B. Study of the muons and muon induced backgrounds in DUSEL using LUX data

In addition to the low energy radiation from surrounding rocks and the construction material, high-energy muons produced by cosmic rays are an important background source at 4850 ft level. The muon flux at 4850 ft level was estimated to be ~ 4.4×10^-9 cm^-2sec^-1, with an expected mean energy of 320 GeV [33] on a spectrum spread over several orders of magnitude. These muons can create complicated backgrounds that may affect the experiment design, data acquisition design, detector performance, and data analysis. For example, high-energy neutrons produced by these muons can penetrate the attenuator and mimic dark matter signal in the LXe detector. Muons with kinetic energy less than 55 MeV (muon Cherenkov threshold energy in water) can be stopped in the water shield without producing Cherenkov light to trigger the water shield. Depending on their incident angle and position, muons with energy up to 400 MeV ~ 600 MeV can also stop in the inner detector after losing their energy in the water shield around it. These stopped muons can either decay (μ⁺/μ^- to positron/electron and neutrinos) or be captured through the semileptonic weak interaction by a proton μ^- + p → ν_μ + n or by a nucleus μ^- + (Z, N) → ν_μ + (Z−1, N+1)*. Since the μ^- -capture cross-section increases rapidly with Z of the target elements [34], besides neutrons produced in the water, over long time μ^--capture processes can make more significant contribution in cosmogenic production [35] in the detector construction materials and in Xenon than in water and scintillation materials used for active vetoing.

For many years, different experiments have been done in major underground laboratories to measure muon and neutron flux and/or spectrum [see references in 33, 36, 37]. With these data, great progress has also been made in the flux parameterization and Monte Carlo simulation [see for example 36, 38, 39, 40, 41]. For the muon flux calculation, it is important to know the average rock composition and density between the lab and the surface, while for evaluation of background from radioactivity and muons one has to know the rock composition around the lab, which can be very different for different underground sites. At present, for certain experiment sites, assuming that the knowledge of rock composition and surface muon profile gives accurate predictions for muon flux and spectrum, reports show Monte Carlo simulations of muon-induced neutron background using GEANT4 and FLUKA can predict the neutron event rate with an accuracy of about a factor of two [ex. 39, 40, 41, 42, 43]. Nevertheless, big uncertainties still exist at higher energies. For example, at 3650 m.w.e. level, the calculated neutron yield starts to be lower than the LVD data at about 100 MeV. It becomes lower by nearly one order of magnitude at about 400 MeV [39]. Ideally any simulation of muon propagation (with MUSIC, MMC, etc.) should be normalized using experimental data; however, comparing with other major underground sites, few measurements of muon and neutron fluxes were done at DUSEL site except several early measurements done in the Davis Cavern [44, 45].

With its sensitivity goal of a cross-section of 7×10^-46 cm² (for WIMPs with mass M=100 GeV), LUX is expected to be sensitive to WIMP signals at a rate of about 6.5×10^-6 dru_r (1 dru_r=1 evt/keV_r/kg/day). To reach this goal, given the identification capability between electron recoils and nuclear recoils, the LUX inner detector is designed to ensure background level at or below 8.3×10^-4 dru_ee for gammas and 3.7×10^-6 dru_r for neutrons prior to applying the charge to light ratio-based discrimination. Water radioactivity goal of U/Th/K less than 2 ppt/3 ppt/4 ppb (~10⁶ lower than the rock) is attained by a commercial purifier. Radon in the purified water will be at the level of about 2 mBq/m³, and will be further reduced with an N₂ purge blanket over time [46]. Given such low internal backgrounds and the LXe (350 kg) and water (300 Ton) mass in a single detector system, the LUX experiment is also an ideal instrument to study in-situ backgrounds in addition to its primary goal of dark matter search. The background results may affect all forth-coming projects in DUSEL. In this proposal we will focus on the following three different, but closely related, measurements and analysis:

Muon flux and multiplicity were measured in several early experiments in the Davis Cavern [44, 45], with a focus on their implications for cosmic ray physics and high-energy interactions. In this proposal we will measure the signal in the water shield with a focus on their connection with the backgrounds in a modern dark matter search experiments.

One interesting measurement is the energy deposition in the water shield together with identified muon component. Based upon the absolute calibration proposed in Section A above, together with detailed simulation of water shield response function to different particles, one can measure the energy deposition of local sub-MeV showers that hit the water shield. By separating different particles (only possible to some extent and on a statistical basis with the current water shield configuration), one can estimate the contributions from muons and other electromagnetic particles on the spectrum. This can be used to further estimate the spectrum and properties of local small showers in the Davis Cavern. In order to identify the muon component from the electromagnetic component in water shield signal, we propose the following two steps:

(1) Add a layer of plastic scintillator at the bottom of the water tank to identify muons that can penetrate the 6-meter water depth from those stopped in the water volume or small shower events. The electronics and eight plastic scintillator detectors (0.2 m² each) are from the South Pole Air Shower Experiment II (SPASE2) [15], which was decommissioned in 2006. Nearly vertical muons of energy E_μ≥~1.6 GeV passing through these scintillator detectors will trigger them at an estimated rate of about 1~5 events per day according to a previous measurement [45] and estimation [33]. To reject the dark noise rate in a single scintillate detector, a coincidence with signal by energy deposition between 1.6 GeV±2σ in the water shield will be first tried. Detailed trigger criteria will be determined by more study of the actual data.

Neutrons are probably among the most important backgrounds that affect almost all underground experiments. For double-beta decay experiments, high-energy neutrons (a few MeV and above) produce background gamma rays via inelastic scattering while thermal neutrons contribute to the gamma ray background through neutron capture. Neutrons at several MeV and above also pose a threat to neutrino detection in low-energy neutrino experiments via inverse beta decay. Neutrons at sub-GeV and GeV energies, although rare, constitute a background for proton decay and atmospheric neutrino experiments. In WIMP dark matter detectors, nuclear recoils of several keV energies by neutron elastic scattering mimic WIMP-nucleus interactions.

Figure 2. Signals of interactions in the LUX detector. Color circles at the top and bottom of the volume represent two arrays of PMTs (Hamamatsu R8778). The hit pattern in the bottom array provides the x-y localization of an event, while the time between the primary (S1) and the secondary (S2) scintillation signals provides the z-localization of the collision.

Figure 3. Calibration data for the LUX prototype detector in Case [52] showing the ratio of charge to light (S2/S1) versus S1-based energy for electron recoils (left) and nuclear recoils (right). In both plots, the red line and the green line represent the mean of distribution, along with 99% and 99.9% ER discrimination levels.
EDELWEISS-II (4,800 m.w.e. level, Frejus site, muon flux ~4×10^-6 /m²/d, fast neutron flux ~1.6×10^-6 /cm²/s [53]) for the first time claimed several coincidences between its muon veto and muon-induced neutrons in its Ge crystals (consisting of 330 g Ge/NTD, 400 g Ge/NbSi and new 400 g Ge/NTD) [54]. However, the rather small rate of ~0.04 coincidences/kg/d for both E≤250 keV neutron- and electron-type recoils limits a detailed investigation of μ-induced neutrons in this experiment. The measurement of muon-induced neutrons reported by the ZEPLIN-II group [55] has not detected any coincidences between low-energy (< 100 keV) events in its xenon vessel and high-energy events (> 0.5 MeV) in its liquid scintillator [43]. Comparing to the 730 kg liquid scintillator shield and 7.2 kg of liquid xenon used in ZEPLIN-II, LUX (300-tons of water and 350 kg of LXe) should have a better chance to see the coincidence between high-energy muons (triggering the water shield) and nuclear recoil in the inner LXe detector. Successful observation of the coincidence between muons and the nuclear recoil signals in the LUX inner detector will give us enormous confidence on muon-induced neutron level in the LUX experiment, which will further provide an anchoring point in the simulation of neutron background level in the Davis Cavern. Accumulating more coincidence events will eventually help to characterize the true fluctuations of muon-induced backgrounds in a real detector, which cannot be done by either calibration with radioactive sources or in present simulation.

Given the importance of neutrons on all underground experiments, we also propose to have more study on muon-induced neutrons in the LUX water shield. Two approaches for tagging neutrons in a water Cherenkov detector were proposed. One is to use the 2.2 MeV gamma from the n + p  d + γ reaction [56]. The second is by adding gadolinium trichloride GdCl₃, which is highly soluble and transparent in solution [57]. Neutron capture on gadolinium yields a 7.9 MeV (80.5%) and an 8.5 MeV (19.3%) gamma cascade. Using these techniques, progress was made recently in measuring high-energy muon induced neutrons in the ZEPLIN-II liquid scintillator [55] and at Super-Kamiokande [58]. The maximum kinetic energy of a Compton-scattered electron by a 2.2 MeV gamma is 1.97 MeV, the so-called “Compton edge”. Super-Kamiokande reported the 8 MeV gamma cascades from neutron capture on gadolinium to have a mean measurable energy of 4.3±0.1 MeV. Taking those numbers in Table 2 for vertical equivalent muons (VEM) or Michel electrons in the Auger tank for example, one expects an average of 0.5 PEs and 1.1 PEs for a 1.97 MeV electron and a 4.3 MeV cascade in the LUX water shield. Without changing its current configuration, tagging neutrons in the LUX water shield by either of these two methods seem marginally doable.

Because of the very low light yield in either of the two processes, neutron tagging efficiency strongly depends on Cherenkov light collection. We will use the verified water shield simulation package to investigate how to improve neutron tagging techniques and Cherenkov light collection efficiency by optimizing PMT locations and using various reflective liners and/or wavelength shifter additives. We may propose, for example, a fully instrumented water shield with greater PMT cathode coverage and/or Gd doping for next generation dark matter experiments. We will also simulate neutron-tagging efficiency in the liquid scintillator proposed for active vetoing in our next projects LZS and LZD and compare all these techniques to optimize the design for next generation dark matter experiment.
B-3. Study the long-term behavior in LUX data and compare with IceCube results

Because the expected event rate is extremely low, most underground experiments have to take years of data to have enough statistics to reach their physics goals. Therefore, monitoring the long-term behavior of their signals (both background signals and “event” signals) is essential in pursuing any physics results. Despite the anisotropy of cosmic ray arrival directions observed by surface array [59] and deep under-ice muon detector [60], one well-known long-term behavior is the annual modulations observed in different experiments at different depths. Two representatives are, (a) the rate in the DAMA dark matter search experiment, (b) the underground muon rate.

(a) DAMA: The DAMA Collaboration reported preliminary results of a positive annual modulation indication in late 1997 [61]. The modulation was later confirmed by the DAMA experiment that consists of an array of nine NaI(Tl) crystals with a total mass of 100 kg operated for a continuous seven-year period that ended in July 2002 [62]. The annual modulated variation in the signal was reported at 6.3σ CL. The newly combined 11 years from data of both experiments (with an exposure of 0.83 ton×year) show an 8.2σ annual modulation signal [63], Figure 4.

DAMA is the only experiment that has claimed to observe an annual modulation in their data compatible with the signal expected from dark matter particles bound to our galactic halo, contrary to the negative results of all other direct DM searches. DAMA statement of detection of dark matter signals has raised many discussions on the WIMP scattering mechanism with nuclei and various halo models [3, 63, 64]. Nevertheless, given various assumptions in the explanation of their signal, it is clear that more analysis is needed to reach a consensus.

Figure 4. Model-independent residual rate of the single-hit scintillation events, measured by the DAMA/LIBRA experiment in the 2-6 keV energy intervals as a function of time, from [63].





Figure 5. Top: Annual muon flux modulation for energies great than 1.3 TeV observed by the LVD experiment [69]. Bottom: The superposition of the mean monthly variations in the muon rate (in percentage on left Y axis), and the mean monthly variation in the effective temperature (in percentage on right Y axis), from [65]. A total of 5.33×10⁶ single muons collected in 1992-1994 were used.
(b) Annual variation of muon flux: The muon flux modulation has been reported by several underground or under-ice experiments, such as the MACRO experiment [65], MINOS [66, 67], IceCube [68] and, very recently, LVD [69, see the top entry in Figure 5]. The muon flux measured by MACRO shows a nearly sinusoidal time behavior with one-year period and a maximum in summer, (see the bottom entry in Figure 5). The plotted effective temperature depends on both the atmosphere temperature profile at different depths and the atmospheric attenuation length for pions and nucleons as described by the formula below,

in which the Λ_π and Λ_N are the atmosphere attenuation lengths for pions and nucleons. The integral is from the surface to the top of the atmosphere. This analysis also showed that muons from the decay of pions and kaons are 77% and 23% in MACRO data. The annual modulation in the IceCube in-ice muon rate was associated with the temperature profile of the stratosphere at pressure layers from 20 hPa to 100 hPa where the first cosmic ray interactions happen [68]. Authors in IceCube also explained the modulation as the result of the seasonal change of the Antarctic atmosphere and the characteristics of cosmic ray interactions in the atmosphere. Given the strong evidence of the correlation of muon flux with the atmospheric temperature, the scale of the modulation also depends on the depth of the experiment and the threshold in the experiment. Studying these effects in LUX data is important because it helps determine the background due to non-dark matter contributions.

It is very much worth pointing out that, using the details provided in [63], the annual modulation amplitude in DAMA experiments with recoil energy between 2-6 keV is (0.0129±0.0016) cpd/kg/keV. This corresponds to relative amplitude of about 1.3±0.1 % against an overall background counting rate of about 1 cpd/kg/keV. The phase is 144±8 days, with the maximum in early June. Meanwhile, in the LVD muon result, the amplitude is 1.5±0.1 % with a phase of 185±15 days and the maximum in early July [69]. Before any solid conclusion can be made whether the similarity is a true effect or just a coincidence, detailed studies with both simulation and new experiment data are needed, especially using data from different experiment such as LUX.
One important lesson from the arguments around the DAMA results is that eliminating any modulation due to cosmic rays or other terrestrial sources by normal matter or processes, annual or not, is essential to understand any observed modulation in dark matter data. In this proposal, we will carry out the following systematic study of modulations in the water shield and LXe data:

(1) Look for modulations in signals in the water shield and in the LXe detector. The total muon rate in the LUX water shield is high enough to see monthly modulation of several percent after 2~3 years of data taking.

(2) Estimate the annual modulation amplitude in muon flux at the 4850 ft level in the Davis Cavern by simulation. In order to include the annual change in the atmosphere, the simulation will be done using cosmic ray primary particle flux. We will also update the atmospheric parameters to include the local atmosphere monitoring data. See more details about this work in Section C below.

(3) If any modulations are measured in the LUX water shield, we will compare them with simulations to cross check the expectations. We will compare them with the muon modulation recorded in IceCube data taken during the same time period to look for any anti-correlations between them. Since LUX and IceCube have different overburdens and are located in different hemispheres and under very different weather and environmental conditions, such combined analysis will provide a unique view in the sense that the two data sets represent different over-burden depths, different locations on the Earth and different view directions in space.

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