---
abstract: 'We evaluate background rejection capabilities and physics performance of a detector composed of two diverse elements: a sensitive target (filled with one or two species of liquefied noble gasses) and an active veto (made of Gd-doped ultra-pure water). A GEANT4 simulation shows that for a direct WIMP search, this device can reduce the neutron background to O(1) event per year per tonne of material. Our calculation shows that an exposure of one tonne $\times$ year will suffice to exclude spin-independent WIMP-nucleon cross sections ranging from $10^{-9}$ pb to $10^{-10}$ pb.'
address: 'Dpto. de F[í]{}sica Teórica y del Cosmos & C.A.F.P.E., Universidad de Granada, Spain'
author:
- 'A Bueno, M C Carmona and A J Melgarejo'
title: 'Direct WIMP identification: Physics performance of a segmented noble-liquid target immersed in a Gd-doped water veto'
---

[*Keywords*]{}: Dark matter, argon, xenon, neutron, background rejection

Introduction
============

Evidence for the existence of dark matter is overwhelming. The first was found by F. Zwicky in 1933 while measuring the rotational velocity of the Coma cluster of galaxies [@Zwicky]. Since then astronomers have gathered more relevant data, which likely point in the direction of the existence of a new form of matter [@Trimble]. For instance, the striking optical and X-ray images, obtained by the Chandra telescope, of the so-known bullet cluster (1E0657-558) [@bullet; @bullet2] cannot be explained simply by advocating that Newtonian dynamics is modified at large scales [@Sanders]. Additional support for dark matter comes from the precise measurement of the cosmic microwave background radiation done by the Wilkinson Microwave Anisotropy Probe (WMAP). Together with the Sloan Digital Sky Survey (SDSS) large-scale structure data, it tells us that only a small fraction of the matter content of the Universe ($\Omega_B = 0.042\pm 0.002$) is of baryonic origin, while the rest is made of a totally unknown new form of matter ($\Omega_{DM} = 0.20\pm 0.02$) [@wmap]. The rest of the energy content of the Universe ($\Omega_\Lambda = 0.76\pm 0.02$) is accounted for by a very smooth form of energy called dark energy.

So far dark matter has been observed only through its gravitational effects, therefore we know little about its fundamental properties. Massive neutrinos contribute to a small fraction of dark matter [@atm; @solar]. However the most plausible hypothesis for potential candidates (generically known as Weakly Interacting Massive Particles, WIMPs) states that they should be neutral weakly-interacting heavy particles with lifetimes comparable to the age of the Universe. No such thing exists in the Standard Model of Particle Physics. However theories beyond it (like, for example, Supersymmetry, Extra Dimensions, etc.) do have particles that naturally arise as dark matter candidates [@Bertone].

Parallel to model building developments, there is an intense and challenging experimental activity devoted to WIMP detection, as well [@Gaitskell]. DAMA/NaI claims to have found evidence for the presence of WIMPs in the Galactic halo [@Bernabei:2000qi]. Using a direct detection method, they have measured an annual modulation, over seven annual cycles (107,731 kg day total exposure), consistent with expectations from a WIMP signature. The collected DAMA/LIBRA data [@Bernabei:2008yi] supports this claim. Considering the data from both experiments (amounting to an exposure of 0.82 tonnes $\times$ yr), the presence of dark matter particles in the galactic halo is supported at 8.2 $\sigma$ C.L. However, the situation is highly controversial since other direct-search experiments, probing similar regions of the parameter space, have found negative results [@Akerib:2004fq; @Chardin:2003vn; @Ahmed:2003su; @warp; @xenon10]. Indirect detection methods have not found signals that could be attributed to WIMP annihilation [@Ambrosio:1998qj; @Desai:2004pq].

To improve current sensitivities and explore in depth the parameter space of the most favoured dark matter models, there is an indisputable need for more massive detectors with enhanced background rejection capabilities. The use of liquefied noble gasses, as target for WIMP interactions, ranks among the most promising detection techniques [@nobleliquids1; @nobleliquids2; @nobleliquids3]. This technology is easily scalable and allows to build detectors in the range of few tonnes of fiducial mass [@andre]. This paper concentrates on evaluating the physics potential of one of such detectors. An effort has been made to design an experiment that allows to reduce as much as possible the background caused by neutron interactions inside the active target. In addition, we consider several independent target units that can be filled with different noble liquids; in this way we can aim at confirming, with a single experiment, that the event rate and the recoil spectral shape follow the expected dependence on A$^2$ for WIMP signals [@pfsmith]. In the following Sections, we describe the basic detector layout and its foreseen physics performance.

Detector description {#sec:det}
====================

Liquid noble elements, used as sensitive medium for direct dark matter searches, are a promising alternative to ionization, solid scintillation and milli-Kelvin cryogenic detectors. When a WIMP particle scatters off a noble element, scintillation photons and ionization electrons are produced due to the interactions of the recoiling nucleus with the neighbouring atoms. The simultaneous detection of primary scintillation photons and ionization charge (or the secondary photons produced when this charge is extracted from the liquid to the gas phase [@rusos]) is a powerful discriminator against backgrounds. Pulse shape provides an additional tool to identify true signals: depending on the nature of the interacting particle, the scintillation light shows a different time dependence [@Hitachi]. In addition, thanks to the high level of purity achieved, these detectors can drift ionization charges for several meters, hence it is conceivable to reach masses of the order of several tonnes. Nowadays XENON [@xenon10], ZEPLIN [@zeplin1; @zeplin2; @zeplin3; @zeplin4], XMASS-DM [@xmass], WARP [@warp] and ArDM [@andre] collaborations use liquid argon or xenon targets to look for WIMPs. Similar detectors can be used to detect the yet unobserved coherent neutrino-nucleus elastic scattering [@betapaper].

Assuming a one tonne detector, we expect an event rate of O(10) events per year of operation for a WIMP-nucleus cross section of 10$^{-10}$ pb. To explore such small cross sections, backgrounds should be reduced to very challenging levels (about 1 event per tonne per year). In case the target is filled with argon, the $^{39}$Ar isotope, which is a beta particle emitter, is a serious source of concern (its activity is approximately 1 Bq per kg of natural argon [@Ar39radio]). However, the most important source of background is due to neutrons produced in detector components or in the rock of the underground cavern. A large fraction of these external neutrons can be rejected using external hydrocarbon shields, active vetoes or a combination of the two [@cline]. High-energy neutrons induced by muon interactions in the rock are a more serious concern. Recently, an innovative neutron multiplicity meter, very similar in concept to the detector discussed in this document, has been proposed to monitor this neutron flux [@akerib]. The flux of internal neutrons can be highly reduced using low activity materials for the inner parts of the detector. However, it is unavoidable that some of them interact with target nuclei mimicking a WIMP signal.

Detectors with a large fiducial volume offer the advantage of an increased probability for neutrons to interact several times, before they exit the target. For WIMPs this is highly unlikely given the small cross sections involved. This fact can be used to further reduce neutron backgrounds. In our case, given the reduced dimensions of the sensitive targets (see below), the signal due to multiple interactions cannot be the main tool for background rejection. To reduce neutron contamination, we propose a detector made of two diverse elements: an external detector, acting as an active veto, made of ultra-pure water doped with gadolinium. This will enhance neutron capture and its posterior identification [@gadzooks]. Immersed in this veto, the internal detector, that acts as target, consists of cells filled with a noble element. This configurations allows to operate the sensitive target with two noble liquids simultaneously. If energy deposits occur, within a certain time window, both in the cell and water, the event is tagged as neutron-like provided the external veto records the typical 8 MeV gamma cascade from neutron capture on gadolinium.

Noble liquid target {#sec:target}
-------------------

We have carried out a full simulation of the detector using GEANT4 [@Allison] (see Figure \[fig:detsim\]). The target is made of 100 low-background metal cylinders (each 40 cm high and 30 cm in diameter). The internal volume, that can be filled with a noble liquid, has 30 cm drift distance and 24 cm in diameter. For our physics studies, the fiducial region corresponds to a cylinder of 6 cm radius and 25 cm high. The fiducial mass amounts up to 0.8 tonnes in case the target is filled with liquid xenon (LXe) and 0.4 tonnes in case liquid argon (LAr) is used. Our device can detect simultaneously the ionization charge and the scintillation light resulting from the scattering of incoming particles off xenon or argon nuclei. Light is read by means of photomultiplier tubes (PMTs) placed at the target bottom. Ionization electrons are drifted to the liquid surface where they are converted into secondary scintillation light that is read by PMTs on top of the cylinders. Charge amplification devices (i.e., GEM, LEM, Micromegas [@Sauli; @Jeanneret; @Giomataris2]) are a possible alternative for charge readout.

This configuration of independent cylinders, apart from the fact of being easily scalable, offers a clear experimental advantage: data taking can proceed with two different targets simultaneously. Cylinders can be filled with argon and xenon, for example. In case a WIMP signal is observed with enough statistical relevance, we can confirm in a single experiment that the event rate and the recoil spectral shape follow the expected dependence on A$^2$.

![ Artist’s view of the detector: (Top) A target cell. (Bottom) Noble liquid target plus active veto.[]{data-label="fig:detsim"}](EPS/cylinder "fig:")\
![ Artist’s view of the detector: (Top) A target cell. (Bottom) Noble liquid target plus active veto.[]{data-label="fig:detsim"}](EPS/det_side_view "fig:")\

Water-Čerenkov neutron detector {#sec:veto}
-------------------------------

The active target is immersed in a water tank (1.6 m height, 6.9 m width and 6.9 m long), made of copper or other low background material. The distance between cylinders is 30 cm. The distance to the veto walls is 60 cm. This distance has been optimized to allow for an efficient neutron capture by gadolinium. The veto contains 70 tonnes of ultra-pure water, once we subtract the volume taken by the sensitive targets and the ancillary system. 1500 9" PMTs (40% photo-coverage), mounted at the water-tank walls, are used to detect the photons produced by neutron capture on Gd. They will detect the light produced by penetrating cosmic muons, as well, thus providing an efficient veto against this kind of events.

Following the approach discussed in [@gadzooks], we have doped the water-filled parallelepiped with highly-soluble gadolinium trichloride (GdCl$_3$). To avoid the absorption of photons by the cylindrical targets and the supporting system associated to them, we propose a solution similar to the one used in the Pierre Auger Observatory [@pao], namely to cover their external walls with Tyvek (a material that shows a reflectivity higher than 90% to Čerenkov light [@justus]). A particular source of concern is the radio-purity of the additive. According to the estimations given in [@gadzooks] and [@sno], the potential background caused by it, especially the alpha particle decays of $^{152}$Gd, is much smaller than what is expected from the sources considered in Section \[sec:results\]. The amount of gadolinium has being chosen in order to minimize the number of neutrons captured by hydrogen nuclei, since we consider the 2.2 MeV gammas coming from this reaction are extremely hard to detect with the outer veto. A dedicated GEANT4 simulation has been carried out to study which is the optimal Gd concentration. A 1 meter radius sphere filled with Gd-doped water has been simulated and neutrons with energies up to 10 MeV have been shot from the center. Figure \[fig:gdconc\] shows the obtained results.

![Number of absorbed particles as a function of the Gd concentration.[]{data-label="fig:gdconc"}](EPS/percent_gd.eps){width=".7\textwidth"}

We observe that while the total number of absorbed particles does not change with Gd concentration, the proportion of Gd-absorbed particles does, saturating at a value $\sim2\%$. Hence, we will use for our calculations a $2\%$ admixture by mass of GdCl$_3$.

To evaluate the veto efficiency, we follow the gammas produced in the 8 MeV cascade following neutron capture by Gd. The detectable signal corresponds to Compton electrons above Cerenkov threshold. More than 90$\%$ of these electrons have energies above 3 MeV, with a mean value of about 5 MeV [@sno]. Nearly 50$\%$ of the Cerenkov photons are detected and only 3$\%$ of them are absorbed by the targets and their associated ancillary system. Considering a global detection efficiency of 15$\%$ for the simulated PMTs, we obtain a light yield of 6 photo-electrons/MeV. Assuming a detection threshold of 3 MeV, our trigger efficiency is $>$95$\%$ for this energy and reaches $\sim$ 100$\%$ at 4 MeV [@hosaka]. The overall detection efficiency for the 8 MeV gamma cascade is $>$90$\%$ and the energy resolution is assumed to be 20$\%$.

Physics performance {#sec:results}
===================

The estimation of the overall background event rate must take into account both internal and external sources of gamma rays and neutrons. We conservatively assume that, due to instrumental limitations, we cannot detect signals below 15 (30) keV of true recoil energy in case we use a xenon (argon) target. On the other hand, we will assume a maximum true recoil energy for WIMP like events of 50 (100) keV for the xenon (argon) target. We note that it has been recently suggested that neutrinos can be a source of background for the next generation of direct-search dark matter experiments [@Monroe:2007]. However, as shown in [@Monroe:2007], for Ar and Xe targets, this background is easily eliminated considering a cut on the true recoil energy above 10 keV. Therefore the cuts we impose throughout this work on the true recoil energy reduce the neutrino contamination to a negligible level.

Contamination from radioactive nuclei, xenon and argon isotopes {#sec:isotopes}
---------------------------------------------------------------

For a target made of argon, an important source of background comes from the presence of radioactive $^{39}$Ar. This is a beta particle emitter with an activity of about 1 Bq per kg of natural argon, which for a single-volume 1 tonne detector translates into a 1 kHz rate. In our case, since the target is divided into hundred independent units, the event rate due to $^{39}$Ar decays does not represent an issue for the design of the data-acquisition system. In addition, the probability to have a $^{39}$Ar decay overlapping with a different sort of interaction is smaller than in the case of a single-volume large-size detector due to the smaller drift times involved.

Regarding the possibility of misidentifying $^{39}$Ar signals as WIMPs, we should note that $\beta$ particles mainly interact with atomic electrons, while nuclear recoils deposit their energy through transfers to screened nuclei [@Lindhard]. This affects the charge generated by an event (for the same energy is around three times bigger for electrons), the charge to light ratio, which is bigger for electrons, and the ratio between the slow and the fast component of the scintillation light of liquid argon (pulse shape discrimination).

According to our simulations, the background due to radioactive nuclei can be reduced to a level well below the one expected from neutrons using the ratio of measured scintillation light over ionization and pulse shape discrimination [@pulse; @warp]. For a nuclear recoil acceptance of 50$\%$, the rejection power against backgrounds caused by electromagnetic particles is $\sim 5 \cdot 10^{-7}$ for each individual target. This rejection power agrees with the results quoted in [@warp] and [@Lippincott:2008]. A further reduction of this kind of background will come from the use of underground-extracted argon [@Galbiati:2007]. Its $^{39}$Ar activity has been recently measured for the first time and shown to be $<$5% of the one present in natural argon. These reasons lead us to not consider further this sort of background.

In case the target is filled with xenon, $^{136}$Xe is the most important radioactive isotope. It decays through double beta decay and therefore, given the small probability of the process, the resulting count rate, in the energy band of interest, is negligible compared to other sources of background, even before any rejection cut is applied.

Krypton and radon are two radioactive nuclides present in commercially available noble gasses and therefore a potential source of background as well. The highest contamination comes from $^{85}$Kr, which $\beta$–decays with an endpoint energy of 678 keV. As has been discussed, impurities of Kr below 10 ppb can be reached [@xenon10], making negligible the contamination produced by those radioactive decays.

Neutrons from target components
-------------------------------

One of the most important sources of background comes from neutrons produced by radioactive contamination of the materials constituting the detector itself. To minimize their rate, the use of copper for all the vessels is likely to be the best possible choice. The radioactive impurities can be reduced below 0.02 ppb in some copper samples which would bring the neutron contamination to below 1 event per year [@ILIAS]. If we conservatively assume a 0.1 ppb contamination, one obtains a neutron production rate of $4.54\times10^{-11}$ s$^{-1}$cm$^{-3}$. Being each cylinder 6 mm thick, its total volume amounts to 2217 cm$^{3}$. This means a total of one neutron per cylinder per year.

The contamination induced by PMTs must be carefully evaluated as well. Main manufacturers continue to optimize the choice of materials used in PMT construction to reduce their radioactivity levels. Typical contamination values for U and Th range from a few tens to several hundreds parts per billion. Among the wide variety of tubes available in the market, it is possible to find out some models specially designed for low background applications where the measured uranium and thorium concentrations in quartz and metal components is of the order of ten or even less ppbs [@Kudryavtsev], giving a yearly production of less than one neutron per PMT. The phototube windows could be coated with Tetra-Phenyl-Butadiene (TPB) to shift the ultra-violet light to the maximum of the phototube spectral response without an increase on contamination. If we assume a rate of 1 neutron emitted per year per PMT and 8 PMTs per cylinder, we expect a total emission of 8 neutrons per cylinder. In total, PMTs and the copper vessel contribute to 9 neutrons emitted per cylinder per year.

Although they will not be considered in the present work, there are several possibilities to reduce the rate of neutrons coming from PMTs. One is to set acrylic light-guides between photomultipliers and the active volume [@Kudryavtsev] which can reduce by a factor 2 the rate of neutrons. Another possibility is to substitute the PMTs on the top of the cylinder by charge readout devices, which can be constructed from low radioactivity materials, having a negligible neutron production rate.

We have studied the background rate due to detector components using a simulated sample that amounts to 50 years of data taking. The results shown in Tables \[tab:detres\] and \[tab:detresXe\] are normalized to one year of operation. Table \[tab:detres\] corresponds to the configuration where LAr is used. Throughout this work, columns labeled as [*Total*]{} refer to the total number of neutrons per year, while columns labeled as [*Not vetoed*]{} refer to those neutrons not being absorbed in the Gd-doped water tank; likewise by $E_{recoil}$ we mean the equivalent recoil energy inferred from the energy measured in the active target.

               Neutrons               Total   Not vetoed
  ---------------------------------- ------- ------------
          Produced in 1 year           900        20
   30 keV $<$ E$_{recoil}<$ 100 keV    19        0.3

  : LAr target: Neutron background from detector components normalized to one year of data taking. \[tab:detres\]

After a simple selection cut based on the nuclear recoil energy, we find a background of 0.3 neutrons per year for a LAr detector with a fiducial mass of 0.4 tonnes. Considering as signal only those neutrons interacting just once inside the active volume, we can get rid of some additional background. However given the small dimensions of the targets, we expect a modest reduction factor from events with multiple interactions. It is important to note that when the active Gd-doped veto is used, the amount of background is reduced by roughly a factor fifty. The results using liquid xenon as target (fiducial mass 0.8 tonnes) are shown in Table \[tab:detresXe\]. The overall background, after the energy cut, amounts to 1 neutron per year. The reduction given by the active veto in this case is only a factor ten. The amount of background for xenon is larger than for argon. The reason comes from the fact that some xenon isotopes like $^{131}$Xe and $^{129}$Xe show a very high cross section for neutron absorption. For the case of a xenon-filled detector, the smaller the dimensions of the target cylinder the better to identify neutrons in the external active veto.

              Neutrons               Total   Not vetoed
  --------------------------------- ------- ------------
         Produced in 1 year           900        64
   15 keV $<$ E$_{recoil}<$ 50 keV    12         1

  : LXe target: Neutron background from detector components normalized to one year of data taking. \[tab:detresXe\]

Neutrons and gamma rays from active veto components
---------------------------------------------------

Assuming the same contamination levels we used in the previous Section to estimate the neutron flux due to copper walls, PMTs, voltage divider bases, etc., we obtain that the active veto system contributes with approximately $10^4$ emitted neutrons per year. The flux of these neutrons is orders of magnitude smaller than the ones that reach the external walls of the detector, after being produced in the rock of the cavern by natural radioactivity (according to Table \[tab:rockres\] it amounts to O(10$^7$) rock-emitted neutrons per year). Therefore the contribution of the neutron-induced background from veto components is added to the contamination induced by the walls of the cavern and will be treated in the next Section, but it represents a small fraction of the total expected background.

Another source of contamination is the gamma ray flux produced by the PMTs of the veto system. They mainly come from the decay of $^{208}$Tl (thorium chain) and $^{214}$Bi (uranium chain). The former produces a 2.6 MeV gamma and the latter emits 2.2 MeV and 2.4 MeV photons. As explained before, we can set a threshold of 3 MeV for the veto system without a significant loss of efficiency. In these conditions, the majority of those gamma rays will fall below threshold. Those reaching the targets can be rejected using the criteria discussed in Section \[sec:isotopes\], and therefore their contribution to the total background will be significantly smaller than the one expected from neutrons.

 Neutrons from surrounding rock
-------------------------------

Neutrons coming from the rock have two possible origins: (1) underground production by cosmic muons (called hereafter “muon–induced neutrons”) and (2) neutrons induced by spontaneous fission and ($\alpha$, n) reactions due to uranium and thorium present in the rock (generically called from now on “radioactive”). The latter have a very soft spectrum (typically energies of few MeV). The energy spectrum from muon–induced neutrons is harder and therefore are more difficult to moderate by the water shielding. Those neutrons may come from larger distances and produce recoils with energies well above the energy threshold set for signal events [@Kudryavtsev]. The active external water veto will efficiently tag crossing muons by Čerenkov light detection. Neutron signals occurring in the noble liquid target in coincidence with water PMT signals will be rejected. There are $\sim10^{7}$ neutron absorptions per year in the water volume. If we assume a 100 $\mu$s veto time per interaction, this will correspond to a total of $\sim20$ min dead time of the detector per year due to neutron interactions.

### Neutrons from radioactivity:

Natural radioactivity can produce neutrons either directly from spontaneous fissions or by means of emitted alpha particles through $(\alpha,
n)$ reactions. To compute the spectrum and the rate of those neutrons, the program SOURCES-4C [@SOURCES] has been used. Since the original program provides $(\alpha,n)$ reactions up to 6.5 MeV $\alpha$ particle energy, we include the modifications done in [@Kudryavtsev] to obtain a more realistic neutron spectrum. The thorium and uranium contamination has been taken as the average of those given in reference [@Amare], namely 18.8 Bq/kg for $^{238}$U and 42 Bq/kg for $^{232}$Th. Secular equilibrium is considered. Accordingly, the computed rates for neutron production amounts to $8.44\times10^{-8}$ s$^{-1}$cm$^{-3}$ from $(\alpha, n)$ reactions and to $7.38\times10^{-8}$ s$^{-1}$cm$^{-3}$ from spontaneous fission. Neutrons have been generated according to the energy spectrum shown in Figure \[fig:enerock\] and propagated through the rock using the GEANT4 simulation code and the prescriptions given in [@Kudryavtsev]. As a result we get the neutron spectrum in the walls of the laboratory. To get the final number of neutrons impinging in the detector outer walls and their energy, we have simulated a cavern of $15\times12\times40$ m$^3$, similar in dimensions to the experimental main hall at Canfranc underground laboratory [@Canfranc]. Table \[tab:rockres\] shows the number of neutrons that reach the detector and those that produce energy deposits in the same range as WIMP interactions. Normalized to one year of data taking, we show the level of expected background for two different distances between the external vessel wall and the first active cylinder a neutron will encounter. With a 60 cm thick water active veto, the number of interactions inside the liquid argon volume is well below 1 per year.

![Energy spectrum of neutrons produced in the rock by natural radioactivity.[]{data-label="fig:enerock"}](EPS/rock_ene.eps){width=".7\textwidth"}

  --------------------------------- ----------------- ----------------- ----------------- -----------------
                                                                                          
              Neutrons                    Total          Not vetoed           Total          Not vetoed
         Produced in 1 year          $4.2\times10^7$   $1.6\times10^7$   $4.2\times10^7$   $1.6\times10^7$
   30 keV$<$$E_{recoil}$$<$100 keV        $175$              $3$               $9$             $<0.1$
  --------------------------------- ----------------- ----------------- ----------------- -----------------

  : Neutron background from rock radioactivity. We assume a LAr target with a fiducial mass of 0.4 tonnes and one year of data taking. Results are shown for two different configurations of the active water veto.\[tab:rockres\]

The study has been repeated considering a liquid xenon target and 60 cm thick water veto. For this configuration, the expected background from rock radioactivity amounts to nearly one event per year (see Table \[tab:rockresXe\]). In accordance with the results got while studying the contamination due to neutrons from detector components, once more the larger cross section for neutron absorption is responsible for having a bigger expected background when xenon is considered as detector target.

              Neutrons                   Total          Not vetoed
  -------------------------------- ----------------- -----------------
         Produced in 1 year         $4.2\times10^7$   $1.6\times10^7$
   15 keV$<$$E_{recoil}$$<$50 keV         $5$               0.7

  : Neutron background from rock radioactivity. A LXe target (0.8 tonnes fiducial mass) has been considered together with an active water veto 60 cm thick. Results are shown for one year of data taking\[tab:rockresXe\]

### Muon-induced neutrons:

Fast neutrons from cosmic ray muon interactions represent an important background for dark matter searches. Unlike charged particles, they can not be tagged by veto systems, and unlike lower energy neutrons from rock radioactivity, they can not be stopped by a passive shielding. However, as proposed in [@akerib], it is possible to place close to the detector some material in which this fast neutrons produce secondary low energy neutrons that can be detected by the proposed veto system when absorbed by Gd.

The total muon-induced neutron flux $\phi_{n}$ as a function of the depth for a site with a flat rock overburden can be estimated as [@Mei:2006]:

$$\phi_{n}=P_0\left(\frac{P_1}{h}\right)e^{-h/P_1}$$

where $h$ is the vertical depth in kilometers water equivalent (km.w.e.), $P_0=4.0\times10^{-7}$ cm$^{-2}$ s$^{-1}$ and $P_1=0.86$ km.w.e.

If we consider the Canfranc underground laboratory, with a depth of $\sim2500$ m.w.e. [@Canfranc], the total neutron flux is $7.52\times10^{-9}$ cm$^{-2}$ s$^{-1}$. The neutron energy spectrum is given by [@Wang:2001]:

$$\frac{dN}{dE_{n}}=A\left(\frac{e^{-7E_{n}}}{E_{n}}+B(E_{\mu})e^{-2E_{n}}\right)$$

$A$ is a normalization constant and $B(E_\mu)=0.52-0.58e^{-0.0099E_\mu}$. The muon energy spectrum can be estimated with the following equation [@Mei:2006]:

$$\frac{dN}{dE_{\mu}}=Ce^{-bh(\gamma_\mu-1)} \cdot \left(E_\mu+
\epsilon_\mu(1-e^{-bh}) \right)^{-\gamma_\mu}$$

where $C$ is a normalization constant, $E_\mu$ is the muon energy in GeV, $b=0.4$/km.w.e, $\gamma_\mu=3.77$ and $\epsilon_\mu=693$ GeV. The previous equations give rise to the energy spectrum displayed in Figure \[fig:muonsrock\].

![Energy spectrum of neutrons produced by muons interacting in the surrounding rock as estimated for the Canfranc lab.[]{data-label="fig:muonsrock"}](EPS/muon_neutron_energy.eps){width=".7\textwidth"}

The angular neutron distribution can be expressed as [@Wang:2001]:

$$\frac{dN}{dcos\theta}=\frac{A}{(1-cos\theta)^{0.6}+B(E_\mu)}$$

with $B(E_\mu)=0.699E_\mu^{-0.136}$.

In order to simulate the fast neutron background, we consider a $10\times10$ m$^2$ surface on the detector from which we simulate neutrons with the specified angular and energy distributions. Together with the detector itself, we simulate a lead block in which neutrons will create secondary particles. We have considered two different configurations (lead block on the top or at the bottom of the detector) and two different thicknesses for the passive lead veto.

[|c|cc|cc|]{} Neutrons & &\
Produced in 1 year & &\
\
30 keV$<$$E_{recoil}$$<$100 keV & &\
Muon veto & &\
\
& & & &\
30 keV$<$$E_{recoil}$$<$100 keV & 149 & 149 & 8 & 11\
Muon veto & 15 & 15 & 0.7 & 1\
\
& & & &\
30 keV$<$$E_{recoil}$$<$100 keV & 34 & 9 & 4 & 0.3\
Muon veto & 3 & 1 & 0.4 & $<0.1$\

According to Table \[tab:muonres\], out of the four configurations studied, the best one corresponds to the case where a 60 cm thick lead block is placed on top of the detector. With this passive veto alone, the background is about ten events per year, provided the lead is 60 cm thick. When combined with the Gd-doped water veto, the background drops well below one event per year. The simulations have been repeated considering liquid xenon as the target material. Results are shown in Table \[tab:muonresXe\]. Again, the expected background coming from muon-induced neutrons is $\sim$1 event per year for the whole detector. However, further reduction can be achieved when water itself is considered as an active veto (as shown in Tables \[tab:muonres\] and \[tab:muonresXe\], where we refer to it as Muon veto). It has been demonstrated that by rejecting events in coincidence with a muon, the contamination level decreases by a factor 10 [@Kudryavtsev]. In our case, this means the overall background would be well below 1 event per year per tonne of target material.

              Neutrons                  Total          Not vetoed
  -------------------------------- ---------------- ----------------
         Produced in 1 year         $2.4\cdot10^5$   $1.9\cdot10^5$
   15 keV$<$$E_{recoil}$$<$50 keV         8               0.7
             Muon veto                   0.8             $<0.1$

  : Background events coming from cosmic muon-induced neutrons using LXe as target material for a data taking period of one year. We assume that a 60 cm thick lead block is installed on top of the detector.\[tab:muonresXe\]

Discussion
==========

As a result of our study, we have seen that the combination of a noble liquid (used as sensitive target) and a Gd-doped active water veto efficiently reduces neutron background. For idealized data taking conditions, if we take as reference value an exposure of one tonne $\times$ year, the total neutron-induced contamination for the case of an argon-filled detector is one event, while two events are expected for the case of xenon (see Table \[tab:summary\]). As shown in Figure \[fig:limit\], in case no statistically significant signal is observed, we can reach sensitivities [@Feldman] for the WIMP-nucleon spin-independent cross section close to 10$^{-10}$ pb. To compute these limits we have assumed a standard dark matter galatic halo [@lewin], an energy resolution that amounts to 25$\%$ for the energy range of interest and 50$\%$ nuclear recoil acceptance. For completeness, we note that the best upper limit to date excludes (at 90$\%$ C.L.) cross sections above $4.5 (4.6)\times 10^{-8}$ pb for a WIMP mass of 30(60) GeV/c$^2$ [@xenon10; @cdmslimit].

  --------------------- ----------------------------------- -----------------------------------
       Background                   LAr target                          LXe target
                         (exposure: 1 tonne $\times$ year)   (exposure: 1 tonne $\times$ year)
   Detector components                  0.9                                 1.2
   Rock radioactivity             $\!\!\!\!<$0.1                            0.9
      Muon-induced                      0.1                                 0.1
      [**Total**]{}                 [**1.0**]{}                         [**2.2**]{}
  --------------------- ----------------------------------- -----------------------------------

  : Total expected backgrounds for two different target configurations. Figures have been normalized to an exposure of one tonne per year.\[tab:summary\]

![Achievable sensitivities for the case sensitive targets are filled either with LAr or LXe. The curves have been computed assuming an exposure of one tonne $\times$ year, 50$\%$ nuclear recoil acceptance. The tool from reference has been used [@DAMNED].[]{data-label="fig:limit"}](EPS/limit.eps){width=".7\textwidth"}

Conclusions
===========

We have evaluated the performance of a detector devised to carry out a direct search for WIMPs. It is made of two sub-detectors: the active target consists of small cylinders filled with a liquefied noble gas. They are immersed inside an ultra-pure water tank doped with gadolinium, that acts as a veto system against neutrons and cosmic muons. This configuration enhances the probability for neutron capture in water and its identification, thus providing a much improved rejection tool against this kind of background. This technique is scalable and allows the construction of large detectors with masses in the tonne range.

We have observed that the use of a Gd-doped veto reduces by about a factor fifty the neutron contamination in case the target is filled with argon and up to a factor ten in case xenon is used.

In case a positive WIMP signal is observed with sufficient statistical power, we can confirm, with a single experiment, that the event rate and the recoil spectral shape follow the expected dependence on A$^2$, since the independent target units can be filled with different noble liquids.

A simulation of the potential background sources has shown that for an exposure of one tonne $\times$ year, we expect a contamination of about one event. If no WIMP signal is observed, our calculation shows that, for idealized data taking conditions, this exposure will suffice to exclude spin-independent WIMP-nucleon cross sections in the range $10^{-9} - 10^{-10}$ pb.

Acknowledgments {#acknowledgments .unnumbered}
===============

We thank S. Navas for useful comments and ideas while reading this manuscript. This work has been done under the auspices of M.E.C. (Grant FPA2006-00684).

References {#references .unnumbered}
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