The DARWIN observatory is a proposed nextgeneration experiment to search for particle dark matter and for the neutrinoless double beta decay of 136 Xe. Out of its 50 t total natural xenon inventory, 40 t will be the active target of a time projection chamber which thus contains about 3.6 t of 136 Xe. Here, we show that its projected half-life sensitivity is 2.4 × 10 27 years, using a fiducial volume of 5 t of natural xenon and 10 years of operation with a background rate of less than 0.2 events/(t • year) in the energy region of interest. This sensitivity is based on a detailed Monte Carlo simulation study of the background and event topologies in the large, homogeneous target. DARWIN will be comparable in its science reach to dedicated double beta decay experiments using xenon enriched in 136 Xe.
Neutrinos are the only known elementary particles that are Majorana fermion candidates, implying that they would be their own antiparticles. The most sensitive probe for the Majorana nature of neutrinos is an extremely rare nuclear decay process called neutrinoless double beta decay (0νββ), where a nucleus with mass number A and charge Z decays by emitting only two electrons and changes its charge by two units (A,Z)-→(A,Z+2) + 2e -. The observation of this decay would mean that lepton number is violated by two units and, in the standard light Majorana neutrino exchange scenario, would yield information about the neutrino mass scale via the effective neutrino Majorana mass m ββ = |Σ i U 2 ei m i |. The sum is over the neutrino mass eigenstates, m i , and U ei , the corresponding entries in the lepton mixing matrix, which are complex numbers. The two-neutrino double beta decay mode (2νββ) is allowed in the Standard Model and has been observed in more than 10 nuclei [1]. In this case, the summed energy of the two electrons is a continuum, while for the 0νββ-decay the distinct signature is a peak at the Q-value, the mass difference between the mother and daughter nuclei.
Experiments can observe a certain decay rate in a detector. The corresponding half-life is inversely proportional to m ββ 2 , 1
assuming that the decay is mediated by the exchange of a light Majorana neutrino. m e is the mass of the electron, G 0ν is the phase space factor, and M 0ν is the nuclear matrix element.
Recent experimental limits on T 0ν 1/2 and m ββ are of the order T 0ν 1/2 ≥ (10 25 -10 26 ) years and m ββ ≤ (0.06-0.17) eV, using a variety of nuclei and detector technologies [2,3].
A particularly suitable isotope to search for the 0νββdecay with is 136 Xe, with Q ββ = (2457.83±0.37) keV [4]. Current experiments use liquid xenon either in its pure form, EXO-200 [5], or xenon dissolved in liquid scintillator, KamLAND-Zen [6], and provide competitive constraints on the half-life. Future detectors that use xenon gas operated at high pressure, NEXT [7,8] and PandaX-III [9], will add tracking capabilities for improved background rejection, while nEXO [10] proposes to operate a total of 5 t of isotopically enriched liquid xenon.
DARWIN [11] is a proposed observatory using 40 t of liquid natural xenon (LXe) in a time projection chamber (TPC) with the primary goal of searching for particle dark matter. Here, we demonstrate that DARWIN has a similar reach to dedicated future neutrinoless double beta decay experiments. This is due to its large, homogeneous target, and its ultra-low background, coupled to the capability of the TPC to simultaneously measure the location, energy, particle type and multiplicity of an event [12].
The paper is organized as follows: in Sect. 2 we provide a brief review of the baseline design of the DARWIN detector and describe the detector model utilized in our simulation study. Section 3 addresses the signal topology and how it is used to reject background events. In Sect. 4 we discuss the expected background sources, while the resulting background spectra and rates are presented in Sect. 5. We discuss DARWIN's sensitivity to 0νββ-decay in Sect. 6 and give a summary and an outlook in Sect. 7.
DARWIN is a next-generation dark matter experiment that will operate a 40 t active (50 t total) liquid xenon TPC with the main goal to probe the entire experimentally accessible parameter space for weakly interacting massive particles (WIMPs) as dark matter candidates. Other physics goals include the search for the 0νββ-decay, the real-time detection of solar pp neutrinos via electron scattering, the observation of supernova and solar 8 B neutrinos via coherent neutrino nucleus scattering and the search for solar axions, galactic axion-like particles and dark photons.
The DARWIN detector is described in detail in [11]. In the baseline scenario, the detector is a cylindrical, two-phase (liquid and gas) xenon TPC with 2.6 m diameter and 2.6 m height. The TPC will be placed in a low-background, double- Interactions in the TPC will give rise to a prompt signal (S1) from photons and a delayed, proportional scintillation signal (S2) from electrons transported by a homogeneous drift field and extracted into the gas phase. Both signals will be detected by photosensor arrays (made of photomultiplier tubes (PMTs), silicon photomultiplier (SiPM), or new types of sensors), providing the x-y-z-coordinates of an interaction, as well as its energy with < 1% 1 σ resolution for MeV energy depositions. Interactions separated by more than 15 mm are assumed to be individually identified in event reconstruction. This allows for separation between single scatters (as expected from 0νββ-decays and dark matter particle interactions) and multiple scatters (as expected from many sources of backgrounds), as well as the definition of an inner (fiducial) volume with reduced background levels. The high density of the liquid xenon (∼3 g/cm 3 ) ensures a short attenuation length for γ -rays.
The final location of the DARWIN experiment is yet to be decided. A good candidate is the Gran Sasso Underground Laboratory (LNGS) in Italy. We will use its overburden in this study.
For the Monte Carlo event generation and particle propagation in geant4 we use a realistic model of the DARWIN detector. Its details are described in the following.
The TPC is enclosed within the outer and inner titanium cryostat (shown in Fig. 1), including torispherical domes, flanges and stiffening rings to minimize the amount of material. A dome-shaped pressurizable titanium vessel is placed on the inner cryostat floor to reduce the volume to be filled with liquid xenon while keeping the material budget low.
A study based on previously-measured specific activities of cryostat materials [13,14] showed that a cryostat made of titanium yields a lower background rate than a stainless steel cryostat of equal mechanical properties. The inner cryostat contains the liquid xenon volume and the TPC. The TPC walls are formed by PTFE reflectors of 3 mm thickness with high reflectivity for the vacuum ultraviolet (VUV) scintillation light, surrounded by 92 cylindrical copper field shaping rings. The structure is reinforced with 24 PTFE support pillars. Titanium frames at the bottom and top of the TPC support the electrodes to establish drift and extraction fields. Two photosensor arrays are located at the top and bottom of the TPC cylinder, consisting of a structural copper support, a PTFE reflector disk, the VUV-sensitive photosensors and the sensors' cold electronics. Because the final sensor type is yet to be chosen for DAR-WIN and R&D on light sensor options [15][16][17][18] is ongoing, the top and bottom sensors have, for the majority of simulations, been simplified to two disks which properly account for the material budget and the associated activities of radioactive isotopes. This allows for a direct comparison between a baseline scenario with PMTs and an alternative based on SiPMs.
All the major components included in the simulations are listed in Table 1. The assumed radioactivity levels of the materials are discussed in Sect. 4 and listed in Table 2.
In a 0νββ-decay, the energy Q ββ is released mainly in the form of kinetic energy of the two electrons. In liquid xenon, the electrons thermalize within O(mm) resulting in a single site (SS) signal topology, as shown in Fig. 2
Bremsstrahlung photons emitted during electron thermalization travel some distance without energy deposition before scattering or being absorbed. Abundantly emitted low energy photons are likely to deposit their energy close to the decay position and remain unresolved in the DARWIN detector. Photons with energies above 300 keV have a mean free path of more than 15 mm and might travel larger distances before interacting. This can result in an energy deposition which is spatially separable and can cause a false identification as a multi site (MS) event, Fig. 2
Energy depositions are therefore spatially grouped using a density-based spatial clustering algorithm [19]. An energy deposition is considered as a new cluster if its distance to any previous energy deposition is larger than our selected separation threshold . Figure 3 shows the efficiency for signal acceptance and background rejection for photons and electrons with an energy of Q ββ as a function of .
The distribution of energy per electron and the angle between the two depend on the yet unknown decay mechanism. We assume a mass mixing mechanism and the most probable decay where the electrons are emitted back-to-back, each with a kinetic energy of Q ββ /2. This assumption is compared in Fig. 3 to the predicted energy and angular distributions in the mass mixing (MM) model and a right-handed current (RHC) model presented in [20].
We assume that a spatial separation between energy depositions of = 15 mm can be resolved in the DARWIN TPC. This results in a signal acceptance of 90.4% (MM: 88.7%, RHC: 86.6%) as SS events. Background events from electrons and photons with Q ββ energy are rejected as MS with an efficiency of 17.7% and 85.1%, respectively. A smaller separation threshold results in a larger fraction of misidentified 0νββ-decays. Simultaneously, electrons from β decays and γ -ray events are more efficiently identified as MS. As we will discuss in Sect. 7, a lower spatial threshold can increase the sensitivity to 0νββ-decays. The decrease in signal acceptance is overcompensated by the improved background rejection.
We discuss all background sources which contribute events within the energy range of [2.3-2.7] MeV around Q ββ . We consider intrinsic background events from radioactive decays (radiogenic) and those induced by cosmic neutrinos, muons and their secondaries (cosmogenic). Intrinsic events are homogeneously distributed in the liquid xenon. Likewise we study radiogenic background radiation from external sources emanating into the target.
The intrinsic background sources originate from noble gas isotopes or from interactions of cosmogenic particles with the xenon target:
- 8 B solar neutrinos are an irreducible background source.
The expected rate of ν-e -scatterings is derived assuming a 8 B-ν flux of φ = (5.46±0.66)×10 6 cm -2 s -1 [21]. The calculation of scattering cross sections follows [22]. The electron neutrino survival probability is conservatively estimated to be P ee = 0.50 +5% -30% for neutrinos with
- 137 Xe from cosmogenic activation: muon-induced neutrons produced in the liquid xenon can thermalize and be captured on a 136 Xe nucleus, producing 137 Xe, as measured by EXO-200 [23]. This isotope decays via a β - process with Q β = 4.17 MeV and a half-life of 3.82 min.
Assuming the depth of LNGS and previous simulations of the muon-induced neutron flux underground [24], we estimate the muon-induced 137 Xe production rate in DARWIN to be (6.9 ± 0.4) atoms/(t•year). Neutrons produced in the solid materials contribute about 5% of this rate. Activation of 136 Xe due to radiogenic neutrons from the TPC materials has been found to be subdominant by more than two orders of magnitude. Activation of xenon in the non-shielded environment of the purification loop is non-negligible, but can be efficiently suppressed by a delayed re-feed of the LXe into the detector. Suppression by three orders of magnitude adds an additional 225 kg to the total xenon budget when cycling 1000 standard liter per minute. -The 2νββ decay spectrum of 136 Xe has been simulated assuming the measured half-life of T 1/2 = (2.165 ± 0.061) × 10 21 years [25]. For the analytic spectrum we use the non-relativistic Primakoff-Rosen approximation for the interaction between nuclei and electrons in the parametrization discussed in [26]. This approximation is conservative as it overestimates the rate around the spectral end point. - 222 Rn in LXe is assumed to be reduced by online cryogenic distillation [27] and stringent material selection to a concentration equivalent to 0.
Long-lived radionuclides are present in each detector material. Their decays, as well as the subsequent decays of their daughter isotopes, might introduce background in the target.
Activity levels for all materials are listed in Table 2 and based on reports from previous or ongoing experiments [13,14].
-The natural decay chains of 238 U, 232 Th and 235 U yield a background contribution primarily from γ -rays emitted by 214 Bi-(E γ = 2.45 MeV) and 208 Tl-decays (E γ = 2.61 MeV). The former two chains were split into their early and late component at 226 Ra and 228 Th, respectively, to account for radiogenic non-equilibrium. -60 Co β-decays dominantly (99.95%) via the two excited states of 60 Ni. The de-excitation is temporally nonresolvable and spatial coincidences of the 1.17 MeV and the 1.33 MeV γ -events contribute to the background. -Among the radio-isotopes from cosmogenic material activation at sea level [29], 44 Ti in the cryostat material is the most relevant, due to its long half-life (T 1/2 = 59.1 years) and the subsequent decay of 44 Sc with γemission at 2.66 MeV. - 222 Rn contamination in the non-instrumented xenon surrounding the TPC can contribute to the 214 Bi-induced γ -background. The rejection based on BiPo tagging described above cannot be applied since the subsequent alpha decays are not observed.
The background sources discussed in Sect. 4 are simulated with the geant4 particle physics simulation toolkit [30], using the detector model presented in Sect. 2.1. The equivalent of at least 100 years of DARWIN run time has been simulated for each material and isotope. In this section, we discuss the methods applied for event selection. The analytical background model, used for the profile-likelihood analy-sis in Sect. 6.2, is also described, and the background results are discussed.
The energy depositions generated by geant4 per event undergo a density-based spatial clustering algorithm [19] to topologically distinguish signal-like single site (SS) from background-like multi site (MS) events, as discussed in Sect. 3. We assume a separation threshold = 15 mm for the DARWIN TPC. This comparatively coarse clustering inevitably results in a fraction of γ -accompanied β-decays from background events, e.g., 214 Bi decays which frequently occur with higher multiplicity, being falsely identified as SS and consequentially contributing to the background.
To account for the finite energy resolution of the detector, the combined energy deposited inside each cluster is smeared according to a resolution of
with a = (0.3171 ± 0.0065) and b = (0.0015 ± 0.0002). At E = Q ββ this corresponds to σ E /E = 0.8%, as demonstrated in the XENON1T TPC [31]. The cluster position is smeared to account for the detector's spatial resolution which is conservatively assumed to be σ x,y = σ z = 10 mm above 2 MeV. Constraining the target to a super-ellipsoidal-shaped fiducial volume (FV) allows us to exploit the excellent selfshielding capabilities of liquid xenon. To compensate for the reduced shielding power in the xenon gas phase, the FV is shifted slightly downwards from the center of the instrumented volume. The fiducial volume is optimized for each FV mass independently. We use the lifetime-weighted combined external background, after the selection of single site events, energy and spatial resolution smearing. Only events with an energy inside the 0νββ-ROI of [2435-2481] keV, defined as the full width at half maximum (FWHM) range of the expected signal peak, are considered. The spatial distribution of external background events inside the active volume is shown in Fig. 4.
The selection of events within a fiducial volume removes all αand β-contributions originating from external sources. The γ -background is shown in Fig. 5 (bottom) for the 20 t fiducial volume. In the 0νββ-ROI the background is composed of the absorption peak from 214 Bi at E Bi = 2.45 MeV and Compton scattered photons, mainly from the 208 Tl line (E Tl = 2.61 MeV). Compton scatterings inside the fiducial volume with the subsequent escape of the scattered lower The relative contributions to the γ -background in the ROI are shown per material of origin in Fig. 5 (top). The similar contribution of cryostat-induced events from the walls and the combined PMT and electronics background originating from the top and bottom sensor array is a result of the optimization of the fiducial volume, which is properly balancing the r -and z-extent.
The spectral shape of the material-induced γ -background is modelled with a Gaussian peak and an exponentially decreasing continuum for each line, as shown in Fig. 5 (bottom). We consider the 2.61 MeV 208 Tl peak, the 2.66 MeV 44 Sc peak and each contribution of 214 Bi with E γ > 2.0 MeV. The ratio between the 214 Bi and the 44 Sc peaks to the 208 Tl peak intensity is established using Monte Carlo data in fiducial volumes sufficiently large to provide high statistics. Similarly, each continuum contribution is tied to The intrinsic background from 8 B neutrinos is assumed to be flat. The spectra corresponding to 137 Xe and 222 Rn are approximated linearly falling in the MeV] range. The slopes are obtained from Monte Carlo studies. The 2νββ spectrum is convolved with the Gaussian energy resolution.
The suppression of the external background with decreasing fiducial mass is shown in Fig. 6, together with the target mass independent intrinsic contributions. The fiducial volume is optimized for T 0ν 1/2 sensitivity, as discussed in detail in Sect. 6.1, and yields 5 t. The resulting background spectrum from intrinsic and external sources is shown for this fiducial mass in Fig. 7.
The intrinsic background in the ROI is dominated by the gently falling β --spectrum of 137 Xe decay. Subdominant contributions are the electron scattering of solar 8 B neutrinos and β --events from 214 Bi-decays which are not vetoed by BiPo tagging. The 2νββ spectrum overlaps negligibly with the ROI, but dominates the background toward lower energies.
The model-estimated background indices for all contributions are summarized in Table 3. To validate the analytic model introduced in Sect. 5.2, we compare the background model estimate with the values derived by weighted event counting in the 5 t fiducial mass data from Monte Carlo. Both results are in agreement within the statistical errors. The model-derived uncertainty on the background, however, is a factor of 4 lower than the Poissonian statistics error in the simple counting approach. The uncertainties on intrinsic background sources account for statistical errors, the variation of the overlap with the 0νββ-ROI based on the energy resolution and systematic uncertainties from (theory-driven) input parameters. The dominant contributions are the ν e survival probability and the neutrino flux ( 8 B ν-e -scattering), the 136 Xe neutron capture cross-section (governing the 137 Xe production rate) and the half-life of 136 Xe (2νββ decay).
We use the background rates predicted in Sect. 5.3 to derive a limit on the half-life sensitivity at 90% confidence level (CL) as well as the 3 σ discovery potential for the 0νββ-decay. The latter is defined as the minimal value of T 0ν 1/2 required to exclude the null hypothesis with a median significance of 99.7% CL.
Based on the figure-of-merit estimator proposed in [32] we calculate the half-life sensitivity at 90% CL as:
with = 0.9 being the detection efficiency of a single site 0νββ-decay event, f ROI = 0.76 the fraction of signal cov-ered by the ROI, α = 0.089 the abundance of 136 Xe in natural xenon, N A the Avogadro number in mol -1 , M Xe the molar mass number of xenon in t/mol, M the fiducial mass in tons, t the exposure time in years, B the background index in t -1 year -1 keV -1 , and ΔE the width of the ROI in keV. The value 1.64 is the number of standard deviations corresponding to a 90% CL. Following Eq. ( 3) and using the background index for the 5 t fiducial mass (Table 3), we obtain a half-life sensitivity of 2.0 × 10 27 years (1.3 × 10 27 years) after 10 (4) years of exposure.
This figure-of-merit estimation is an established tool to directly compare 0νββ sensitivities of different experiments using common statistical methods and assumptions. It also allows for a straightforward assessment of the sensitivity as a function of different parameters, such as the fiducial mass. It does not, however, consider background uncertainties, but assumes perfect knowledge of the background rates.
To account for and effectively constrain the background uncertainties, we apply a profile-likelihood analysis based on the background model discussed in Sect. 5.2. The inserted signal is a Gaussian peak with Q ββ and σ E (Q ββ ) according to Eq. ( 2), which is scaled by the 136 Xe atoms in the target volume, an activity corresponding to T 0ν 1/2 and the detection efficiency, as shown in Fig. 7.
Background uncertainties from the model are treated as nuisance parameters with Gaussian constraining terms in the likelihood. For external background contributions, their variances are obtained either by the model fit on the spectrum corresponding to 5 t FV ( 208 Tl peak intensity and slope parameter) or extrapolation of the model parameters from larger fiducial volumes into the low fiducial mass range ( 214 Bi / 208 Tl peak ratio, 208 Tl continuum / 208 Tl peak intensity). The uncertainty on the subdominant contribution from 44 Sc has been neglected. For the intrinsic contributions, the variances correspond to the square of the errors listed in Table 3. The corresponding slope uncertainties are negligible.
We obtain a T 0ν 1/2 sensitivity limit of 2.4 × 10 27 years for a 10 years exposure with 5 t fiducial mass. The corresponding 3 σ discovery potential after 10 years exposure is 1.1 × 10 27 years.
The DARWIN observatory will reach a sensitivity to the neutrinoless double beta decay of 136 Xe of 2.4 × 10 27 years T 1/2 exclusion limit (90% CL) and a discovery sensitivity (3 σ ) of T 1/2 = 1.1 × 10 27 years after 10 years of exposure.
In the baseline scenario discussed above, the assumptions on radio-purity and detector performance are considered realistic or even conservative. In an optimistic scenario, the external background could be reduced by a factor of three or more. The required measures include the use of less radioactive PMTs (with reduced mass of ceramic [33]) and/or low radioactivity SiPMs, more stringent material selection to reach lower levels of radio-activity for PTFE [34], copper [35] and titanium, as well as more radio-pure electronics.
Intrinsic backgrounds, dominated by the muon-induced activation of 136 Xe, are difficult to mitigate assuming the muon flux at 3500 meter water equivalent (mwe) depth of LNGS. A time-and spatial-muon veto might allow for suppression by up to a factor of two at an acceptable exposure loss. The 137 Xe contribution would, however, become subdominant in a sufficiently deep laboratory. A total intrinsic background suppression by a factor of five or even eight could then be reached assuming a reduced BiPo tagging inefficiency of 0.1% and 0.01%, respectively. Assuming a factor five reduction in external sources the latter scenario leads to a solar 8 B neutrino dominated background.
The sensitivity could be increased by further exploitation of the SS/MS discrimination, discussed in Sect. 3. Despite increased signal rejection, the gain in background reduction dominates for spatial separation thresholds down to = 3 mm. The cluster separation in the x-y-plane would benefit from a higher granularity photosensor top array, featuring e.g. SiPMs. The z-position reconstruction is already more accurate and a combined three dimensional charge signal analysis will optimize the separation.
The largest sensitivity increase can be achieved with a combination of the above mentioned measures. Figure 8 shows the fiducial volume mass dependency (top) and time evolution (bottom) of the DARWIN half-life limit sensitivity (90% CL) calculated with the figure-of-merit estimator (see Sect. 6.1) for the baseline and different optimistic scenarios. The latter assume reduced spatial separation threshold , intrinsic and external background rates. Figure 9 trans- [8][9][10]37] lates the half-life limit sensitivity to the effective Majorana neutrino mass m ββ using Eq. ( 1), where the m ββ range corresponds to the range of published nuclear matrix elements [36]. Under the conservative baseline assumptions, DARWIN reaches a m ββ limit of [18-46 meV]. The neutrino dominated scenario yields a limit in the [11-28 meV] range. Future dedicated neutrinoless double beta decay experiments using either 136 Xe or other isotopes are aiming for a similar science reach as DARWIN, as shown for comparison in Table 4 and in Fig. 8 (bottom).
The objective of detecting particle dark matter with a sensitivity down to the neutrino floor requires the DAR-WIN observatory to be an ultra-low background experiment. It additionally features a high 136 Xe target mass, excellent energy resolution and single site discrimination capability. In the presented baseline scenario DARWIN will reach a sensitivity that approaches that of the tonne-scale proposed 0νββ Fig. 9 Effective Majorana neutrino mass vs. lightest neutrino mass. The sensitivity reach after 50 t×years of exposure is shown for the baseline and the optimistic neutrino dominated scenario. The horizontal bands stem from the range of nuclear matrix elements [36]. Global sensitivity according to [38], oscillation parameters from [39,40] experiments. Under more optimistic assumptions, requiring adaptations to the baseline design, DARWIN will explore the full inverted hierarchy and will compete with the most ambitious proposed 0νββ projects.