDM signals even in the worst case scenario. We compare the results with the sensitivities for a best case scenario (zero-background assumption) 2 and a two-year exposure of the detector.
It is informative to understand the many topological differences between µ-induced background events and the signals. We display the possible event shapes of µinduced background (upper panel) and iBDM signal of interest (lower panel) in FIG. 2. For background events, a hard photon emission (red wavy lines), which can show a visible gap with the radiation length being O(10 cm) [26], may arise either after (upper left diagram) or before (upper right diagram) the "sneaking-in" muon (red solid lines) begins to leave an e-like track. Note that for both cases, the incoming (sneaking-in) muon, the outgoing (elike) muon, and the hard photon lie on a common plane. In other words, the line extending the momentum direction of the e + e − pair from the γ conversion should meet the line extending the momentum direction of the outgoing e-like track, within the detector position resolution. For signal events, three event shapes are possible. Firstly, if primary scattering and secondary decay take place promptly, all three electron tracks are expected to start at a single vertex point (lower left diagram). Secondly, if χ 2 decays instantly but the dark photon X is long-lived (lower middle diagram), the direction extended by the total momentum of an e + e − pair from X decay should point back the beginning point associated with the 1 The number 0.09% resulted from 2016 data of the MicroBooNE detector. The corresponding number including 2017 data is even smaller, although not public yet [23]. 2 Note also that it is possible to keep the zero-background assumption following the proposal that all the cosmic muon background events can be rejected by considering the Earth shielding effect in a surface-based detector [25].  electron recoil track, within the detector position resolution. Finally, if χ 2 is long-lived, it decays to χ 1 and an e + e − pair via a three-body process. Unlike the previous case, the line extending the momentum direction of the e + e − pair does not intersect with that of recoil electron (lower right diagram).
Other plausible situations were considered, such as dimuon simultaneous scattering and muon-initiated deep inelastic scattering in both active and passive volumes against the iBDM signals. Each muon of these background events must satisfy the aforementioned criteria i) and iv) for the major background which suppress the number of background at least 10 −5 for each muon. Also, the probabilities that a single electron faking the e + e − and a single photon faking an electron signal are below 10% and 7%, respectively [24]. Then, taking into account the number of two simultaneously incoming muons within the detector resolution (2.5·10 9 /yr) and the muons inducing the deep inelastic scattering (1.6 · 10 5 /yr), we predict the corresponding minor background events are less than ∼ 0.025 and ∼ 0.11 per year per detector, respectively.
We have checked other high-energy cosmic particles such as electrons/positrons and pions, but their contribution is negligible because their fluxes at sea level are smaller than that for the muon by 3 − 4 orders of magnitude [20] and their corresponding stopping powers in material are larger than that of the muon. However, the neutron flux is only a factor of 100 less than the muon flux and not negligible. Neutrons with GeV-range energies couple to matter via the strong force, thus they quickly break apart in material. On the other hand, MeV-range neutrons can sneak in the detector fiducial volume and (predominantly) scatter off nuclei. However, considering that two simultaneous "sneaking-in" neutrons would be required produce two e-like nucleon recoil tracks, we estimate that the number of the expected events is much smaller than one.
Finally, we discuss potential atmospheric neutrino backgrounds. The DUNE Collaboration performed a dedicated study on its event rates including oscillations in 350 kt·yr with a LArTPC, fully or partially contained in the detector fiducial volume [7]. From the fully contained electron-like sample, we estimate ∼ 40 yr −1 kt −1 which may include multi-track events which can be background to the iBDM signals. 3 We compared this number with the Super-Kamiokande (SK) atmospheric neutrino data [28] and an official eBDM analysis conducted by the SK Collaboration [29], and found that the number is comparable to the number of events with single-ring, e-like, 0-decay electrons, and 0-tagged neutrons at the SK.
For the multi-track atmospheric neutrino interactions, the DUNE CDR does not provide detailed information, but an SK study [28] reported the number of multiring, e-like events from which we estimate ∼ 5 yr −1 kt −1 . Given the fiducial volumes of the ProtoDUNE detectors defined in Table I and the fact that extra tracks typically originating from meson decays in neutrino events can be well-identified at ProtoDUNE, the expected number of neutrino background events to the iBDM signals is negligible.

IV. PHENOMENOLOGY
We first discuss ways of presenting model-independent experimental reaches with respect to various physics models conceiving eBDM and/or iBDM signatures. To this end, we consider the number of signal events, N sig = σ FA t exp N e , where σ is the cross section of either χ 1 e − → χ 1 e − for eBDM or χ 1 e − → χ 2 e − for iBDM, F is the flux of χ 1 , A is the acceptance, t exp is the exposure time, and N e is the number of target electrons inside the fiducial volume. For the iBDM case, the branching fraction of χ 2 → χ 1 e − e + is assumed to be 1. Note that the characteristics of the experiment determine the last two parameters (t exp and N e ) and refer to Table I for those of ProtoDUNE. By contrast, the product of the first two parameters (σ and F) depends on all model parameters such as coupling constants and masses. Finally, we assume that the acceptance A (defined as 1 if the interaction is fully contained in the fiducial volume, and 0 otherwise) is determined by the distance between the primary and the secondary vertices lab while all the other effects from selection criteria, threshold energy, detector response, and so on are encapsulated in the quantity σ . 4 A possible presentation scheme is to show modelindependent reaches in the plane of σ F vs. lab which can be formally expressed as [14] σ F > N 90 from that at the DUNE because they are placed in different depths below the surface. We have explicitly checked and found that such an effect is at most O(1%) for the energy scale of our interest. Also, the MSW effect [26,27] may require a more precise estimate, which is expected to be subleading, hence beyond the scope of this paper. 4 Obviously, A for eBDM signals is defined as 1 as all visible particles (here recoil electron only) come out of a single interaction point, i.e., no displaced vertex.
where the numerator N 90 s corresponds to the 90% C.L. upper limit of the signal events with Poisson statistics. N 90 s = 2.3 under a zero-background assumption which is our optimistic scenario and N 90 s = 17.8 in our worst case scenario where the number of background events is ∼ 100. Note that all model-dependent information is encoded in the left-hand side, whereas the right-hand side takes only experimental specifications and lab which alters event-to-event. We simply follow the suggestion in Ref. [14] and exhibit the experimental sensitivity in the plane of σ F − max lab with max lab being the maximum laboratory-frame mean decay length of a long-lived particle (here either X or χ 2 ). We display the experimental reaches of the ProtoDUNE detectors for a one-year run period in the top panels of FIG. 3, assuming a cumulatively isotropic χ 1 flux. The left panels show the sensitivities assuming the worst case scenario of 100 background events, while the right panels include the experimental reaches in the best case, zero-background scenario. In the right panels, we also show the sensitivities when Pro-toDUNE takes cosmic data for two years for comparison. Note that N 90 s takes 24.6 for the worst scenario as the total number of expected background events during 2-year data collection doubles, i.e., ∼ 200. Given a model having a BDM process, one can simply evaluate σ , F, and max lab [see Appendix B of Ref. [14] for useful formulae associated with our benchmark model in (2)] to find the corresponding coordinate in the plane. If it appears above a certain curve, the model point of interest is excluded with respect to the associated experiment/detector, and otherwise it remains an allowed point.
While this way of presentation is useful per se, a more familiar form is available. The flux F is a function of the mass of the dominant relic χ 0 as shown in Eq. (1). So, moving the flux factor in the inequality of Eq. (3) to the right-hand side, we are able to show the experimental sensitivities in terms of σ vs. m 0 (= E 1 ) for a given A which is uniquely mapped to a value of max lab . This scheme is reminiscent of the sensitivity plot in the plane of spin-independent or spin-dependent cross section vs. the mass of the dominant relic DM which is usually reported by ordinary DM direct detection experiments. Example curves are shown in the bottom panels of FIG. 3 with three different decay lengths. The black vertical dotted line represents the absolute lower bound for visible tri-track events due to the threshold energy of 30 MeV. The actual lower bound may involve minor model-dependence; for a given m 0 , it gets closer to the absolute one as m 1 becomes lighter and/or δm vanishes. Note that the case with max lab = 0 is relevant to not only signals with overlaid vertices, i.e., prompt iBDM ones, but elastic scattering signals because the latter involves a single interaction point with the absolute lower bound extended down to m 0 = 30 MeV.
Since we take a dark photon scenario as in (2), it is interesting to interpret the parameter reach sensitivities in the usual m X vs. plane, with m X being the dark photon mass. We find the minimum value of for a given m X by scanning along the boundary curve in (σ F, max lab ), with the mass parameters m 0,1,2 and coupling constants fixed. The expected reaches at ProtoDUNE are shown in FIG. 4 under the assumption that X decays either invisibly (top panels) or visibly (bottom panels). For the former case, we assume m X > 2m 1 in order that the invisible decay modes dominate the visible ones. Our selection of mass spectra appears in each legend, and g 11/12 = 1 for the eBDM/iBDM signals in both cases. The current exclusion limits (brown regions) are extracted from Refs. [30] (top) and [31] (bottom). The left panels show the coverage in a worst case scenario assuming 100 background interactions for a one-year exposure and the right panels include the sensitivities in a best case scenario (zerobackground assumption) and a two-year exposure of the detector for comparison.
We report the experimental sensitivities for some inelastic scattering scenarios (δm ≡ m 2 − m 1 = 0), fixing mass parameters as shown in each legend. We clearly see that our searches in the iBDM channels probe param-eter regions that are uncovered by existing experimental constraints, by about an order of magnitude in the axis depending on the parameter choice. In the left panels, we also show the results corresponding to different threshold energies, optimistic case 20 MeV (dotted) and pessimistic case 45 MeV (dashed), on top of the baseline value 30 MeV (solid), and find that the coverage in parameter space is mildly affected by the value of energy threshold. Note that no eBDM results appear here. The reason is that our estimate for the muon-induced cosmic background to the single-track event is order 10 7 − 10 8 per year so that sensitivity curves merely lie in the brown regions. In other words, a suitable cosmic background control should be preceded in order to achieve experimental reach towards unexplored parameter space via eBDM channels [25]. The left panels show the coverage in a worst case scenario assuming 100 background events (denoted as 100-BG) for a one-year exposure and the right panels include the sensitivities in the best case scenario (zero-background assumption denoted as zero BG) and a two-year exposure of the detector for comparison.

V. CONCLUSIONS AND OUTLOOK
ProtoDUNE possesses an excellent sensitivity to a wide range of BDM parameter space, hence allows a deeper understanding in non-minimal dark-sector physics. We encourage many theorists to explore phenomenology of their own new physics models at ProtoDUNE. Moreover, our physics study can be extended to proton scattering and is widely applicable to other existing/future surfacebased detectors.