Muon-induced background study for underground laboratories

We provide a comprehensive study of the cosmic-ray muon flux and induced activity as a function of overburden along with a convenient parametrization of the salient fluxes and differential distributions for a suite of underground laboratories ranging in depth from $\sim 1$ to 8 km.w.e.. Particular attention is given to the muon-induced fast neutron activity for the underground sites and we develop a depth-sensitivity relation to characterize the effect of such background in experiments searching for WIMP dark matter and neutrinoless double-beta decay.

Figure 1

Measurements of the differential muon flux as a function of slant depth from Castagnoli [67], Barrett [68], Miyake [69], WIPP [4], Soudan [23], Kamioka [12], Boulby [6], Gran Sasso [8, 70], Fréjus [11] and Sudbury [7]. Note that the measurements for Kamioka [12] and Sudbury [7] are reported as the number of muons per day. We calculate the effective detector acceptance for these two measurements in order to obtain the muon flux. The solid curve is our global fit function described by Eq. (1).

Figure 2

The relative deviation between the global fit function and the measured data on the differential muon flux from Castagnoli [67], Barrett [68], Miyake [69], WIPP [4], Soudan [23], Kamioka [12], Boulby [6], Gran Sasso [70], Fréjus [11] and Sudbury [7]. The horizontal lines indicate the root-mean-square deviation amongst the residuals.

Figure 3

The total muon flux measured for the various underground sites summarized in Table  as a function of the equivalent vertical depth relative to a flat overburden. The smooth curve is our global fit function to those data taken from sites with flat overburden [Eq. (4)].

Figure 4

The relative deviation between data on the total muon flux and our global fit function. The horizontal lines indicate the root-mean-square deviation amongst the residuals based upon the experimental uncertainties in the measurements.

Figure 5

The ratio of stopping muons to throughgoing muons, relative to the vertical direction, as a function of depth. The ratio is calculated assuming the Majorana-like detector geometry discussed later in this paper assuming a 60 kg target mass of germanium surrounded by 40 cm of lead.

Figure 6

The muon energy spectrum local to the various underground sites calculated using Eq. (8). The areas under the curves are normalized to the vertical muon intensity for comparison purposes.

Figure 7

The muon angular distribution local to the various underground sites based on Eq. (3). All curves have been normalized to the total muon intensity for comparison purposes.

Figure 8

The neutron production rate in liquid scintillator versus the mean muon energy. Data points with uncertainties are experimental measurements from Hertenberger [25], Boehm [27], Bezrukov [26], Enikeev [28], the LVD data [29] and Aglietta [30]. The solid curve is our global fit to the data after correcting the LVD data point for quenching effects described in the text. Our global-fit curve describes the data well but the FLUKA simulations tend to underestimate the neutron production rate by about 35%.

Figure 9

The quenching function relating the effective or visible energy in liquid scintillator versus the kinetic energy imparted to a recoiling proton induced by neutron scattering (adopted from Ref. 33).

Figure 10

The relative deviation between our global fit function and the measured neutron production rate as a function of the mean muon energy. The uncertainties represent the experimental uncertainties on the measured data points and the horizontal lines indicate the root-mean-square deviation on the residuals.

Figure 11

The muon-induced neutron production rate versus the mean muon energy after correcting the neutron multiplicity in the FLUKA simulation.

Figure 12

Simulation of the muon-induced neutron production rate versus the atomic weight of the medium.

Figure 13

Simulation of the muon-induced neutron production rate versus $Z^2/A$ of the medium.

Figure 14

The total muon-induced neutron flux deduced for the various underground sites displayed. Uncertainties on each point reflect those added in quadrature from uncertainties in knowledge of the absolute muon fluxes and neutron production rates based upon our simulations constrained by the available experimental data.

Figure 15

The muon-induced neutron production rate predicted for some common detector shielding materials. Note that minor variations due to neutron backscattering have been neglected in these calculations.

Figure 16

The differential energy spectrum for muon-induced neutrons as measured in the LVD experiment before and after correcting for proton-recoil quenching effects described in the text. All models shown are normalized to the uncorrected LVD data point at proton-recoil energy of 0.4 GeV. Note that the corrected data point at 0.4 GeV still overlaps with the uncorrected value since the quenching factor is close to unity at this energy. The FLUKA simulations reproduce the shape of the differential energy spectrum well following the correction to the LVD data.

Figure 17

The differential energy spectrum for muon-induced neutrons at the various underground sites. The bin width is 50 MeV.

Figure 18

Simulation of the muon-induced neutron angular distribution for neutrons produced relative to the primary muon track.

Figure 19

Calculated neutron multiplicity at different experimental sites. Shown is a solely FLUKA calculation without correcting multiplicity using Eq. (10).

Figure 20

The fraction of muon-induced neutrons emerging as a function of distance from the primary muon track in several media. The curves exhibit distinct features relevant to neutron production and propagation in the media. At short range from the muon track, neutron production increases with distance as the nuclear and electromagnetic shower develops, however, neutron production weakens after about 50 cm from the muon track and propagation/attenuation of neutrons in the medium dominates.

Figure 21

Relative attenuation factors for the muon and muon-induced activities as a function of overburden. The curves are normalized, arbitrarily, to unity for the shallower depth defined by the WIPP site at $1.585\mathrm{km}.\mathrm{w}.\mathrm{e}.$ Roughly, an attenuation factor of about 1 order of magnitude is achieved for every $1.5\mathrm{km}.\mathrm{w}.\mathrm{e}.$ increase in depth.

Figure 22

The predicted event rates for spin-independent WIMP-nucleon scattering (dotted line) in Ge assuming a WIMP-nucleon cross section of ${\sigma }_p=10–46\mathrm{c}{\mathrm{m}}^2$ and a 100 GeV WIMP mass. Muon-induced neutron backgrounds are also displayed for comparison, indicating the need for greater and greater depth as experiments evolve in scale and sensitivity.

Figure 23

The depth-sensitivity relation (DSR) derived for the CDMS-II detector geometry for the two shielding configurations described in the text. The muon-induced background is dominated by elastic scattering of neutrons depositing visible energy in a 10 to 100 keV window. Specific points are shown, for example, at the depth of the Soudan mine where the CDMS-II detector has been operating. Uncertainties reflect those present due to uncertainties in the rock composition and in generating the muon-induced fast neutron flux.

Figure 24

A simulation of the muon-induced background for a Majorana-like experiment operating at an equivalent overburden provided by the Gran Sasso Laboratory. In (a) we show the full spectrum with an expanded profile in (b) spanning the region of interest (ROI) around the $Q$-value for neutrinoless double-beta decay at 2039 keV. The peak at 2023 keV is characteristic of that produced via the $76\mathrm{Ge}(n,n^{\prime }\gamma )$ reaction.

Figure 25

The depth-sensitivity relation (DSR) derived for a Majorana-like experiment showing, specifically, the results from this work assuming the detector is operated at a depth equivalent to the Gran Sasso Laboratory. The raw event rate in the energy region of interest of 0.026 events/keV-kg-year can be reduced by a factor of 7.4 by exploiting the detector granularity, pulse-shape discrimination (PSD), and detector segmentation. The upper curve displays the background simulated in the case that no active neutron veto is present and the lower curve indicates the reduction that would ensue if an active neutron veto were present that is 99% efficient.

Figure 26

The neutron energy spectrum arising from $(\alpha ,n)$ reactions due to radioactivity in the rock. We predict a harder energy spectrum in Gran Sasso rock relative to standard rock owing to the presence of carbon and magnesium.

Figure 27

The energy spectrum for fast neutrons produced by $(\alpha ,n)$ reactions in the rock compared to those induced by muon interactions in the rock with and without shielding. The lower energy neutrons $(<10\mathrm{MeV})$ are quickly absorbed using polyethylene shielding, however, the high-energy portion of the muon-induced neutron flux persists. The addition of lead shielding adjacent to a detector can also create an additional source of muon-induced neutrons.

Figure 28

The $(\alpha ,n)$-induced background versus polyethylene shielding thickness for the CDMS-II and Majorana detectors considered in this work. The upper limit on the spin-independent WIMP-nucleon cross section obtained by the CDMS II Collaboration [59] is shown in the upper panel for comparison along with that predicted for the muon-induced neutron background at Soudan and Sudbury. The lower panel includes our predicted value for the background in the Heidelberg-Moscow experiment (KKDC) [71] before and after the reduction obtained using detector granularity, pulse-shape discrimination (PSD), and detector segmentation.