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Cosmic Ray Muon Flux at the Sanford Underground Laboratory at Homestake

Measuring the muon flux is important to the Sanford Underground Laboratory at Homestake, for which several low background experiments are being planned. The nearly-vertical cosmic ray muon flux was measured in three locations at this laboratory: on the surface (1.149 \pm 0.017 x 10^-2 cm^-2 s^-1 sr^-1), at the 800-ft (0.712 km w.e.) level (2.67 \pm 0.06 x 10^-6 cm^-2 s^-1 sr^-1), and at the 2000-ft (1.78 km w.e.) level (2.56 \pm 0.25 x 10^-7 cm^-2 s^-1 sr^-1). These fluxes agree well with model predictions.

The Homestake Mine in Lead, South Dakota, USA was identified in 2007 as the final candidate site for the Deep Underground Science and Engineering Laboratory (DUSEL). In advance of the federal funds to further develop the mine, the South Dakota Science and Technology Authority (SDSTA), which operates the Sanford Underground Laboratory, is offering an early science program mainly to characterize aspects of the site environment. It is located at 44.35 • N, 103.77 • W, with a surface elevation of 1620 m above sea level. Initially, the LUX (Large Underground Xenon) dark matter search [1] and the Majorana neutrinoless double beta decay experiment [2] will be located there. Measurements of external backgrounds, including cosmic ray muons as well as gammas and neutrons, will be of paramount importance to the design of these sensitive rare-event searches.
The differential muon flux at the 4850 ft. (4.40 km water equivalent) level at Homestake was measured by Cherry et al [3]. However, more measurements are needed to characterize the muon flux as a function of depth. This paper describes new measurements of the cosmic ray muon flux at three locations: the surface (in a building that provided ∼1 m w.e. of shielding), the 800 ft. (0.712 km w.e.) level, and the 2000 ft. (1.78 km w.e.) level. We present a comparison between our reported flux and the model of [4], and we find agreement between our experimental results and that model.
Cosmic-ray muon flux as a function of depth has been studied by many experiments at underground facilities around the world. Measurements of the muon flux per unit solid angle as a function of slant depth from Castagnoli [5], Barrett [6], Miyake [7], WIPP [8], Soudan [9], Kamioka [10], Boulby [11], Gran Sasso [12,13], Fréjus [14] and Sudbury [15] have been used to develop a model, which can be used to predict the muon flux per unit solid angle as a function of depth [4].

Methods
The muon detector consists of four fast plastic scintillation counters (Saint-Gobain BC-408), each a square with a side length of 30.5±0.1 cm. As shown in Figure 1, the distance from the top to the bottom counter is 64.0 cm. Two of these counters are 0.5 cm thick, and the others are 1.0 cm thick. Each is coupled by a trapezoidal acrylic lightguide to a Photonis XP2020 photomultiplier with Photonis VD124K base. Waveforms from each detector are recorded by a 12-bit flash analog-to-digital conversion module with a sampling frequency of 170 MHz; it filters the data onboard with field programmable gate arrays and transmits digitized pulses through an Ethernet interface to a standard personal computer.
The detector station also includes a 1.2 L liquid scintillation counter filled with Eljen Technologies EJ-301 or EJ-309 material. This counter has been used to study techniques for neutron counting in the underground environment; a future publication will quantify neutron backgrounds in the mine.
The gamma ray flux at each of the sites is at the level of 1 cm −2 s −1 ; the counting rate for background gamma events in each of the plastic scintillator detectors is therefore ∼1 kHz. Nearly all of the gamma flux is at energies of 2.5 MeV or less, as was reported in [16]. A substantial coincidence requirement is needed to distinguish cosmic ray muon events from the gamma background. At the 2000 ft. depth, a two-fold coincidence analysis was found to be dominated by the gamma background, and at shallower depths they still represent a substantial correction. Consequently, all of our results are based on studies where we require that at least three of the four detectors record a pulse within a ∼70 ns time interval. Because of the higher counting rate and reduced sensitivity to several systematic uncertainties, we present the three-fold coincidence analysis as our primary result, and a four-fold coincidence analysis (where all four detectors are required to fire simultaneously) as a partially independent check. In particular, the agreement between the three-fold and four-fold coincidence  results demonstrates that secondary particles such as high-energy electrons produced by muon interactions do not affect the counting rate substantially relative to the precision of this measurement.
A geometric Monte Carlo calculation was used to determine the solid angle accepted by each of these analysis methods. It took into account only the size and position of each of the detector elements, assuming straight muon tracks. As shown in Figure 2, it was used to determine the acceptance probability as a function of polar angle P (θ), which was then integrated to determine the accepted solid angle: When a four-fold coincidence is required, the accepted solid angle is 0.226 sr; it is 0.457 sr when only a three-fold coincidence is required. If we assume an incident muon distribution proportional to cos 2 θ, 90% of the flux in the threefold coincidence analysis would be within 25 • of vertical, while 90% of the flux in the four-fold coincidence analysis would be within 19 • of vertical.
This Monte Carlo program was also used to study the systematic uncertainty arising from misalignment of the detector elements. A horizontal displacement of one detector element in this program by 2 cm, which is believed to represent the worst realistic possibility for the data collected on the 800 ft. level, changed the calculated solid angle by a maximum of 0.4% for the three-fold coincidence analysis and 1.1% for the four-fold coincidence analysis. The alignment on other levels is believed to have been substantially better, with a maximum possible displacement of 1 cm.
The energy scales of the detectors were calibrated based on the observed pulse amplitude spectra for four-fold coincident events. All such events on the surface and at the 800 ft. level were presumed to be minimum-ionizing particles that would give a most probable energy deposition of 1.0 MeV in the thin detectors and 2.0 MeV in the thick detectors. These energies were computed from the scintillator density of 1.032 g/cm 3 , assuming the minimumionizing dE/dx given by the Bethe-Bloch equation [17]. At the surface and the 800 ft. depth, there was sufficient statistical power to allow the calibration to be determined in situ. At the 2000 ft. depth, a calibration from the surface was applied; this method would have been preferred at the 800 ft. depth as well, but detector repairs required recalibration to be completed underground. The digitization hardware thresholds were set as low as practical, corresponding to approximately 0.4 MeV for the thin detectors and 0.9 MeV for the thick detectors. Analysis thresholds were then established at 0.75 MeV in the thin counters and 1.5 MeV in the thick counters. These thresholds require a total energy deposition of at least 3 MeV for a three-fold coincidence, which is beyond the endpoint of the gamma spectrum, but still maintains an efficiency for muons that can be determined effectively.
The efficiency corrections associated with these energy cuts were determined from the data. At the surface, we assumed that all four-fold coincident events were caused by minimum-ionizing particles; other particles from atmospheric showers would have been shielded effectively by the ∼1 m w.e. provided by the building above the detector. Therefore, we computed the ratio of the number of events that passed the analysis cuts to the the total number of recorded four-fold coincidences where only the hardware thresholds were used.
Having determined this efficiency on the surface, we then applied it to data collected at the 2000 ft. level. The uncertainty associated with this procedure includes a statistical component from the finite number of coincidences at the surface. However, another part of the uncertainty is related to the stability of the detector gain, and therefore the energy scale, especially as the detector was being moved underground. We checked for these gain shifts using three standard beta/gamma calibration sources, 22 Na, 60 Co, and 90 Sr, collecting pulse height spectra before and after relocating the detector. Averaging the results from these sources, we found gain reductions of 0.8%, 2.0%, 4.7%, and 3.1% for the four detector elements. We corrected the energy scale in the analysis according to these results, and we treated the 1.0% uncertainty in each detector calibration as the systematic error for the efficiency in the result from the 2000 ft. level. Examination of the energy distribution in each detector showed that the singledetector rate would change by 0.4% for each percent change in the assumed energy scale, and a Monte Carlo simulation verified the naive predictions that such a change would give a modification of 0.4% to the three-fold coincidence analysis and 1.6% to the four-fold coincidence analysis.
Because it was necessary to recalibrate the detector while it was at the 800 ft. level, a different procedure was applied there. We determined separately for each scintillator the fraction of four-fold coincidence events where only the hardware threshold was imposed that would be cut by applying the energy threshold in that scintillator. We incorporated these efficiencies into the geometric Monte Carlo simulation program and observed the change in the number of accepted three-fold and four-fold coincidence events in order to determine the overall efficiency. The uncertainty associated with this procedure is taken to be purely statistical; any systematic drift in the energy scale should present a negligible effect, as the detector remained untouched underground at nearly constant temperature. The computed efficiency was substantially higher than before, because an upgraded flash ADC electronics module was installed when the detector was relocated to the 800 ft. level; the new module included an integrating filter that improved the effective energy resolution of the system.
The start and stop times of each data file run were determined from the acquisition computer's internal clock, which is synchronized using the Network Time Protocol with a stratum 2 server. These times were used for the primary determination of the experiment's live time. In addition, the flash ADC module was set to generate periodic sampling triggers every 0.8 s, and these triggers were counted for a subset of the data as a cross-check and found to agree within 0.1%. The time base on the flash ADC board is derived from a crystal oscillator that is specified for accuracy and stability to ±50 ppm.

Results
We have determined that the rate of throughgoing muons on the surface, on the lower floor of the SDSTA administration building (∼1 m w.e.), is     Table 1 provides more details on the measurements that led to these flux values, and it compares them to the corresponding results from the four-fold coincidence analysis method. Figure 3 shows the muon flux as a function of the depth, comparing the measured fluxes to the prediction of a parameterization model [4]. The agreement between the measurements and predictions for different levels is within 20% in all cases. The integrated muon fluxes at the different levels are also compared to the prediction of a flat-earth model [4]. Figure 4 illustrates the agreement, which is clearly excellent over five orders of magnitude in flux. We have considered the effect of the large open cut in the mine; while it is quite deep, the slant depth to our experimental sites is large enough that it has a negligible effect on the flux. Consequently, we have used these models to predict the differential and integral fluxes at levels of scientific interest, as summarized in Table 2.

Acknowledgments
We thank Jaret Heise, Tom Trancynger, and all of the staff at the Sanford Laboratory for their valuable support. We also thank Uwe Greife of the Colorado School of Mines for allowing us to use his laboratory resources for this project. This work was supported by the National Science Foundation under grant NSF-PHY-0758120.  Figure 3: Muon flux as a function of depth, placing these measurements in the context of previous results from Castagnoli [5], Barrett [6], Miyake [7], WIPP [8], Soudan [9], Kamioka [10], Boulby [11], Gran Sasso [12], Fréjus [14] and Sudbury [15], and comparing them with a parameterization model [4]. The three data points for Homestake are from this work (filled black circles) and Cherry et al. [3] (filled black square).  Table 2: Differential (per unit solid angle) and integral fluxes calculated at several levels in the Homestake Mine using modeling techniques described in [4] that have been calibrated by the results described in this paper. Major experimental campuses are proposed for the 4850 ft. and 7400 ft. levels, while 8000 ft. is the deepest level.