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# 36. Particle Detectors for Non-Accelerator Physics

Revised 2024. See the various sections for authors.

<table><tbody><tr><td>36.1</td><td>Introduction</td><td>649</td></tr><tr><td>36.2</td><td>High-energy cosmic-ray hadron and gamma-ray detectors</td><td>649</td></tr><tr><td>36.2.1</td><td>Atmospheric fluorescence detectors</td><td>649</td></tr><tr><td>36.2.2</td><td>Atmospheric Cherenkov telescopes for high-energy gamma ray astronomy</td><td>651</td></tr><tr><td>36.3</td><td>Large neutrino detectors</td><td>652</td></tr><tr><td>36.3.1</td><td>Deep liquid detectors for rare processes</td><td>652</td></tr><tr><td>36.3.2</td><td>Neutrino telescopes</td><td>654</td></tr><tr><td>36.3.3</td><td>Radio emission from (ultra-)high energy particle showers</td><td>657</td></tr><tr><td>36.4</td><td>Large time-projection chambers for rare event detection</td><td>661</td></tr><tr><td>36.4.1</td><td>Dark matter and other low energy signals</td><td>663</td></tr><tr><td>36.4.2</td><td>0νββ Decay</td><td>664</td></tr><tr><td>36.5</td><td>Sub-kelvin detectors</td><td>665</td></tr><tr><td>36.5.1</td><td>Motivation for Sub-kelvin Detectors</td><td>665</td></tr><tr><td>36.5.2</td><td>Detector Types</td><td>666</td></tr><tr><td>36.5.3</td><td>Experimental Applications</td><td>668</td></tr><tr><td>36.6</td><td>Low-radioactivity background techniques</td><td>670</td></tr><tr><td>36.6.1</td><td>Introduction</td><td>670</td></tr><tr><td>36.6.2</td><td>Radio-purity assay</td><td>671</td></tr><tr><td>36.6.3</td><td>Radon and its progeny</td><td>671</td></tr><tr><td>36.6.4</td><td>Surface backgrounds</td><td>672</td></tr><tr><td>36.6.5</td><td>Mitigation of backgrounds and active background discrimination</td><td>672</td></tr></tbody></table>

## 36.1 Introduction

Non-accelerator experiments have become increasingly important in particle physics and astrophysics. From them comes the evidence of physics beyond the SM, with the discovery of neutrino oscillations and adiabatic flavor conversion. Explored energies range from the meV scale to above the EeV, some 24 orders of magnitude. The physics and the design of the detectors vary as a consequence. Some experiments look at astrophysical high-energy phenomena using the atmosphere as a detector in the fluorescence and Cherenkov observatories or the polar ice and the ocean water in neutrino telescopes. Experiments on extremely rare events, such as neutrino-less double beta decay, solar neutrinos and dark matter induced scattering, need dedicated fully equipped deep underground laboratories, existing in different countries. Critical is the research to push back the ultra-low radioactive background frontier, with dedicated facilities in these laboratories. Detectors range from hyper-pure liquid scintillators, both organic and not, to thermalized and ballistic phonon detectors at the sub-Kelvin temperature, to dual phase noble fluid TPCs, etc. Space-based detectors also use some unique instrumentation, but these are beyond the present scope of this review. Gravitational wave detectors are not included as well.

## 36.2 High-energy cosmic-ray hadron and gamma-ray detectors

### 36.2.1 Atmospheric fluorescence detectors

Revised March 2024 by L.R. Wiencke (Colorado School of Mines).

Cosmic-ray fluorescence detectors (FDs) use the atmosphere as a giant calorimeter to measure isotropic scintillation light that traces the development profiles of extensive air showers. An extensive air shower (EAS) is produced by the interactions of ultra high-energy ($E > 10^{17}$ eV) subatomic particles in the stratosphere and upper troposphere. The amount of scintillation light generated by an EAS is proportional to the energy deposited in the atmosphere and nearly independent of the primary species. With energies extending beyond $10^{20}$ eV, ultra high energy cosmic rays (UHECRs) are the highest energy subatomic particles

known to exist. In addition to particle arrival directions, energy spectra and primary composition, the astroparticle science investigated with FDs also includes multi-messenger studies, searches for high energy photons, neutrinos, monopoles and deeply penetrating forms of dark matter. The Pierre Auger Observatory FD also measures UV scintillation that traces the development of ring-shaped atmospheric transient luminous events, called Elves, in the ionosphere that are initiated by strong lightning [1].

Previous experiments with FDs included the pioneering Fly's Eye [2, 3], and the High Resolution Fly's Eye (HiRes and HiRes prototype) [4]. The history of the fluorescence technique includes earlier studies in the 1950's and 1960's [5, 6]. The current generation of experiments include the Telescope Array (TA) [7] in the northern hemisphere, and the larger Pierre Auger Observatory (Auger) [8] in the southern hemisphere. (Discussion, with extensive references, of current and possible future UHECR experiments can be foundx[ in 9].) Auger and TA are hybrid observatories. Their FD telescopes overlook sparse arrays of particle detectors on the ground. Select parameters are listed in Table 36.1. TA and Auger have each one FD site populated with additional telescopes that view up to 60° in elevation to measure lower EASs using a combination of scintillation and direct Cherenkov light. As part of a fourfold coverage upgrade of TA (TAx4), 12 HiRes refurbished telescopes have been installed at the north and south-east sites of TA. A set of prototype FD telescopes, dubbed FAST [10], have observed EASs at the TA site using design that features wide field of view PMTs, fast timing and economical optics for a next-generation ground-based observatory. A second prototype has been installed at the Pierre Auger Observatory.

The fluorescence light is emitted primarily between 290 and 430 nm (Figure 36.1) with major lines at 337, 357, and 391 nm, when relativistic charged particles, primarily electrons and positrons, excite nitrogen molecules in air, resulting in transitions of the 1P and 2P systems. Reviews and references for the pioneering and recent laboratory measurements of fluorescence yield, $Y(\lambda, P, T, u)$, including dependence on wavelength ($\lambda$), temperature ($T$), pressure ($p$), and humidity ($u$) may be found in Refs. [11–13]. The results of various laboratory experiments have been combined (Figure 36.2) to obtain an absolute average and uncertainty for $Y(337$ nm, 800 hPa, 293 K, dry air) of $7.04 \pm 0.24$ ph/MeV after corrections for different electron beam energies and other factors. The units of ph/MeV correspond to the number of fluorescence photons produced per MeV of energy deposited in the atmosphere by the electromagnetic component of an EAS.

<figure><img src="image_241.png" /><figcaption>**Figure 36.1:** Measured fluorescence spectrum excited by 3 MeV electrons in dry air at 800 hPa and 293 K. Airfly experiment. Figure from Ref [14].</figcaption></figure>

An FD element (telescope) consists of a non-tracking spherical mirror of less than astronomical quality, a “camera” of photomultiplier tubes (PMTs) near the focal plane, and a flash ADC readout system with a pulse and track-finding trigger scheme [8, 16]. The major experiments listed in Table 36.1 all use conventional PMTs (for example, Hamamatsu R9508 or Photonis XP3062) with
<table><caption>**Table 36.1:** Parameters of major fluorescence detectors. Note 1: Year when all FD sites were operational. Note 2: At TA 1 of the 3 FD sites features 24 telescopes from the HiRes experiment. Note 3: A-C for one telescope where A is the full area and C the area obscured by the camera and support structures. Thus A-C is the effective light collecting area. For the modified Schmidt design at Auger, the area of the entrance pupil, A, is listed because the pupil is smaller than the mirror and thus defines the entrance aperture. For the other experiments, the area of the mirror, A, is listed</caption><thead><tr><th>Observatory</th><th>Fly's Eye</th><th>HiRes</th><th>Telescope Array</th><th>Pierre Auger</th></tr></thead><tbody><tr><td>Location</td><td>Dugway UT US</td><td>Dugway UT US</td><td>Delta UT US</td><td>Malargüe AR</td></tr><tr><td>Start-End</td><td>1981-1992</td><td>1996-2006</td><td>2008-present</td><td>2005-present</td></tr><tr><td>Sites (note 1)</td><td>2 (1986)</td><td>2 (1999)</td><td>3 (2008)</td><td>4 (2008)</td></tr><tr><td>Separation</td><td>3.3 km</td><td>12.6 km</td><td>31-40 km</td><td>39-62 km</td></tr><tr><td>Telescopes/site</td><td>67,18</td><td>21,42</td><td>12+8,12,14+10+4</td><td>6, 6, 6, 6+3</td></tr><tr><td>Pixel FOV</td><td>5.5°</td><td>1°</td><td>1°</td><td>1.5°</td></tr><tr><td>Telescope FOV</td><td>≈18° × ≈18°</td><td>16° × 13.5°</td><td>18° × 15° (note 2)</td><td>30° × 28.1°</td></tr><tr><td>Azi × Elv</td><td></td><td></td><td></td><td></td></tr><tr><td>Light collection area (note 3)</td><td>1.95 m² - 0.25 m²</td><td>3.72 m² - 0.5 m²</td><td>6.8 m² - 0.85 m² (for 2 sites)</td><td>3.80 m² - 0.80 m² (modified schmidt)</td></tr><tr><td>Energy Scale</td><td>≤40%</td><td>≈20%</td><td>≈20%</td><td>14%</td></tr><tr><td>Uncertainty</td><td></td><td></td><td></td><td></td></tr></tbody></table>

<figure><img src="image_242.png" /><figcaption>**Figure 36.2:** Fluorescence yield values and associated uncertainties at 337 nm (Y$_{337}$) in dry air at 800 hPa and 293 K. The methodology and corrections that were applied to obtain the average and the uncertainty are discussed extensively in this reference. The vertical axis denotes different laboratory experiments that measured FY. The gray bars show three of the original measurements to illustrate the scale of the corrections applied. Figure from Ref [15].</figcaption></figure>

grounded cathodes and AC coupled readout. Segmented mirrors have been fabricated from slumped or slumped/polished glass with an anodized aluminum coating or fabricated using shaped aluminum that was then chemically anodized with AlMgSiO$_{5}$. A broadband UV filter (custom fabricated, BG-3, or Schott MUG-6) reduces background light such as starlight, airglow, man-made light pollution, and airplane strobe-lights.

At 10$^{20}$ eV, where the flux drops below 1 EAS/km$^2$century, the aperture for an eye of adjacent FD telescopes that span the horizon can reach 10$^4$ km$^2$ sr. FD operation requires (nearly) moonless nights and clear atmospheric conditions, which typically imposes a duty cycle of about 10%. Arrangements of LEDs, calibrated diffuse sources [17], pulsed UV lasers [18], LIDARs$^1$ and IR detectors that are sensitive to clouds are used for photometric calibration, atmospheric calibration [19], and determination of exposure [20]. For purposes of optical transmission, the atmosphere is treated as having a dominant molecular component and a secondary aerosol component. The latter is well described [21] by molecular scattering theory and models derived from radiosonde measurements. The aerosol component can include dust, haze and pollution and the aerosol optical depth profile must be measured on site in the UV during FD data taking.

The EAS generates a track consistent with a light source moving

at $v = c$ across the FOV. The number of photons ($N_γ$) as a function of atmospheric depth (X) can be expressed as [12]

$$ \frac{dN_{\gamma}}{dX} = \frac{dE_{\text{dep}}^{\text{tot}}}{dX} \int Y(\lambda, P, T, u) \cdot \tau_{\text{atm}}(\lambda, X) \cdot \varepsilon_{\text{FD}}(\lambda) d\lambda, \quad (36.1) $$

where $τ_{atm}(λ, X)$ is the atmospheric transmission, including wavelength (λ) dependence, and $ε_{FD}(λ)$ is the FD efficiency. $ε_{FD}(λ)$ includes geometric factors and collection efficiency of the optics, quantum efficiency of the PMTs, and other throughput factors. The typical systematic uncertainties, $τ_{atm}$ (10%) and $ε_{FD}$ (photometric calibration 10%), currently dominate the systematic uncertainty the absolute EAS energy scale. FD energy resolution, defined as event-to-event statistical uncertainty, is typically less than 10% for final data samples used for science analysis.

Analysis methods to reconstruct the EAS profile and deconvolve the contributions of re-scattered scintillation light, and direct and scattered Cherenkov light are described in [2] and more recently in [23]. The EAS energy is typically obtained by integrating over the Gaisser-Hillas function [24]

$$ E_{\text{cal}} = \int_{0}^{\infty} [w_{\text{max}} \left( \frac{X - X_0}{X_{\text{max}} - X_0} \right)^{(X_{\text{max}} - X_0)/\lambda} e^{(X_{\text{max}} - X)/\lambda}] dX, \quad (36.2) $$

where $E_{cal}$ is the energy of electromagnetic energy component of the EAS and $X_{max}$ is the atmospheric slant depth at which the shower reaches its maximum energy deposit rate. This maximum $dE/dX$ is denoted as $w_{max}$. $X_0$ and $\lambda$ are two shape parameters. The energy of the primary cosmic ray is obtained by correcting $E_{cal}$ upward by about 10% to account for the invisible energy carried by particles that do not interact in the atmosphere. Auger reported a data-driven method to estimate the invisible energy from the muon number at ground level and Xmax to reduce systematic uncertainties [25]. Energy resolution, $\Delta E/E$, of 15-20% is achievable, provided the geometric fit of the EAS axis is constrained, typically by multi-eye stereo projection or hybrid observations, and the profile fit of EAS development along the track is constrained by the observed rise and fall about $X_{max}$. An example of a recorded EAS light profile and its corresponding $dE/dX$ development profile are shown in Fig. 36.3. The EAS generates a track consistent with a light source moving at $v = c$ across the FOV. The number of photons ($N_γ$) as a function of atmospheric depth (X) can be expressed as [12] In 2023 the Pierre Auger Collaboration published a public data release [26] of the 100 highest energy cosmic ray events collected over a 17-year span through 2020 with an additional 9 energetic hybrid events used in the calibration procedure. In 2024 the collaboration reported the first comparison of $X_{max}$ measurements [27] between fluorescence and radio detectors at the same location. This comparison includes a subset of 53 airshowers that were observed by the two detectors simultaneously.

<footnote>$^1$LIDAR stands for "Light Detection and Ranging" and refers here to systems that measure atmospheric properties from the light scattered backwards from laser pulses directed into the sky.</footnote>
<figure><img src="image_243.png" /></figure>

**Figure 36.3:** Example light profile (left) of one EAS recorded by the Pierre Auger FD and the corresponding profile (right) of energy deposited in the atmosphere vs atmospheric slant depth. The light profiles include the estimated components of Cherenkov light that have been scattered out of the forward beam by the molecular and aerosol (Mie) components of the atmosphere. The reconstructed energy of this EAS was $3.0 \pm 0.2 \times 10^{19}$ eV. Figure from Ref [22].

An FD that would look down on the earth's atmosphere from space orbit to view a much larger area than ground based instruments is an active area of R&D. Prototypes that have been built and flown in orbit include the pioneering TUS instrument [28], [29] operated 2016-2018 onboard the Lomonosov satellite. The JEM-EUSO collaboration has flown prototype FD telescopes on stratospheric balloon flights in 2014 (EUSO-Balloon) [30], 2017 (EUSO-SPB1) [31] and 2023 (EUSO-SPB2) [32]. The Mini-EUSO [33] FD continues recording terrestrial UV emission by looking down through a 25 cm diameter UV-transmitting window inside the International Space Station since 2019. The Probe of Extreme Multimessenger Astrophysics (POEMMA) project has completed a detailed conceptual design study for a twin-satellite mission [34] that would observe UHECRs and PeV scale cosmogenic tau neutrinos.

### 36.2.2 Atmospheric Cherenkov telescopes for high-energy gamma ray astronomy

Revised October 2023 by J. Holder (Delaware U.; Delaware U., Bartol Inst.).

A wide variety of astrophysical objects are now known to produce high-energy γ-ray photons. Leptonic or hadronic particles, accelerated to relativistic energies in the source, produce γ-rays typically through inverse Compton boosting of ambient photons or through the decay of neutral pions produced in hadronic interactions. At energies below ~30 GeV, γ-ray emission can be efficiently detected using satellite or balloon-borne instrumentation, with an effective area approximately equal to the size of the detector (typically < 1 m²). At higher energies, a technique with

much larger effective collection area is desirable to measure astrophysical γ-ray fluxes, which decrease rapidly with increasing energy. Atmospheric Cherenkov detectors achieve effective collection areas of >$10^5$ m² by employing the Earth's atmosphere as an intrinsic part of the detection technique.

As described in Chapter 30, a hadronic cosmic ray or high energy γ-ray incident on the Earth's atmosphere triggers a particle cascade, or air shower. Relativistic charged particles in the cascade generate Cherenkov radiation, which is emitted along the shower direction, resulting in a light pool on the ground with a radius of ~130 m. Cherenkov light is produced throughout the cascade development, with the maximum emission occurring when the number of particles in the cascade is largest, at an altitude of ~10 km for primary energies of 100 GeV–1 TeV. Following absorption and scattering in the atmosphere, the Cherenkov light at ground level peaks at a wavelength, $\lambda \approx 300–350$ nm. The photon density is typically ~100 photons/m² for a 1 TeV primary, arriving in a brief flash of a few nanoseconds duration. This Cherenkov pulse can be detected from any point within the light pool radius by using large reflecting surfaces to focus the Cherenkov light on to fast photon detectors (Fig. 36.4).

<figure><img src="image_244.png" /></figure>

**Figure 36.4:** A schematic illustration of an imaging atmospheric Cherenkov telescope array. The primary particle initiates an air shower, resulting in a cone of Cherenkov radiation. Telescopes within the Cherenkov light pool record elliptical images; the intersection of the long axes of these images indicates the arrival direction of the primary, and hence the location of a γ-ray source in the sky

Modern atmospheric Cherenkov telescopes, such as those built and operated by the VERITAS [35], H.E.S.S. [36] and MAGIC [37] collaborations, consist of large (> 100 m²) segmented mirrors on steerable altitude-azimuth mounts. A camera made from an array of photosensors is placed at the focus of each mirror and used to record a Cherenkov image of each air shower. In these imaging atmospheric Cherenkov telescopes, single-anode photomultipliers tubes (PMTs) have traditionally been used (2048, in the case of H.E.S.S. II), but silicon devices now feature in more modern designs. The telescope cameras typically cover a field-of-view of 3 – 10° in diameter. Images are recorded at kHz rates, the vast majority of which are due to showers with hadronic cosmic-ray primaries. The shape and orientation of the Cherenkov images are used to discriminate γ-ray photon events from this cosmic-ray background, and to reconstruct the photon energy and arrival direction. γ-ray images result from purely electromagnetic cascades and appear as narrow, elongated ellipses in the camera plane. The long axis of the ellipse corresponds to the vertical extension of the air shower, and points back towards the source position in the field-of-view. If multiple telescopes are used to view the same shower ("stereoscopy"), the source position is simply the in-
tersection point of the various image axes. Cosmic-ray primaries produce secondaries with large transverse momenta, which initiate sub-showers. Their images are consequently wider and less regular than those with γ-ray primaries and, since the original charged particle has been deflected by Galactic magnetic fields before reaching the Earth, the images have no preferred orientation.

The measurable differences in Cherenkov image orientation and morphology provide the background discrimination which makes ground-based γ-ray astronomy possible. For point-like sources, such as distant active galactic nuclei, modern instruments can reject over 99.999% of the triggered cosmic-ray events, while retaining up to 50% of the γ-ray population. In the case of spatially extended sources, such as Galactic supernova remnants, the background rejection is less efficient, but the technique can be used to produce γ-ray maps of the emission from the source. The angular resolution depends upon the number of telescopes which view the image and the energy of the primary γ-ray, but is typically less than 0.1° per event (68% containment radius) at energies above a few hundred GeV.

The total Cherenkov yield from the air shower is proportional to the energy of the primary particle. The image intensity, combined with the reconstructed distance of the shower core from each telescope, can therefore be used to estimate the primary energy. The energy resolution of this technique, also energy-dependent, is typically 15–20% at energies above a few hundred GeV. Energy spectra of γ-ray sources can be measured over a wide range, depending upon the instrument characteristics, source properties (flux, spectral slope, elevation angle, etc.), and exposure time. The effective energy range is typically from 30 GeV to 100 TeV and peak sensitivity lies in the range from 100 GeV to a few TeV.

The first astrophysical source to be convincingly detected using the imaging atmospheric Cherenkov technique was the Crab Nebula [38], with an integral flux of $2.1 \times 10^{-11}$ photons cm$^{-2}$ s$^{-1}$ above 1 TeV [39]. Modern imaging atmospheric Cherenkov telescopes have sensitivity sufficient to detect sources with less than 1% of the Crab Nebula flux in a few tens of hours. The TeV source catalog now consists of over 200 sources (see e.g. Ref. [40]). A large fraction of these were detected by scanning the Galactic plane from the southern hemisphere with the H.E.S.S. telescope array [41]. Recent reviews of the field include [42] and [43], and a historical overview can be found in [44].

Major upgrades of the existing telescope arrays include the 2012 addition of a 28 m diameter central telescope to H.E.S.S. (H.E.S.S. II). Cherenkov telescopes also play an important role in hybrid air-shower detector systems such as TAIGA [45] and LHAASO [46]. Development for the next generation instrument, the Cherenkov Telescope Array Observatory (CTAO), is now at an advanced stage. CTAO will consist of a northern and a southern hemisphere observatory, with a combined total of more than 60 telescopes [47]. Telescopes of three different sizes are planned, spread over an area of > 1 km$^2$, providing wider energy coverage, improved angular and energy resolutions, and an order of magnitude improvement in sensitivity relative to existing imaging atmospheric Cherenkov telescopes. A number of prototype telescopes are already operating, exploiting technological developments in telescope structural design and high-speed data acquisition. Novel features of some designs include dual mirror optics and silicon photo-detectors. In particular, the first 23 m diameter “Large Size Telescope” is now operating regularly on La Palma, and is producing scientific results [48]. The wide range of physics questions that CTAO will address is summarized in [49].

## 36.3 Large neutrino detectors

### 36.3.1 Deep liquid detectors for rare processes

Revised October 2023 by K. Scholberg (Duke U.) and C.W. Walter (Duke U.).

Deep, large detectors for rare processes tend to be multi-purpose with physics reach that includes not only solar, reactor, supernova and atmospheric neutrinos, but also searches for baryon

number violation and lepton number violation, searches for exotic particles and beyond-the-standard-model physics, and neutrino and cosmic-ray astrophysics in different energy regimes. The detectors may also serve as targets for long-baseline neutrino beams for neutrino oscillation physics studies. In general, detector design considerations can be divided into high- and low-energy regimes, for which background and event reconstruction issues differ. The high-energy regime, from about 100 MeV to a few hundred GeV, is relevant for proton decay searches, atmospheric neutrinos and high-energy astrophysical neutrinos. The low-energy regime (a few tens of MeV or less) is relevant for supernova, solar, reactor and geological neutrinos.

Large water Cherenkov and scintillator detectors (see Table 36.2) usually consist of a volume of transparent liquid viewed by photomultiplier tubes (PMTs) (see Sec 35.2); the liquid serves as active target. PMT hit charges and times are recorded and digitized, and triggering is usually based on coincidence of PMT hits within a time window comparable to the detector’s light-crossing time. Because photosensors lining an inner surface represent a driving cost that scales as surface area, very large volumes can be used for comparatively reasonable cost. Some detectors are segmented into subvolumes individually viewed by PMTs, and may include other detector elements (e.g., tracking detectors). Devices to increase light collection, e.g., reflectors or waveshifter plates, may be employed. A common configuration is to have at least one concentric outer layer of liquid material separated from the inner part of the detector to serve as shielding against ambient background. If optically separated and instrumented with PMTs, an outer layer may also serve as an active veto against entering cosmic rays and other background events. The PMTs for large detectors typically range in size from 20 cm to 51 cm diameter, and typical quantum efficiencies are in the 20–25% range for scintillation and water-Cherenkov photons. PMTs with higher quantum efficiencies, 35% or higher, are now available. The active liquid volume requires purification and there may be continuous recirculation of liquid. For large homogeneous detectors, the event interaction vertex is determined using relative timing of PMT hits, and energy deposition is determined from the number of recorded photoelectrons. A “fiducial volume” is usually defined within the full detector volume, some distance away from the PMT array. Inside the fiducial volume, enough PMTs are illuminated per event that reconstruction is considered reliable, and furthermore, entering background from the enclosing walls is suppressed by a buffer of self-shielding. PMT and detector optical parameters are calibrated using laser, LED, or other light sources. Quality of event reconstruction typically depends on photoelectron yield, pixelization and timing.

Because in most cases one is searching for rare events, large detectors are usually sited underground to reduce cosmic-ray-related background (see Chapter 30). The minimum depth required varies according to the physics goals [50].

#### 36.3.1.1 Liquid scintillator detectors

Past and current large underground detectors based on hydrocarbon scintillators include LVD, MACRO, BUST (Baksan), Borexino, KamLAND and SNO+; JUNO is a future detector. Experiments at nuclear reactors include CHOOZ, Double CHOOZ, Daya Bay, and RENO. Organic liquid scintillators (see Section 35.3) for large detectors are chosen for high light yield and attenuation length, good stability, compatibility with other detector materials, high flash point, low toxicity, appropriate density for mechanical stability, and low cost. They may be doped with waveshifters and stabilizing agents. Popular choices are pseudomeric (1,2,4-trimethylbenzene) with a few g/L of the PPO (2,5-diphenyloxazole) fluor, and linear alkylbenzene (LAB), with light yield ~ $10^4$ photons/MeV. In a typical detector configuration there will be active or passive regions of undoped scintillator, non-scintillating mineral oil or water surrounding the inner neutrino target volume. A thin vessel or balloon made of nylon, acrylic or other material transparent to scintillation light may contain the inner target; if the scintillator is buoyant with respect to its buffer, ropes may hold the balloon in place. For phototube surface coverages in the 20–40% range, yields in the few hundreds of photoelectrons per MeV of energy deposition can be obtained.
<table><caption>**Table 36.2:** Properties of large detectors for rare processes. If total target mass is divided into large submodules, the number of subdetectors is indicated in parentheses. Projects with first data expected in 2024 or later are indicated in italics.</caption><thead><tr><th>Detector</th><th>Mass, kton<br>(modules)</th><th>PMTs<br>(diameter, cm)</th><th>ξ</th><th>p.e./MeV</th><th>Dates</th></tr></thead><tbody><tr><td>BUST</td><td>0.33, scint (3150)</td><td>1/module (15)</td><td>segmented</td><td>40</td><td>1980–</td></tr><tr><td>MACRO</td><td>0.56, scint (476)</td><td>2-4/module (20)</td><td>segmented</td><td>18</td><td>1989–2000</td></tr><tr><td>LVD</td><td>1, scint. (840)</td><td>3/module (15)</td><td>segmented</td><td>15</td><td>1992–</td></tr><tr><td>KamLAND</td><td>0.41*, scint</td><td>1325(43)+554(51)†</td><td>34%</td><td>460</td><td>2002–</td></tr><tr><td>Borexino</td><td>0.1*, scint</td><td>2212 (20)</td><td>30%</td><td>500</td><td>2007–2021</td></tr><tr><td>SNO+</td><td>0.78, scint‡</td><td>9394 (20)</td><td>47%</td><td>400–600</td><td>2021–</td></tr><tr><td>CHOOZ</td><td>0.005, scint (Gd)</td><td>192 (20)</td><td>15%</td><td>130</td><td>1997–1998</td></tr><tr><td>Double Chooz</td><td>0.017, scint (Gd)(2)</td><td>534/module (20)</td><td>13%</td><td>180</td><td>2011–2017</td></tr><tr><td>Daya Bay</td><td>0.160, scint (Gd)(8)</td><td>192/module (20)</td><td>5.6%§</td><td>100</td><td>2011–2020</td></tr><tr><td>RENO</td><td>0.032, scint (Gd)(2)</td><td>342/module (25)</td><td>12.6%</td><td>100</td><td>2011–</td></tr><tr><td>JUNO</td><td>20.0*, scint</td><td>17612 (51)/25600 (8)</td><td>77.9%</td><td>1200</td><td>2024 (exp.)</td></tr><tr><td>IMB-1</td><td>3.3*, H₂O</td><td>2048 (12.5)</td><td>1%</td><td>0.25</td><td>1982–1985</td></tr><tr><td>IMB-2</td><td>3.3*, H₂O</td><td>2048 (20)</td><td>4.5%</td><td>1.1</td><td>1987–1990</td></tr><tr><td>Kam I</td><td>0.88/0.78*, H₂O</td><td>1000/948 (51)</td><td>20%</td><td>3.4</td><td>1983–1985</td></tr><tr><td>Kam II</td><td>1.04*, H₂O</td><td>948 (51)</td><td>20%</td><td>3.4</td><td>1986–1990</td></tr><tr><td>Kam III</td><td>1.04*, H₂O</td><td>948 (51)</td><td>20%¶</td><td>4.3</td><td>1990–1995</td></tr><tr><td>SK I</td><td>22.5*, H₂O</td><td>11146 (51)</td><td>40%</td><td>6</td><td>1996–2001</td></tr><tr><td>SK II</td><td>22.5*, H₂O</td><td>5182 (51)</td><td>19%</td><td>3</td><td>2002–2005</td></tr><tr><td>SK III-V</td><td>22.5*, H₂O</td><td>11129 (51)</td><td>40%</td><td>6</td><td>2006–2020</td></tr><tr><td>SK-Gd</td><td>22.5*, H₂O (Gd)</td><td>11129 (51)</td><td>40%</td><td>6</td><td>2020–</td></tr><tr><td>Hyper-K</td><td>187*, H₂O||</td><td>>20000 (51)**</td><td>>20%</td><td>>6</td><td>2027 (exp.)</td></tr><tr><td>SNO</td><td>1, D₂O/1.7, H₂O</td><td>9438 (20)</td><td>31%††</td><td>9</td><td>1999–2006</td></tr><tr><td>DUNE</td><td>40*, Ar (4)</td><td>TBD‡‡</td><td>TBD‡‡</td><td>TBD‡‡</td><td>2028 (exp.)§§</td></tr></tbody></table>

*Indicates typical fiducial mass used for data analysis; this may vary by physics topic.

†Measurements made before 2003 only considered data from the 43 cm PMTs.

‡SNO+ ran with water fill from May 2017 to July 2019.

§The effective Daya Bay coverage is 12% with top and bottom reflectors.

¶The effective Kamiokande III coverage was 25% with light collectors.

||A second staged module is being investigated.

**Additional photosensor modules and PMTs are planned.

††The effective SNO coverage was 54% with light collectors.

‡‡Photodetector technology and coverage varies according to TPC type and is not yet fully determined.

§§Modules will be constructed in a phased approach.

Typical energy resolution is about $5-7\%/\sqrt{E(\text{MeV})}$ [51,52], and typical position reconstruction resolution is a few tens of cm at $\sim 1$ MeV, scaling as $\sim N^{-1/2}$, where N is the number of photoelectrons detected.

Shallow detectors for reactor neutrino oscillation experiments require excellent muon veto capabilities. For $\bar{\nu}_e$ detection via inverse beta decay on free protons, $\bar{\nu}_e + p \rightarrow n + e^+$, the neutron is captured by a proton on a $\sim 180$ µs timescale, resulting in a 2.2 MeV $\gamma$ ray, observable by Compton scattering and which can be used as a tag in coincidence with the positron signal. The positron annihilation $\gamma$ rays may also contribute. Inverse beta decay tagging may be improved by addition of Gd at $\sim 0.1\%$ by mass, which for natural isotope abundance has a $\sim 49,000$ barn cross-section for neutron capture (in contrast to the 0.3 barn cross-section for capture on free protons). Gd capture takes $\sim 30$ µs, and is followed by a cascade of $\gamma$ rays adding up to about 8 MeV. Gadolinium doping of scintillator requires specialized formulation to ensure adequate attenuation length and stability.

Scintillation detectors have an advantage over water Cherenkov detectors in the lack of Cherenkov threshold and the high light yield. However, scintillation light emission is nearly isotropic, and therefore directional capabilities are relatively weak. Liq-uid scintillator is especially suitable for detection of low-energy events. Radioactive backgrounds are a serious issue, and include long-lived cosmogenics such as $^{14}$C. To go below a few MeV, very careful selection of materials and purification of the scintillator is required (see Section 36.6). Fiducialization and tagging can reduce background. One can also dissolve neutrinoless double beta decay ($0\nu\beta\beta$) isotopes in scintillator. This has been realized by KamLAND-Zen, which deployed a 1.5 m-radius balloon containing enriched Xe dissolved in scintillator inside KamLAND, and $^{130}$Te is planned for SNO+.

### 36.3.1.2 Water Cherenkov detectors

Very large imaging water detectors reconstruct ten-meter-scale Cherenkov rings produced by charged particles (see Section 35.5). The first such large detectors were IMB and Kamiokande. The only currently existing instance of this class of detector, with fiducial mass of 22.5 kton and total mass of 50 kton, is Super-Kamiokande (Super-K, SK). Hyper-Kamiokande (Hyper-K) plans at least one, and possibly two, detectors with 187-kton fiducial mass. For volumes of this scale, absorption and scattering of Cherenkov light are non-negligible, and a wavelength-dependent factor $\exp(-d/L(\lambda))$ (where d is the distance from emission to the sensor and L(λ) is the attenuation length of the medium) must be included in the integral of Eq. (35.6) for the photoelectron yield. Attenuation lengths on the order of 100 meters have been achieved.

Cherenkov detectors are excellent electromagnetic calorimeters, and the number of Cherenkov photons produced by an $e/\gamma$ is nearly proportional to its kinetic energy. For massive particles, the number of photons produced is also related to the energy, but not linearly. For any type of particle, the visible energy $E_{\text{vis}}$ is defined as the energy of an electron which would produce the same number of Cherenkov photons. The number of collected photoelectrons depends on the scattering and attenuation in the water along with the photo-cathode coverage, quantum efficiency and the optical parameters of any external light collection systems or protective material surrounding them. Event-by-event corrections are made for geometry and attenuation. For a typical case, in water $N_{\text{p.e.}} \sim 15 \xi E_{\text{vis}}(\text{MeV})$, where $\xi$ is the effective fractional photosensor coverage. Cherenkov photoelectron yield per MeV of energy is relatively small compared to that for scintillator, e.g., $\sim 6$ pe/MeV for Super-K with a PMT surface coverage of $\sim 40\%$. In spite of light yield and Cherenkov threshold issues, the intrinsic directionality of Cherenkov light allows individual particle tracks
to be reconstructed. Vertex and direction fits are performed us-
ing PMT hit charges and times, requiring that the hit pattern be
consistent with a Cherenkov ring.

High-energy (~100 MeV or more) neutrinos from the atmo-
sphere or beams interact with nucleons; for the nucleons bound
inside the $^{16}$O nucleus, nuclear effects must be considered both
at the interaction and as the particles leave the nucleus. Various
event topologies, with final-state particles contained, exiting, or
entering the detector, can be distinguished by their timing and
fit patterns, and by presence or absence of light in a veto. At
high energies, multi-photoelectron hits are likely and the charge
collected by each PMT (rather than the number of PMTs fir-
ing) must be used; the energy resolution in this case is approx-
imately 2%/√ξ $E_{\text{vis}}$(GeV). The absolute energy scale in this
regime can be known to ~2-3% using cosmic-ray muon energy
deposition, Michel electrons and π⁰ from atmospheric neutrino
interactions. Typical vertex resolutions for GeV energies are a
few tens of cm [53]. Angular resolution for determination of the
direction of a charged particle track is a few degrees. For a neu-
trino interaction, because some final-state particles are usually
below Cherenkov threshold, knowledge of direction of the incom-
ing neutrino direction itself is generally worse than that of the
lepton direction, and dependent on neutrino energy.

Multiple particles in an interaction (so long as they are above
Cherenkov threshold) may be reconstructed, allowing for the ex-
clusive reconstruction of final states. In searches for proton decay,
multiple particles can be kinematically reconstructed to form a
decaying nucleon. High-quality particle identification is also pos-
sible: γ rays and electrons shower, and electrons scatter, which
results in fuzzy rings, whereas muons, pions and protons make
sharp rings. These patterns can be quantitatively separated with
high reliability using maximum likelihood methods [54]. Sources
of background for high energy interactions include misidentified
cosmic muons and anomalous light patterns when the PMTs some-
times “flash” and emit photons themselves. The latter class of
events can be removed using its distinctive PMT signal patterns,
which may be repeated. More information about high energy
event selection and reconstruction may be found in reference [55].

In spite of the fairly low light yield, large water Cherenkov
detectors may be employed for reconstructing low-energy events,
down to e.g. ~ 4-5 MeV for Super-K [56]. Low-energy neutrino
interactions of solar neutrinos in water are predominantly elastic
scattering off atomic electrons; single electron events are then re-
constructed. At solar neutrino energies, the visible energy resolu-
tion (~30%/√ξ E<sub>vis</sub>(MeV)) is about 20% worse than photoelec-
tron counting statistics would imply. Using an electron LINAC
and/or nuclear sources, approximately 0.5% determination of the
absolute energy scale has been achieved at solar neutrino energies.
Angular resolution is limited by multiple scattering in this energy
regime (25-30°). At these energies, radioactive backgrounds be-
come a dominant issue. These backgrounds include radon in the
water itself or emanated from detector materials, and γ rays from
the rock and detector materials. In the few to few tens of MeV
range, radioactive products of cosmic-ray-muon-induced spalla-
tion are troublesome, and are removed by proximity in time and
space to preceding muons, at some cost in dead time. Gadolinium
doping using 0.2% Gd<sub>2</sub>(SO<sub>4</sub>)<sub>3</sub> has now been initiated for Super-
K to improve selection of low-energy ν̄e and other events with
accompanying neutrons [57].

The Sudbury Neutrino Observatory (SNO) detector [58] was
the only instance of a large heavy water detector. In addition to
an outer 1.7 kton of light water, SNO contained 1 kton of D<sub>2</sub>O,
giving it unique sensitivity to neutrino neutral current (ν<sub>x</sub> + d →
ν<sub>x</sub> + p + n), and charged current (ν<sub>e</sub> + d → p + p + e<sup>-</sup>) deuteron
breakup reactions. The neutrons were detected in three ways:
via capture on deuterons, via capture on dissolved <sup>35</sup>Cl, and via
specialized <sup>3</sup>He counters.

36.3.1.3 Noble liquid detectors

Noble liquids scintillate and can be used as the active medium for particle detection. Detectors employing argon and xenon are also used as time-projection chambers (TPCs), either as dual-phase low-energy recoil detectors, or as track-imaging detectors.

Noble-liquid detectors with low energy (few to few tens of keV) capabilty for detecting electronic and nuclear recoils are employed for dark matter and other rare event searches and are described in Sec. 36.4. These detectors can also be employed for some of the same physics (baryon number violation, astrophysical neutrino transient searches, etc.) as for the other large detectors described here, especially as they approach tens of ton scale and higher (e.g., DARWIN, DarkSide-20, ARGO). Track-imaging time-projection chambers, which are described in detail Section 36.4, have a dynamic range reaching down to the few to few tens of MeV scale, enabling sensitivity to e.g., solar and supernova burst neutrinos. Surface LArTPCs have significant cosmic backgrounds, but may still have sensitivity to astrophysical transients such as supernova burst neutrinos. DUNE will be sufficiently deep to have sensitivity to steady-state low-energy neutrino sources such as solar neutrinos.

36.3.2 Neutrino telescopes

Revised February 2024 by U.F. Katz (Erlangen U.) and C. Spier-
ing (DESY, Zeuthen).

The primary goal of neutrino telescopes (NTs) is the detection of astrophysical neutrinos, in particular those which are expected to accompany the production of high-energy cosmic rays in astrophysical accelerators. NTs in addition address a variety of other fundamental physics issues like the indirect search for dark matter, studies of neutrino oscillations, searches for exotic particles like magnetic monopoles or study of cosmic rays and their interactions [59–61]. Electromagnetic radio frequency detectors for high energy neutrinos are discussed in "Radio emission from (ultra-) high energy particle showers" section 36.3.3.

<figure><img src="image_245.png" /><figcaption>**Figure 36.5:** Average over the effective $\nu_\mu$ and $\bar{\nu}_\mu$ areas for IceCube as an example of a cubic-kilometre NT, as a function of neutrino energy for three intervals of the zenith angle $\theta$. The values shown here correspond to a specific event selection for point source searches.</figcaption></figure>

NTs are large-volume arrays of “optical modules” (OMs) installed in open transparent media like water or ice, at depths that completely block the daylight. The OMs are sensitive to individual photons of the Cherenkov light induced by charged secondary particles produced in reactions of high-energy neutrinos in or around the instrumented volume. The time of photon-induced signals (“hits”) is registered with a precision of a few nanoseconds. The neutrino energy, $E_\nu$, and direction can be reconstructed from the hit pattern recorded. NTs typically target an energy range $E_\nu \gtrsim 100$ GeV; sensitivity to lower energies is achieved in dedicated setups with denser instrumentation.

In detecting cosmic neutrinos, three sources of backgrounds
have to be considered: (i) atmospheric neutrinos from cosmic-ray
interactions in the atmosphere, which can be separated from cos-
mic neutrinos on a statistical basis, or, for down-going neutrinos,
by vetoing accompanying muons; (ii) down-going punch-through
atmospheric muons from cosmic-ray interactions, which are sup-
pressed by several orders of magnitude with respect to the ground level due to the large detector depths and can be further reduced by selecting upward-going or high-energy neutrinos or by self-veto methods; (iii) random backgrounds due to photomultiplier (PMT) dark counts, ⁴⁰K decays (mainly in sea water) or bioluminescence (only water). Atmospheric neutrinos and muons allow for investigating neutrino oscillations and cosmic ray anisotropies, respectively. Since 2012, it has become obvious that a precise measurement of the energy-zenith-distribution of atmospheric neutrinos in the energy range from a few to about 100 GeV may allow for determining the neutrino mass hierarchy by exploiting matter-induced oscillation effects in the Earth [62, 63].

Neutrinos can interact with target nucleons *N* through charged current ($\bar{\nu}_{\ell}N \rightarrow \ell\mp X$, CC) or neutral current ($\bar{\nu}_{\ell}N \rightarrow \bar{\nu}_{\ell}X$, NC) processes. A CC reaction of a $\bar{\nu}_{\mu}$ produces a muon track and a hadronic particle cascade, whereas all NC reactions and CC reactions of $\bar{\nu}_e$ produce particle cascades only. CC interactions of $\bar{\nu}_{\tau}$ can have either signature, depending on the $\tau$ decay mode. Of particular interest is the so-called double-bang signature, where the $\tau$ decays sufficiently far away from the primary interaction to create a second, distinguishable cascade (typically at PeV energies and above). In most astrophysical models, neutrinos are expected to be produced through the $\pi/K \rightarrow \mu \rightarrow e$ decay chain, i.e., with a flavour ratio $\nu_e : \nu_\mu : \nu_\tau \approx 1 : 2 : 0$. For sources outside the solar system, neutrino oscillations turn this ratio to $\nu_e : \nu_\mu : \nu_\tau \approx 1 : 1 : 1$ upon arrival on Earth.

The total neutrino-nucleon cross section is about $10^{-34}$ cm² at $E_\nu = 20$ TeV and rises roughly linearly with $E_\nu$ below this energy and as $E_\nu^{0.3-0.5}$ above, flattening out towards high energies. The CC:NC cross-section ratio is about 2:1. At energies above several TeV, neutrino absorption in the Earth becomes noticeable; for vertically upward-moving neutrinos (zenith angle $\theta = 180^\circ$), the survival probability is 74 (27, < 2)% for 10 (100, 1000) TeV. The energy transferred to the final-state lepton varies between 0 and 100% of $E_\nu$, with a mean of 50% (65%) for neutrinos (antineutrinos) at 100 GeV and 75% for both neutrinos and antineutrinos at 10 PeV.

The final-state lepton follows the initial (anti)neutrino direction with an average mismatch angle of about $\langle\phi_{\nu\ell}\rangle \approx 1^\circ/(E_\nu/\text{TeV})^{0.55}$, with a steeper decrease beyond 10 TeV, reaching $0.005^\circ$ at 1 TeV [64]. These values indicate the intrinsic kinematic limit to the angular resolution of NTs. For CC $\bar{\nu}_\mu$ reactions at energies above about 10 TeV, the angular resolution is dominated by the muon reconstruction accuracy of a few times $0.1^\circ$ at most. For muon energies $E_\mu \gtrsim 1$ TeV, the increasing light emission due to radiative processes allows for reconstructing $E_\mu$ from the measured Cherenkov light intensity with an accuracy of $\sigma(\log E_\mu) \approx 0.3$; at lower energies, $E_\mu$ can be estimated from the length of the muon track if it is contained in the detector. These properties make CC $\bar{\nu}_\mu$ reactions the prime channel for the identification of individual astrophysical neutrino sources.

Hadronic and electromagnetic particle cascades at the relevant energies are 5–20 m long, i.e., short compared to typical OM spacings. The total amount of Cherenkov light provides a direct measurement of the cascade energy with an accuracy of about 20% at energies above 10 TeV and 10% beyond 100 TeV for events contained in the instrumented volume. Except for double-bang events, the neutrino flavour and reaction mechanism can, however, be determined on a statistical basis at best, and neutrinos from NC reactions or $\tau$ decays may carry away significant “invisible” energy. Above 100 TeV, the average directional reconstruction accuracy of cascades is better than 10 (2) degrees in polar ice (sea water), the difference being due to the inhomogeneity of the ice and stronger light scattering in ice. These features, together with the small background of atmospheric $\bar{\nu}_e$ and $\bar{\nu}_\tau$ events, makes the cascade channel particularly interesting for searches for a diffuse, high-energy excess of extraterrestrial over atmospheric neutrinos. Cascade events can also be used to complement the muon channel in searches for point sources or transient signals, albeit with inferior angular accuracy compared to muon tracks.

The detection efficiency of a NT is quantified by its effective area, e.g., the fictitious area for which the full incoming neutrino

flux would be recorded (see Figure 36.5). The increase with $E_\nu$ is due to the rise of neutrino cross section and muon range, while neutrino absorption in the Earth causes the decrease at large $\theta$ for large $E_\nu$. Identification of downward-going neutrinos requires stringent event selection to suppress atmospheric muons, hence the cut-off towards low $E_\nu$ at low $\theta$. Due to the small cross section, the effective area is many orders of magnitude smaller than the geometrical dimension of the detector; a $\bar{\nu}_\mu$ with 1 TeV can, e.g., be detected with a probability of the order $10^{-6}$ if the NT is on its path.

Due to the long muon range, CC interactions of up-going $\bar{\nu}_\mu$ can be detected from far outside the instrumented volume. This method also works for horizontal neutrinos up to about $10^\circ$ above the horizon (depth dependent), where the background from atmospheric muons become prohibitive. Alternatively, one can select events that start inside the instrumented volume and thus remove incoming muons that generate early hits in the outer layers of the detector. Such a veto-based event selection is sensitive to neutrinos of all flavours from all directions, albeit with a reduced efficiency since a part of the instrumented volume is sacrificed for the veto. Such a muon veto, or vetoing events with a coincident signal in the surface array, also rejects down-going atmospheric neutrinos that are accompanied by muons from the same air shower and thus reduces the atmospheric-neutrino background. Actually, the breakthrough in detecting high-energy cosmic neutrinos was first achieved with this technique.

Note that the fields of view of NTs at the South Pole and in the Northern hemisphere are complementary for each reaction channel and neutrino energy.

### 36.3.2.1 The Projects

Table 36.3 lists past, present and future neutrino telescope projects and their main parameters.

### 36.3.2.2 Properties of media

The efficiency and quality of event reconstruction depend strongly on the optical properties (absorption and scattering length, intrinsic optical activity) of the medium in the spectral range of bialkali photocathodes (300–550 nm). Large absorption lengths result in a better light collection, large scattering lengths in superior angular resolution. Deep-sea sites typically have effective scattering lengths of > 100 m and, at their peak transparency around 450 nm, absorption lengths of 50–65 m. The absorption length for Lake Baikal is 22–24 m. The properties of South Polar ice vary strongly with depth; at the peak transparency wave length (400 nm), the scattering length is between 5 and 75 m and the absorption length between 15 and 250 m, with the best values in the depth region 2200–2450 m and the worst ones in the layer 1950–2100 m.

Noise rates measured by PMTs with a diameter of 25 cm in deep polar ice are about 0.5 kHz per PMT and almost entirely due to radioactivity in the OM components. The corresponding rates in sea water are typically 60 kHz, mostly due to ⁴⁰K decays. Bioluminescence activity can locally cause rates on the MHz scale for seconds; the frequency and intensity of such “bursts” depends strongly on the sea current, the season, the geographic location, and the geometry of the detector elements. Experience from ANTARES shows that these backgrounds are manageable without a major loss of efficiency or experimental resolution.

### 36.3.2.3 Technical realisation

Optical modules (OMs) and PMTs: An OM is a pressure-tight glass sphere housing one or several PMTs with a time resolution in the nanosecond range, and in most cases also electronics for control, high-voltage generation, operation of calibration LEDs, time synchronisation and signal digitisation.

Hybrid PMTs with 37 cm diameter have been used for NT-200, conventional hemispheric PMTs with 20 cm diameter for AMANDA and with 25 cm diameter for ANTARES, IceCube and Baikal-GVD. A novel concept has been chosen for KM3NeT. Each OM (43 cm) is equipped with 31 PMTs (7.5 cm), plus control, calibration and digitisation electronics. Advantages are that (i) the overall photocathode area exceeds that of a 25 cm PMT by more than a factor of 3; (ii) the individual readout of the PMTs results in a very good separation between one- and two-photoelectron
<table><caption>**Table 36.3:** Past, present and future NT projects and their main parameters. The milestone years give the times of project start, of first data taking with partial configurations, of detector completion, and of project termination. Projects with first data expected past 2024 are indicated in italics. The size refers to the largest instrumented volume reached during the project development. The status of projects under construction is reported as of February 2024. See [61] for references to the different projects where unspecified.</caption><thead><tr><th>Experiment</th><th>Milestones</th><th>Location</th><th>Size (km³)</th><th>Remarks</th></tr></thead><tbody><tr><td>DUMAND</td><td>1978/-/-/1995</td><td>Pacific Ocean</td><td></td><td>Terminated due to technical/funding problems</td></tr><tr><td>NT-200</td><td>1980/1993/1998/2015</td><td>Lake Baikal</td><td>10<sup>-4</sup></td><td>First proof of principle</td></tr><tr><td>GVD [65]</td><td>2012/2015/-/-</td><td>Lake Baikal</td><td>ca. 1</td><td>High-energy ν astronomy first 12 clusters installed</td></tr><tr><td>AMANDA</td><td>1990/1996/2000/2009</td><td>South Pole</td><td>0.015</td><td>First deep-ice NT</td></tr><tr><td>IceCube [66]</td><td>2001/2005/2010/-</td><td>South Pole</td><td>1.0</td><td>First km<sup>3</sup>-sized detector</td></tr><tr><td>IceCube-Gen2 [67,68]</td><td>2014/-/-/-</td><td>South Pole</td><td>5-10</td><td>Planned future extension of IceCube covering low and high energies, a surface array and radio detection</td></tr><tr><td>NESTOR</td><td>1991/-/-/-</td><td>Med. Sea</td><td></td><td>2004 data taking with prototype</td></tr><tr><td>NEMO</td><td>1998/-/-/-</td><td>Med. Sea</td><td></td><td>R&D project, prototype tests</td></tr><tr><td>ANTARES</td><td>1997/2006/2008/2022</td><td>Med. Sea</td><td>0.010</td><td>First deep-sea NT</td></tr><tr><td>KM3NeT/ARCA [63]</td><td>2013/2021/-/-</td><td>Med. Sea</td><td>ca. 1</td><td>High-energy configuration for neutrino astronomy. Under construction, data taking with 28 strings</td></tr><tr><td>KM3NeT/ORCA [63]</td><td>2014/2020/-/-</td><td>Med. Sea</td><td>0.007</td><td>Low-energy configuration for neutrino mass hierarchy. Under construction, data taking with 18 strings</td></tr><tr><td>KM3NeT Phase 3</td><td>2013/-/-/-</td><td>Med. Sea</td><td>ca. 3</td><td>Possible future extension, 6 ARCA blocks + ORCA</td></tr><tr><td>P-ONE [69]</td><td>2018/-/-/-</td><td>Pacific Ocean</td><td>O(1)</td><td>Planned future NT, R&D phase</td></tr><tr><td>TRIDENT [70]</td><td>2021/-/-/-</td><td>South China Sea</td><td>O(10)</td><td>Planned future NT, R&D phase</td></tr></tbody></table>

signals which is essential for online data filtering and random background suppression; (iii) the hit pattern on an OM provides directional information; (iv) no mu-metal shielding against the Earth magnetic field is required. Figure 36.6 shows the OM designs of IceCube and KM3NeT.

**Readout and data filtering:** In current NTs the PMT data are digitised in situ: for ANTARES and Baikal-GVD in special electronics containers close to the OMs, for IceCube and KM3NeT inside the OMs. For IceCube, data are transmitted via electrical cables of up to 3.3 km length, depending on the location of the strings and the depth of the OMs; for ANTARES, KM3NeT and Baikal-GVD optical fibre connections have been chosen (several 10 km for the first two and 4 km for GVD).

The full digitised waveforms of the IceCube OMs are transmitted to the surface for pulses appearing in local coincidences on a string; for other pulses, only time and charge information is provided. For ANTARES (time and charge) and KM3NeT (time and time over threshold), all PMT signals above an adjustable threshold are sent to shore.

The data are subsequently processed on online computer farms, where multiplicity- and topology-driven filter algorithms are applied to select event candidates. The filter output data rate is about 10 GByte/day for ANTARES and of the order 1 TByte/day for IceCube (100 GByte/day transferred via satellite) and KM3NeT.

**Calibration:** For efficient event recognition and reconstruction, the OM timing must be synchronised at the few-nanosecond level and the OM positions and orientations must be known to a few 10 cm and a few degrees, respectively. Time calibration is achieved by sending synchronisation signals to the OM electronics and also by light calibration signals emitted in situ at known times by LED or laser flashers (ANTARES, KM3NeT). Precise position calibration is achieved by measuring the travel time of light calibration signals sent from OM to OM (IceCube) or acoustic signals sent from transducers at the sea floor to receivers on the detector strings (ANTARES, KM3NeT, Baikal-GVD). Absolute pointing and an-

gular resolution can be determined by measuring the “shadow of the moon” (i.e., the directional depletion of muons generated in cosmic-ray interactions). IceCube and ANTARES have both shown that they have angular resolution below 1°, confirming MC calculations which indicate a precision of ≈ 0.5° for energies above 10 TeV. For KM3NeT, simulations indicate that sub-degree precision in the absolute pointing can be reached within a few weeks of operation.

**Detector configurations:** IceCube [66] (see Figure 36.7) consists of 5160 Digital OMs (DOMs) installed on 86 strings at depths of 1450 to 2450 m in the Antarctic ice; except for the DeepCore region, string distances are 125 m and vertical distances between OMs 17 m. 324 further DOMs are installed in IceTop, an array of detector stations on the ice surface above the strings. DeepCore is a high-density sub-array at large depths (i.e., in the best ice layer) at the centre of IceCube.

The NT200 detector in Lake Baikal at a depth of 1100 m consisted of 8 strings attached to an umbrella-like frame, with 12 pairs of OMs per string. The diameter of the instrumented volume was 42 m, its height 70 m. Meanwhile (February 2024), the Baikal collaboration has installed the first 12 clusters of a future cubic-kilometre array, GVD [65]. It will consist of 18 clusters, each with 288 OMs at 8 strings, plus several single strings between the clusters; its completion is scheduled for 2027.

The operation of ANTARES (see [61] and references therein) was terminated in 2022. It comprised 12 strings with lateral distances of 60–70 m, each carrying 25 triplets of OMs at vertical distances of 14.5 m, located at depths of 2.1–2.4 km, starting 100 m above the sea floor. An additional string held devices for calibration and environmental monitoring. A system to investigate the feasibility of acoustic neutrino detection was also implemented.

KM3NeT will consist of building blocks of 115 strings each, with 18 OMs per string. Operation of the first strings deployed has successfully verified the KM3NeT technology and sensitivity. In the upcoming phase of its staged implementation, KM3NeT
<figure><img src="image_246.png" /><figcaption>**Figure 36.6:** Schematic views of the digital OMs of IceCube (left) and KM3NeT (right).</figcaption></figure>

<figure><img src="image_247.png" /><figcaption>**Figure 36.7:** Schematic view of the IceCube neutrino observatory comprising the deep-ice detector including its nested dense part DeepCore, and the surface air shower array IceTop. The IceCube Lab houses data acquisition electronics and the computer farm for online processing. Operation of AMANDA was terminated in 2009.</figcaption></figure>

aims at two building blocks for neutrino astronomy, with vertical distances between OMs of 36 m and a lateral distance between adjacent strings of 90 m (ARCA, for *Astroparticle Research with Cosmics in the Abyss*) and at one block for the measurement of the neutrino mass hierarchy, with vertical distances between OMs of 9 m and a lateral distance between adjacent strings of about 20 m (ORCA, for *Oscillation Research with Cosmics in the Abyss*) [63]. The installation of ARCA near Capo Passero, East of Sicily (depth

3440 m) and of ORCA near Toulon (depth 2450 m) is ongoing and as of now (February 2024) 28/18 strings have been deployed for ARCA/ORCA and are continuously operated. Completion of the full ARCA and ORCA arrays is planned for 2028.

P-ONE (*Pacific Ocean Neutrino Experiment*) [69] is a new initiative in its R&D phase, envisaging a large NT in the Pacific Ocean off the Canadian coast. It is intended to use an existing deep-sea cable infrastructure and to optimise the sensitivity for horizontal neutrinos with energies of about 100 TeV and beyond.

TRIDENT (Tropical Deep-Sea Neutrino Telescope) is a proposed future neutrino telescope in the South China Sea with an instrumented volume of 7.5 km³. R&D and site exploration efforts are ongoing and a pathfinder (TRIDENT Phase-1) is planned to be commissioned around 2026 [71].

### 36.3.2.4 *Results*

See Sect. 30.4 for a summary of the results from neutrino telescopes.

### 36.3.2.5 *Plans beyond 2023*

Within the future IceCube-Gen2 project, it is planned to extend the sensitivity of IceCube towards both higher and lower energies. To increase the detector sensitivity at high energies, a large-volume extension is envisaged, combined with a radio array for highest-energy neutrinos and a surface array providing also a powerful veto against atmospheric events [67, 68]. A substantially denser instrumentation of a sub-volume of DeepCore will be achieved with 7 closely spaced strings to be deployed in 2025/26 (the IceCube Upgrade), aiming to cover a low-energy program, to better calibrate the existing IceCube detector and the archival data, and to test new technologies. More information on the future extensions of GVD and KM3NeT and on P-ONE and TRIDENT are given above and in Table 36.3.

### 36.3.3 *Radio emission from (ultra-)high energy particle showers*

Revised August 2023 by S.R. Klein (NSD LBNL; UC Berkeley) and A. Nelles (DESY, Zeuthen; Erlangen U.).

Coherent radio-frequency (RF) electromagnetic radiation is an attractive signature to search for particle cascades produced by interactions of high-energy particles. RF signatures have been used to study both cosmic-ray air showers and to search for neutrino-induced showers. This article will discuss the radio signal generation, the relevant energy regime and the application in de-
tectors. Air showers are discussed in more detail in two recent reviews [72, 73]. At lower energies, incoherent optical Cherenkov radiation is frequently used, as discussed in "Neutrino telescopes" section 36.3.2. This article uses the general definitions and properties of neutrino telescopes as described in 36.3.2.

### 36.3.3.1 Signal generation and its characteristics

As discussed in the "Passage of Particles Through Matter" review Sec. 34 the electromagnetic component of a high energy shower gives rise to radio emission. For the signal generation itself the type of primary particle is irrelevant. However, the signal medium is important. It must be non-conducting (and non-absorptive at RF frequencies). The different shower length scales (radiation length, $X_0$) between air and the solid materials used for neutrino searches leads to surprisingly large differences in shower development. Due to the interaction with the medium the shower contains more electrons than positrons, which results in a net charge excess and leads to coherent Cherenkov emission, also known as Askaryan effect [74–76]. In air, during propagation through the geomagnetic field, the relative motion of electrons and positrons is affected, which leads to a varying transverse current, usually referred to as the geomagnetic effect [72]. Both effects may be described more generally as being due to radiation from a time-varying net charge [77]. Their relative importance is governed by the density of the medium, as the electric field scales as the net charge excess, and a lower density allows the geomagnetic effect to gain importance. Thus, in solid materials the emission from the Askaryan effect dominates, but it is a < 20% correction in air showers.

Coherent radiation is possible at wavelengths longer than the instantaneous thickness of the shower along an observer's line of sight. Since air showers have a larger extent than showers in solid media, their coherent radiation appears at lower frequencies [78].

High-frequency radiation is concentrated around the Cherenkov angle $\theta_C$. Viewed directly on the Cherenkov cone, the electric field strength, $\epsilon_{Ch}$ at a frequency $f$ from an electromagnetic shower from a $\nu_e$ with energy $E_\nu$ in ice may be roughly parameterized as [79, 80]

$$ \epsilon_{Ch}(V/\text{mMHz}) = 2.53 \times 10^{-7} \frac{E_\nu}{1\text{TeV}} \frac{f}{f_c} \left[ \frac{1}{1 + (f/f_c)^{1.44}} \right]. \quad (36.3) $$

The electric field strength increases linearly with frequency, up to a cut-off frequency $f_c$, which is set by the transverse size of the shower [81, 82]. The maximum wavelength $c/f_c$ is roughly the Moliere radius divided by $\cos(\theta_C)$ where $\theta_C$ is the Cherenkov angle. The cutoff frequencies depend on the density (which affects the Moliere radius). They are about 1 GHz in ice, about 3 GHz in the lunar regolith, and below 100 MHz in air.

Near $f_c$, radiation is narrowly concentrated around $\theta_C$ [81, 82]. At lower frequencies, the limited length of the emitting region leads to a broadening in emission angle around the Cherenkov cone. Away from $\theta_C$, the electric field from Eq. (36.3) is reduced by [79],

$$ \frac{\epsilon}{\epsilon_{Ch}} = \exp \left( -\frac{1}{2} \frac{(\theta - \theta_C)^2}{(2.2^\circ \times [1\text{GHz/f}])^2} \right). \quad (36.4) $$

The angular distribution of the signal around $\theta_C$ can be parameterized by a Gaussian peak modulated by a $\sin\theta$. In both ice and the lunar regolith, $\theta_C$ is about 56°, in air only 1°. Close to $\theta_C$, the 1 GHz maximum frequency in ice/regolith leads to a generated pulse width of ≈ 1 nsec.

These equations are appropriate for ice. More general parameterizations can be found in [80, 83].

More accurate calculations of the predicted radio signal, in particular air showers are not easily parameterized, but require detailed Monte Carlo simulations. For air showers, these are built on microscopic air shower simulations, calculate the emission from all individual particles in the shower development and add them for different observer positions [72]. For neutrinos, most approaches calculate (directly or from a parameterization) the Askaryan signal from a shower profile. The signal is then propagated through the medium and into an antenna model [80].

At energies above $10^{16}$ eV in ice, the Landau-Pomeranchuk-Migdal effect lengthens electromagnetic showers, by reducing the cross-sections for bremsstrahlung and pair production [84]. The lengthening of the shower leads to a narrowing of the radio emission around the Cherenkov cone, and a reduction in high-frequency emission away from the cone [80]. At higher energies, this leads to two separate components of the Askaryan radiation from a neutrino interaction: an un-altered component from the hadronic portion of the shower and an angularly narrowed component from the LPM-lengthened electromagnetic shower. The width of the narrowed component scales as $E_\nu^{1/3}$. If these two components can be observed separately, they could, in principle, be combined to determine the inelasticity of the neutrino interaction [85], allowing for improved measurements of low-$x$ parton distributions and searches for beyond-standard-model interactions.

Similarly, energetic outgoing $\mu^\pm$ and $\tau^\pm$ from neutrino interactions will dominantly lose energy via stochastic pair production and photonuclear interactions. These secondary particles will produce electromagnetic showers that can be detected by radio detectors, if they are above threshold energy. This will enable multiple detections of the same particle track and thus present interesting reconstruction opportunities [86].

At still higher energies, above $10^{20}$ eV, the LPM effect strengths, and the electromagnetic shower splits into multiple subshowers with significant separation. When these separations become large enough, the subshowers will effectively become independent radiators, with the total emission showing substantial event-by-event variation, depending on the division into subshowers [84]. Because of this, many experiments that study higher energy (well above $10^{20}$ eV) neutrinos focus on the hadronic shower from the struck nucleus. This contains an average of only about 20% of the energy, but with fewer large fluctuations.

### 36.3.3.2 Energy regime of radio detectors

The electric field amplitude is linearly proportional to the shower energy. Since the signal is a radio wave, the field amplitude decreases as $1/R$, plus potential absorption in the intervening medium, while the energy fluence decreases as $1/R^2$, again, plus potential absorption. The detection threshold depends on the distance to the antenna and the bandwidth and noise characteristics of the antenna and detector. For an antenna located in the detection medium, at a distance of 1 km the typical threshold is around $10^{17}$ eV. For stand-off (remote sensing) detectors, the threshold rises roughly linearly with the distance. These thresholds can be reduced by using directional antennas and/or combining the signals from multiple antennas using beam-forming techniques.

RF detectors are used to search for energetic neutrinos from three types of sources: astrophysical objects (i.e. extending measurements of the neutrino energy spectrum observed at TeV to PeV energies upward in energy), cosmogenic neutrinos associated with cosmic-ray-cosmic microwave background radiation (CMBR) interactions, and neutrinos from beyond-standard-model physics. These types are very roughly associated with energies below $10^{18}$ eV, the energy range $10^{18}$ to $10^{20}$ eV, and above $10^{20}$ eV.

Cosmogenic neutrinos are produced when ultra-high energy (UHE) protons with energy $E > 5 \times 10^{19}$ eV interact with photons from the CMBR, infrared light from old stars, and other extragalactic background light. These protons are excited to a $\Delta^+$ resonance which may decay via $\Delta^+ \to n\pi^+$, leading to neutrinos with energies above $10^{18}$ eV [87, 88]. The cosmogenic neutrino signal depends heavily on the fraction of UHE cosmic-rays that are protons. For a 100% proton composition (disfavored by most data [89]), observing a cosmogenic neutrino signal of at least a few events per year requires a solid or liquid detector with an active volume of about 100 km$^3$.

To reach the effective volumes necessary to observe the expected low fluxes of UHE neutrinos, common, naturally occurring, non-conducting solid (or potentially liquid) media, with a long absorption length for radio waves are needed. Optical Cherenkov and acoustical detectors are limited by short (< 100 m) attenuation lengths [90] so would require a prohibitively expensive number of sensors. The radio detection technique has been used to detect air
showers, targeting neutrinos as well as cosmic rays, and to search for neutrino showers in ice, salt domes and the lunar regolith.

### 36.3.3.3 Reconstruction of particle energy and direction and background suppression

Since radio detectors view the interaction from afar, the reconstruction techniques differ from optical neutrino telescopes.

Radio detection is a calorimetric measurement, thus provides good energy estimates of the shower energy. The energy fluence (integrated pulse power) of the signal scales quadratically with shower energy. It also depends on the distance to the shower, through potential attenuation losses and the usual $1/R$ loss in electric field amplitude. The arrival times in antennas and a spherical wave approximation can be used to determine the interaction vertex, although some uncertainty due to the viewing angle with respect to the Cherenkov angle may remain, if not corrected for by using the frequency information. If the radio signal travels through media where the index of refraction varies (like the firn of glacial ice), then ray-tracing techniques may be required to follow the signal back to the interaction point. For buried antennas, the bending of the signal trajectories due to the index of refraction creates an opportunity. For some geometries, there may be two paths to the detector: a 'direct' path, with minor bending, and a second where the signal is bent beyond horizontal, bouncing off the surface before reaching the antenna. By measuring the time difference between the two paths, the distance to the interaction vertex may be determined; this greatly simplifies the energy determination [91,92]. For most neutrino interactions (except for $\nu_e$ charged-current interactions), the shower energy is less than the neutrino energy. The uncertainty on the interaction inelasticity is a major contributor to the uncertainty in the neutrino energy, along with uncertainties on the distance between the antenna(s) and the interaction vertex [93].

Reconstruction of the neutrino arrival direction depends on several aspects of the signal. First, the direction from the antenna to the interaction site must be determined. This can be done by using the relative timing from separated antennas, or using beam-forming techniques with multi-element arrays. For air showers, the signal arrival direction is (almost) equal to the particle arrival direction, with corrections being obtainable by fitting a hyperbolic wavefront [72, 73].

For showers in solid/liquid media, the arrival direction with respect to the interaction point - antenna vector is determined from two additional angles. The frequency spectrum can be used to determine the angle between signal arrival direction and Cherenkov cone according to Eq. (36.4) [94]. The second angle can be determined from the polarization of the signal. The radio signal is produced with a linear polarization in the plane containing both the particle direction and the radio wave direction. These two angles can be combined to determine the direction, subject to a (usually) four-fold ambiguity, due to uncertainty as to whether the antenna is inside or outside the Cherenkov cone, and because the particle direction can be flipped 180° without affecting the observed signal. Often, some of these solutions can be rejected because they correspond to long path lengths through the Moon or the Earth, where the neutrino would be absorbed.

Spectral information is crucial for the reconstruction and background rejection. However, large bandwidth antennas typically disperse (i.e. broaden) the pulses. As long as the dispersion can be compensated for and backgrounds controlled, a large bandwidth detector is the most sensitive.

All radio experiments must contend with background. Common sources are anthropogenic noise, antenna/preamp noise, charge generated by blowing snow, lightning, and, at low frequencies, radiation from the Milky Way. While narrowband noise impacts triggering and contaminates signal quality, impulsive backgrounds could mimic a signal. One of the major issues for radio-detection experiments is anthropogenic noise. Most anthropogenic noise has distinctive characteristics (such as being narrow-band, and coming from near the horizon) which makes it relatively easy to reject during data analysis, via narrow-band filters and other techniques [72]. However, these factors complicate triggering and reduce data purity. This is even an issue in Antarctica, where communication radios and passing satellites can mimic showers,

at least at the trigger level. The need to limit anthropogenic noise has led most experimental groups to select remote locations for their detectors. Still, experiments have used approaches to reduce trigger-level noise, and/or to reject background at the analysis level. For example, for multi-element arrays, the threshold drops as the square root of number of antennas, since the signal adds in-phase while the backgrounds add with random phases [95]. It seems, however, that triboelectric signals recorded in periods with winds exceeding 10 m/s are a problematic trigger-level background, for experiments in polar regions [96] and will require removal during analysis.

Most dedicated air shower experiments have used radio antennas in combination with at least one other detector technology, such as scintillation counters, if the site quality is not sufficient and/or computing power on autonomous stations is limited. One exception is ARIANNA, which is located in an uninhabited part of Antarctica, enabling them to efficiently self-trigger on air showers [97].

Lunar experiments (discussed below) use different techniques to reduce the anthropogenic background. Some experiments use multiple antennas, separated by at least hundreds of meters; by requiring a coincidence within a small time window, anthropogenic noise can be rejected. With good enough timing, beam-forming techniques can be used to further reduce the background. An alternative approach is to use beam forming with multiple feed antennas viewing a single reflector, to ensure that the signal points back to the moon.

Due to the similarity in the radio emission of air showers and neutrino showers, the more abundant cosmic rays can act as background to neutrino searches. In-ice detectors need to suppress in-air emission that is refracted into the ice, emission that is created from developing air showers continuing in the ice, as well as from stochastic energy-losses of atmospheric muons. Lunar experiments may faces challenges in separating neutrino interactions from cosmic ray interactions.

### 36.3.3.4 Recent experiments

Figure 36.8 shows some current limits from neutrino searches, including from prototype arrays. Except for LOFAR, which is fully operational, projected limits from future experiments are not shown in the figure.

#### i. Ice

The most common dense medium transparent to radio waves is ice. Natural ice is an attractive medium for neutrino detection with radio attenuation lengths from over 300 m to 1 km [108]. The attenuation length varies with frequency and ice temperature, with higher attenuation in warmer ice. Although glacial ice is mostly uniform, the top ≈ 100 m of ice, the 'firn,' exhibits a gradual transition from packed snow at the surface (typically $\rho = 0.35 \text{ g/cm}^3$) to solid ice ($\rho = 0.92 \text{ g/cm}^3$) below [109]. The thickness of the firn varies with location; it is thicker in central Antarctica than in the coastal ice sheets or in Greenland. The varying density has several implications.

The index of refraction depends linearly on the density, so radio waves curve downward in the firn. This bending reduces the effective volume of surface or aerial antennas. A surface antenna cannot see near-surface interactions at large horizontal distances. There are also indications that the increase in firn density is non-monotonic [110, 111]. This leads to non-monotonic changes in index of refraction which may create waveguides that trap a small fraction of the radio energy and propagate it horizontally.

In one type of experiment, antennas mounted on high-altitude balloons observe the ice from above. Radio signals from in-ice neutrino interactions propagate to the surface, traverse the ice-air interface, and then travel to the balloon. The surface roughness of the ice can affect signals as they transition from the ice to the atmosphere. The best known example, ANITA, has made four flights around Antarctica, floating at an altitude around 35 km [112]. Its 32/40/48 (depending on the flight) dual-polarization horn antennas scanned the surrounding ice, out to the horizon (650 km away). Because of the small angle of incidence, ANITA could use polarization information to separate signals from back-
<figure><img src="image_248.png" /></figure>

**Figure 36.8:** Representative 3-flavor (summed, assuming equal fluxes of each flavor) differential (over one decade in energy) limits from different experiments and prototype experiments. Shown are limits from the IceCube ultra-high energy $\nu$ search [98], the Auger search for earth-skimming $\nu_{\tau}$ [99], the LUNASKA/Parkes [100] and NuMoon lunar searches [101], the ANITA balloon experiment [102], ARA [103] and ARIANNA prototypes [104], along with projections for the LOFAR array [105]. The dashed blue line is the extrapolation of the IceCube through-going $\nu_{\mu}$ flux measured at lower energies (few 10s of TeV to 10 PeV), with spectral index $\alpha = -2.37$ [106]. Because of the long extrapolation, this should only be treated as a rough reference. The ARA and ARIANNA limits are from prototype arrays, and indicate the energy range that might be covered, with far higher sensitivity by larger arrays. The shaded area is the allowed region for cosmogenic neutrinos, from a recent global analysis that included the measured cosmic-ray spectrum and composition [107].

ground; $\nu$ signals should be vertically polarized, while most background from cosmic-ray air showers should be horizontally polarized.

As with all radio-detection experiments, ANITA had to contend with anthropogenic backgrounds. The ANITA collaboration uses their multiple antennas as a phased array to achieve good pointing accuracy, with a resolution of 0.2-0.4° in elevation, and 0.5-1.1° in azimuth. They rejected all events that pointed toward known or suspected areas of human activity. ANITA has set the most stringent flux limits yet on neutrinos with energies above $10^{20}$ eV [102]. The ANITA experiment has also reported several anomalous events, matching cosmic ray signals, but with unexpected polarization signature, which the collaboration has indicated might be from Earth-skimming $\nu_{\tau}$ [113, 114]. However, this interpretation is controversial.

Because of the significant source-detector separation, ANITA is most sensitive at energies above $10^{19}$ eV. A lower energy threshold requires a smaller antenna-target separation.

Other ice based experiments use antennas located within the active volume, allowing them to reach thresholds around $10^{17}$ eV, or lower with phased array antennas. This approach was pioneered by the RICE experiment [115] which buried 18 half-wave dipole antennas in holes drilled for AMANDA at the South Pole, at depths from 100 to 300 m. The hardware was sensitive from 200 MHz to 1 GHz. Each antenna fed an in-situ preamplifier which transmitted the signals to surface digitizing electronics.

More recently, two groups have deployed prototype arrays which have explored different detector concepts. The Askaryan Radio Array (ARA) deployed surface and buried antennas at the South Pole [116], while the Antarctic Ross Ice shelf Antenna Neutrino Array (ARIANNA) installed surface antennas on the Ross Ice Shelf [104], about 110 km north of McMurdo station. ARIANNA offered the possibility of detecting downward-going $\nu$, from the radio waves reflected off the ice-sea water interface on the bottom of the Ross Ice Shelf, while ARA took advantage of the colder,

deeper ice at the South Pole, with its longer radio attenuation length. ARA buried antennas up to 200 m deep to be able to observe a larger portion of ice, due to the refraction of the signal in the firn. In contrast, ARIANNA deployed antennas just below the surface, allowing them to use high-gain, but large log periodic dipole antennas. Recently, phased-array trigger techniques have been demonstrated that can reduce the energy threshold by a factor of several [95, 117].

Both experiments use stations which operate independently, spaced far enough to maximize sensitivity, but where only a small fraction of neutrino events will be visible in multiple stations. Each station includes multiple antennas, which will be sensitive to both horizontal and vertical polarization. The expected angular resolution is a few degrees [94].

In 2021, the Radio Neutrino Observatory Greenland (RNO-G) started deploying stations at Summit Station. RNO-G is planned to consist of 35 stations, which employ ARIANNA-style surface antennas, an ARA-style phased array and deep antennas, and draw heavily on ANITA's electronics heritage [118].

## ii. The Moon

Because of its large size and non-conducting regolith, and the availability of large radio-telescopes, the Moon is an attractive target [119]. Conventional radio-telescopes are quite well suited to lunar neutrino searches, with natural beam widths not too dissimilar from the size of the Moon. Still, there are experimental challenges. The attenuation length is typically estimated to be 9m/f(GHz) [120], so only near-surface interactions can be studied. The composition of the lunar regolith is not well known, and there are significant uncertainties due to this uncertainty. One big limitation of lunar experiments is that the 385,000 km target-antenna separation leads to energy thresholds above $10^{20}$ eV.

The effective volume probed by experiments depends on the geometry, which itself depends on the frequency range used. At high frequencies $f$, the electric field strength is high, leading to a lower energy threshold, but the sensitive volume is limited because the Cherenkov cone only points toward the Earth for a narrow range of geometries. Lower frequency radiation is more isotropic, so the effective volume is larger, but, because the electric field is weaker, the energy threshold is higher. The $1/f$ dependence of the attenuation length in the lunar regolith further increases the effective volume at low frequencies. The frequency range affects the energy dependence of the sensitivity. As can be seen in Fig. 36.8, a low-frequency experiment like NuMoon (which covered 115-180 MHz) has good sensitivity, but only above about $10^{14}$ GeV, while Lunaska/Parkes, which observed in the range 1200-1500 MHz, has a higher flux limit, but is sensitive above about $10^{12.5}$ GeV.

Current limits and projected sensitivities are sensitive to many details. A recent review [121] compared different radio-detection experiments using a common framework, and found some significant shifts in sensitivities due to, e.g. different assumptions about lunar composition and inelasticities.

With modern technology, it is increasingly viable to search over very broad frequency ranges [122]. One technical challenge is due to dispersion (frequency dependent time delays) in the ionosphere. Dispersion can be largely removed with a de-dispersion filter, using either analog circuitry or post-collection digital processing.

## iii. Air

Radio detection in air is sensitive to all particles inducing air showers. Radio-detection can be used to determine the energy of cosmic rays, as done by e.g. the Auger and Tunka-Rex experiments [123, 124]. Radio signals can also be used to infer the altitude for shower-maximum, where the shower contains the most particles, as done by e.g. the LOFAR and Tunka-Rex collaborations [124, 125]. This altitude is sensitive to the cosmic-ray composition. Reconstructing the particle arrival direction is much easier in air since the Cherenkov angle, and thus the radio wave-front, aligns with the axis to 1°. Radio-detection is also useful for energy cross-calibrations between different experiments and may
be able to provide an independent energy scale calibration for air shower arrays [126].

One variation on the radio-detection approach is to look for ra-
dio emission from Earth-skimming $v_{\tau}$ [127,128]. Although $v_{\tau}$ are
much less commonly produced than $v_{\mu}$ and $v_{e}$, over astrophysical
distances, oscillations lead to a $v_{e}:v_{\mu}:v_{\tau}$ ratio near 1:1:1, for
almost all non-exotic acceleration and propagation mechanisms.

If the $v_{\tau}$ traverse the Earth and interact while traveling up-
ward, the resulting $\tau^{\pm}$ may exit the Earth before decaying. 83%
of the time, the decay produces a hadronic or electromagnetic
shower in the atmosphere [129]. Experiments have searched for
these upgoing showers, and for the resulting optical Cherenkov
and coherent RF radiation. The threshold energy dependence for
these searches depends on several factors, notably including the
average $\tau^{\pm}$ decay length, which increases linearly with energy. For
somewhat lower energy $v_{\tau}$, with shorter decay lengths, a moun-
tain may serve as a target, with $\tau^{\pm}$ expected to emerge from the
other side. The Pierre Auger observatory sets stringent limits on
this neutrino flux at energies above $10^{17}$ eV [99].

36.3.3.5 *Future experiments*

Looking ahead, RNO-G [118] will continue deployment until
2026 and reach the largest yearly sensitivity of any radio array
thus far. Further out, the proposed IceCube-Gen2 expansion in-
cludes a substantial radio array component [68], which will be
sensitive to both neutrinos from the ice and air showers from cos-
mic rays. PUEO, a successor of ANITA has been funded and is
scheduled for its first flight in 2025 [130].

In the near future, several large radio detector arrays should
reach significantly lower energies for lunar neutrino detection. The
LOFAR array is taking data with 36 detector clusters spread over
Northern Europe [105]. In the longer term, the Square Kilometer
Array (SKA) with its 1 km² effective area will push thresholds
down to near $10^{20}$ eV [122]. The SKA will also study air showers.

A number of dedicated prototype $v_{\tau}$ radio-detection experi-
ments exist. The GRAND Collaboration, e.g., is proposing to de-
ploy a large array of simple autonomous radio stations optimized
for near-horizontal signals [131]. The Pierre Auger Collaboration
is currently upgrading their surface array to include radio anten-
nas at all water Cherenkov detectors. This array will improve the
sensitivity of the instrument to horizontal showers, both for com-
position sensitivity for cosmic rays and for the detection of Earth
skimming neutrinos [132].

36.4 Large time-projection chambers for rare
event detection

Written August 2023 by L. Baudis (Zurich U.).

Initially developed for particle physics experiments at accelera-
tors (see Section 35.6.5), the concept of a Time Projection Cham-
ber (TPC) [133] evolved and is now tailored to a large range of
applications, most notably to experiments in astroparticle physics
searching for rare interactions deep underground. Present and
proposed experiments designed to observe interactions of dark
matter and other exotic particles, second order weak nuclear de-
cays, as well as neutrinos from a variety of sources are based on
TPCs operated with pure noble elements, either in gaseous or liq-
uid form. The detectors aim for large target masses, low energy
thresholds (keV-scale) and ultra-low levels of backgrounds from
radioactivity and cosmic rays. Historical introductions, reviews
of the operation principles, instrumentation and technological as-
pects, as well as applications, are found in Refs. [134–138].

The two most common noble fluids employed as detector media
in present TPCs for rare event searches are argon and xenon, ei-
ther as a high-pressure gas, or in liquid phase, or in liquid and gas
phase (dual-phase). An interaction within the active volume of
a TPC will create ionisation electrons and scintillation photons.
The prompt scintillation signal is detected with one or two arrays
of photosensors, while the ionisation electrons, which drift in the
pure medium under the influence of an external, uniform electric
field, are observed either directly with charge sensors, or via pro-
portional scintillation, or electroluminescence. Since transverse
electron diffusion is small, albeit non-negligible, the ionisation

signal provides the *x* − *y* information of the interaction site, with
the *z*-information coming from the drift time measurement. The
TPC thus yields a three-dimensional event localisation, enabling
fiducial volume selections and differentiation between single- and
multiple-scatters in the active volume. These features are crucial
for filtering out rare events from the much higher backgrounds
due to residual radioactivity of detector components. The spe-
cific energy loss (*dE/dx*) depends on the primary interacting par-
ticle, and leads to a distinct ratio of scintillation to ionisation
for gammas/electrons, alphas and fast neutrons, allowing for fur-
ther background discrimination. Two examples for the operation
principle of TPCs for rare event detection are shown in Fig. 36.9.

<figure><img src="image_249.png" /></figure>

Figure 36.9: Operation principle of TPCs for rare event detection: a high-pressure gas (left) and a dual (liquid/gas) phase (right) TPC. A particle interaction yields a prompt scintillation signal (S1) and a delayed, amplified proportional scintillation signal (S2). The latter is caused by ionisation electrons drifted in a homogeneous electric field (and, for dual phase TPCs, extracted into the gas phase above the liquid). In these examples, both S1 and S2 signals are observed with photosensor arrays placed behind the anode and cathode (left), or at the top and bottom (right) of the TPC. The position information along the drift field is inferred from the time difference between the two light signals, while the position in the transverse plane to the field is derived from the S2 light pattern in the photosensor plane close to the electroluminiscent light production site.
The properties of liquid argon as detection medium in a TPC are reviewed in Section 35.7. Here some properties for xenon are given in Tab. 36.4. In the liquid phase, the high xenon density allows for compact, large and homogeneous detector geometries with efficient self-shielding against external radiation, given that the cross sections for the photoelectric effect, Compton scattering and pair production scale as $Z^5/E_γ^{7/2}$, $Z/E_γ$ and $Z^2 \ln(2E_γ)$, respectively, for incoming X-rays and gammas with energy $E_γ$. The radioactive isotopes $^{124}$Xe, $^{126}$Xe, $^{134}$Xe and $^{136}$Xe have very long half-lives, and their second-order weak decay modes are subject to investigation (see Section 36.4.2).

In an argon or xenon detector, the energy loss of an incident particle is shared between ionisation, excitation and sub-excitation electrons liberated in the ionisation process. The average energy loss in ionisation is slightly larger than the ionisation potential, as it includes multiple ionisation processes. In their condensed phases, argon and xenon exhibit a band structure of electronic states, with the band gap energy being around 14.3 eV and 9.3 eV for liquid argon and xenon, respectively. In gaseous xenon, the ionisation potential is about 12.1 eV. Scintillation arises from excited atoms (excitons) and from ions, via recombination, with the emitted vacuum-ultraviolet (VUV) photons in single bands centred at $\lambda = 128$ nm for argon and $\lambda = 175$ nm for xenon. The excited dimers (or excimers), at their lowest excited level, deexcite to the dissociative ground state by the emission of a single VUV photon. This comes from the large energy gap between the lowest excitation and the ground levels, forbidding other decay channels such as non-radiative transitions. The scintillation light has two decay components due to de-excitation of spin singlet and spin triplet states of the excited dimers to the ground state. The singlet and triplet states refer to the total spin quantum number ($s=0$ or $s=1$) of the excited Rydberg electron and the angular momentum due to the molecular orbit, with the shorter and longer decay shapes being produced by the de-excitation of $s=0$ states and $s=1$ states, respectively. The different pulse decay time for different type of particle interactions, and thus ionisation densities, is employed to discriminate electronic from nuclear recoils in dark matter detectors. While this is very effective in liquid argon, due to the large time separation of $(6 \pm 1)$ ns versus $(1500 \pm 100)$ ns, it is difficult to put in practice for xenon [139], considering the much smaller separation, $(2.2 \pm 0.3)$ ns versus $(27 \pm 1)$ ns, of the two components.

The recombination-independent, mean energy required to produce a single detectable quantum (photon or electrons), called the W-value, assumes that each recombining electron-ion pair produces an exciton, which leads to a photon. In liquid argon, the W-value is $(19.5 \pm 1.0)$ eV [148]. In liquid xenon, the widely-adopted W-value is $(13.7 \pm 0.2)$ eV, measured with 122 keV $\gamma$-rays from an external $^{57}$Co source [149]. Recently, a lower value of $11.5_{-0.3}^{+0.2}$ (syst.) eV was obtained in a small TPC with internal sources at energies between 2.8 keV and 42 keV [150], consistent with the value measured at the MeV-scale, $11.5 \pm 0.5$ (syst.) $\pm 0.1$ (stat.) eV with the EXO-200 detector [151]. The ionisation and scintillation W-values in gaseous xenon are 24.8 eV and $(76 \pm 6)$ eV, respectively [152].

The partition between excitation and ionisation depends on the density of the electron-ion pairs produced along the track of a particle, and the recombination fraction depends on the applied electric field, as well as on the ionisation density in the track. While several phenomenological models exist to describe electron-ion recombination as a function of stopping power and electric drift field (see [134] and discussions therein), a solid theory of energy loss of low-energy ions in noble fluids is still missing. For nuclear recoils as generated by interactions of neutrons, neutrinos or hypothetical WIMPs, an energy-dependent quenching is introduced via the Lindhard factor $\mathcal{L}$ [153], with $\mathcal{L}$ being around $0.2-0.25$ and $0.15-0.2$ in liquid argon [154] and xenon [155], respectively, at nuclear recoil energies in the range 3-100 keV. A comprehensive framework to simulate scintillation and ionisation yields in argon and xenon as a function of interaction type, energy and electric field in a TPC is the Noble Element Simulation Technique (NEST) [156].

To calibrate the energy scale and determine the energy reso-

lution of low-background TPCs, mono-energetic lines from external (e.g., $^{57}$Co, $^{60}$Co, $^{137}$Cs, $^{228}$Th, etc) and internal ($^{83m}$Kr, $^{37}$Ar) calibration sources, as well as from neutron activation lines (e.g., $^{129m}$Xe, $^{131m}$Xe in xenon) are used. Relative energy resolutions ($\sigma/\mu$) at the level of 4-6% at energies of a few tens of keV and 2-3% at energies of a few 100 keV were reached in argon and xenon TPCs, respectively. At higher energies, relevant for the neutrinoless double beta decay of $^{136}$Xe, relative resolutions of 0.67%, 0.8% and 1.2% around 2.5 MeV were obtained by LZ [157], XENON1T [158] and EXO-200 [159], respectively. Superior energy resolutions are attained in high-pressure gas TPCs with electroluminiscent amplification [160], with a relative resolution of 0.4% obtained in the NEXT-White detector [161]. This is due to the fact that the Fano factor in pure gaseous xenon, $F_{GXe} = 0.15 \pm 0.02$, is about two orders of magnitude smaller than in the liquid phase.

To achieve a high collection efficiency for both ionisation and scintillation signals, the concentration of impurities is reduced and maintained at a level below one part per $10^9$ (ppb) oxygen equivalent. While the light can be strongly reduced by the presence of water vapour, the ionisation signal also requires high purity in terms of molecules with high electronegative affinity. The purity is commonly expressed via the electron drift lifetime, $\tau_e$, which is the time over which the number of drifting electrons, $n_e$, is reduced by a factor e: $n_e(t) = n_e(t_0) \exp(-t/\tau_e)$. Ideally, $\tau_e$ should be a few times larger than the total drift time in a TPC, to prevent charge losses. Lifetimes > 10 ms were achieved both in argon and xenon (corresponding to impurity concentrations $\ll 1$ ppb O$_2$ equivalent) via continuous recirculation and purification in the liquid or gas phase.

The drift velocity of electrons, which depends on the drift field $E_d$ and the electron mobility $\mu$ as $v_d = \mu \cdot E_d$, has been measured for drift fields between $\sim (10-10^4)$ V/cm. It also depends on the temperature in the medium and the impurity concentration, often making the comparison between different measurements difficult. In general, the drift velocity raises from about 0.25 mm/$\mu$s at low fields to 2 mm/$\mu$s at high fields in both argon and xenon. As electrons drift in the electric field, the initial electron cloud spreads both in longitudinal and transversal direction to the field, expressed in terms of longitudinal $D_L$ and transversal $D_T$ diffusion coefficients, with $D_L < D_T$ and $D_L/D_T \approx 1$ for fields approaching zero. In argon, $D_L$ was measured as $\sim 4.2 \text{ cm}^2/\text{s}$ at 200 V/cm [162], $\sim 3.7 \text{ cm}^2/\text{s}$ at 274 V/cm [163], $\sim 7.2 \text{ cm}^2/\text{s}$ at 500 V/cm and $D_T$ as $\sim 12 \text{ cm}^2/\text{s}$ [164]. In xenon, $D_L$ is around $100 \text{ cm}^2/\text{s}$ at low fields, reaching $\sim 25 \text{ cm}^2/\text{s}$ at higher drift fields [142], while $D_T$ has been measured to be $\sim 55 \text{ cm}^2/\text{s}$ at fields between (20-600) V/cm [165]. As an example, the spatial distribution of an initially point-like electron cloud, after a drift time $t$, is $\sigma_D = \sqrt{2Dt}$, resulting in a value of $\sim 20$ mm for 1 ms drift and a $25 \text{ cm}^2/\text{s}$ diffusion coefficient.

The scintillation light can be attenuated by absorption on impurities or due to Rayleigh scattering, the latter depending strongly on the wavelengths of the photons and the optical properties of the materials. Since only the combined effect is observed, it is nontrivial to disentangle the two contributions. A combination of measurements and theoretical calculations yield total attenuation and Rayleigh scattering lengths between 55-110 cm and 60-99 cm for argon and 30-50 cm and 30-50 cm for xenon detectors, with refractive indexes between 1.34 and 1.57-1.72, respectively, and absorption lengths >100 cm [134, 166].

Background sources for rare-event searches, their mitigation techniques and radio-purity assays are discussed in Section 36.6 of this Review. The main backgrounds in large TPCs are due to decays of other noble isotopes mixed with the argon and xenon ($^{39}$Ar, $^{85}$Kr, $^{222}$Rn), from natural, anthropogenic or cosmogenic radioactivity of detector materials in close proximity to the target ($^{238}$U, $^{232}$Th, $^{40}$K, $^{60}$Co), and from muons and their secondary particles, including *in situ* production of isotopes which are sufficiently long-lived to render their vetoing difficult (e.g., $^{137}$Xe in xenon TPCs). Astrophysical neutrinos cause largely irreducible backgrounds in dark matter detectors, but deliver exciting physics signatures in their own right. To mitigate the $^{39}$Ar background, argon is extracted from underground sources (CO$_2$ wells), $^{85}$Kr
<table><caption>**Table 36.4:** Physical properties, volume fraction in the atmosphere, radioactive isotopes of the noble element xenon.</caption><thead><tr><th>Property [unit]</th><th>Xe</th></tr></thead><tbody><tr><td>Atomic number, mean atomic mass [g/mol]</td><td>54, 131.29</td></tr><tr><td>Boiling T<sub>b</sub> and melting T<sub>m</sub> point at 1 atm [K]</td><td>165.0, 161.4</td></tr><tr><td>Gas density at 1 atm and 298 K (T<sub>b</sub>) [g/l]</td><td>5.40 (9.99)</td></tr><tr><td>Liquid density at T<sub>b</sub> [g/cm<sup>3</sup>]</td><td>2.94</td></tr><tr><td>Volume ratio (ρ<sub>liduid</sub>/ρ<sub>gas</sub>)</td><td>526</td></tr><tr><td>Dielectric constant of liquid</td><td>1.95</td></tr><tr><td>Scintillation light yield (in liquid, at 122 keV) [140]</td><td>63 photons/keV</td></tr><tr><td>Wavelength (peak centred at)</td><td>175 nm</td></tr><tr><td>Decay time constants (s=0, s=1)</td><td>2.2 ns, 27 ns</td></tr><tr><td>Refractive index</td><td>1.69</td></tr><tr><td>Electron mobility* [142]</td><td>0.29 mm<sup>2</sup>/(μs V) (≤100 V/cm)<br>0.01 mm<sup>2</sup>/(μs V) (≥100 V/cm)</td></tr><tr><td>Volume fraction in Earth's atmosphere [ppm]</td><td>0.087</td></tr><tr><td>Isotopes with spin, abundance [%]</td><td><sup>129</sup>Xe, 26.44; <sup>131</sup>Xe, 21.18</td></tr><tr><td>Radioactive isotopes, abundance [%] and T<sub>1/2</sub> [y]</td><td><sup>136</sup>Xe, 8.87; 2.2×10<sup>21</sup> [143, 144]<br><sup>124</sup>Xe, 0.095; 1.1×10<sup>22</sup> [145]<br><sup>134</sup>Xe, 10.4; >8.7×10<sup>20</sup> (90% C.L.) [146]<br><sup>126</sup>Xe, 0.089; >1.9×10<sup>22</sup> (90% C.L.) [147]</td></tr></tbody></table>

and $^{222}$Rn are reduced by cryogenic distillation, exploiting the different vapour pressures of the different noble gases, or with gas chromatography using synthetic charcoal. In xenon detectors, $^{nat}$Kr concentrations of < 50 ppq [167] and $^{222}$Rn concentrations of 0.8 µBq/kg were achieved by cryogenic distillation in argon TPCs, $^{39}$Ar concentrations of (0.73 ± 0.11) mBq/kg were demonstrated [168].

An overview of large TPCs for rare event searches is given in Table 36.5.

### 36.4.1 Dark matter and other low energy signals

TPCs built to search for particle dark matter are based on the two-phase principle. Starting with total masses of a few kilogram the detectors evolved and reached active target masses at the tonne- and more recently multi-tonne scale. Concomitantly, the background levels in the most inner regions constantly decreased, with current electronic recoil rates of 15 events/(t y keV) in the energy region below 100 keV for xenon detectors [169]. Typically, the TPCs contain two arrays of photosensors, one immersed in the liquid, and one in the gas phase above the liquid at similar low temperature. The xenon scintillation light can be observed directly by PMTs with synthetic silica (quartz) windows or with VUV-sensitive SiPMs, while for argon detectors, tetraphenyl butadiene (TPB) is used to shift the 128 nm light to 420 nm, given that it is absorbed by quartz windows.

The DarkSide-50 experiment [168] operated a 50 kg TPC with liquid argon depleted in $^{39}$Ar until 2019. DarkSide-20k [170], to operate 51.1 t of underground LAr in an octagonal TPC, the walls made of gadolinium-loaded acrylic panels, with two arrays of SiPMs, is under construction in Hall C of the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. A larger, 400 t LAr detector, Argo, has been proposed for SNOLAB in Canada. After the successful operation of TPCs for LUX, PandaX-II and XENON1T, the current generation of xenon detectors, LUX-ZEPLIN (LZ) [171] at the Sanford Underground Facility (SURF) in USA, PandaX-4T [172] at the China Jinping Laboratory (CJPL) and XENONnT [173] at LNGS, employ several tons of LXe as active target mass. Their overall TPC design is rather similar, with cylindrical, polytetrafluoroethylene (PTFE) enclosed target regions viewed by two arrays of low-radioactivity, 3-inch diameter Hamamatsu R11410 PMTs. The PTFE has a high reflectivity for the Xe scintillation light [174]. Next-generation detectors, at the 50 t LXe scale or beyond, have been proposed with DARWIN/XLZD [175, 176] and PandaX-xT [177]. Recent constraints on various dark matter candidates are presented in

Section 27.6. The search for WIMP dark matter is ongoing, with the sensitivity goal of current experiments to the spin-independent WIMP-nucleon cross section around $1.5×10^{-48}$ cm$^2$ at 40-50 GeV/c$^2$ mass [171, 173].

Owing to low electronic recoil backgrounds and low energy thresholds in noble liquid TPCs, high-sensitivity searches for dark matter electron scattering with particle candidates from a hidden sector, for keV-scale axion-like-particles (ALPs) and dark photons via absorption in LXe, as well as searches for solar axions, became feasible (see Section 27.6). Looking at ionisation-only signals allows for a further reduction of the energy threshold, given the much higher efficiency to detect an ionisation electron compared to a primary scintillation photon (typically 90% versus 10%). While this gain comes at the expense of higher backgrounds, it allows nonetheless to set stringent limits on light dark matter electron interactions at masses from a few tens of MeV to a few GeV, as shown by DarkSide-50 [178], PandaX-4T [179], XENONnT [180] and LZ [181]. Further, current-generation dual-phase TPCs have reached target masses which will allow for the first time the detection of solar pp neutrinos via elastic neutrino-electron scattering at energies down to 1 keV and of $^8$B neutrinos via coherent elastic neutrino-nucleus scattering (CEνNS).

Dual-phase TPCs were successful in gradually scaling up their target mass and in reducing the background levels for each iteration, while maintaining a low-energy threshold of ~1 keV for electronic recoils. Notwithstanding, the construction of next-generation detectors at the multi-ten-tons scale poses multiple technological challenges. The background goals are such that electronic and nuclear recoils rates are below the ones from irreducible astrophysical neutrino interactions. This requirement sets the goals for the intrinsic $^{222}$Rn and $^{85}$Kr concentrations: the background from the decay of these isotopes should be significantly lower than the solar pp-neutrino elastic scattering rate. This translates into 0.1 µBq/kg for $^{222}$Rn$^2$ and 0.1 ppt for $^{nat}$Kr, assuming a $^{85}$Kr/$^{nat}$Kr ratio of $2×10^{-11}$ mol/mol. While $^{nat}$Kr concentrations of < 50 ppq were already achieved, for $^{222}$Rn a factor of about 10 reduction compared to the current values is needed. This calls for a high liquid throughput (close to 1 t/hour) with efficient cooling power based on cryogenic heat pumps and radon-free heat exchangers. Cryogenic distillation or charcoal chromatography must go hand in hand with selection of low radon

<footnote>*Measured values in two benchmark regimes, so-called "cold" and "hot" electrons [141]. In the first case, the electron energies are due to thermal bath of the xenon fluid and they rapidly gain energy with increasing field; in the second case, the electrons have gained most of their energy through acceleration in the field and experience increased energy loss on their path due to collisions with Xe atoms.</footnote>

<footnote>$^2$A $^{222}$Rn concentration of 0.1 µBq/kg corresponds to less than one radon atom per 100 mol of xenon. The main background is due to $^{214}$Bi β-decays which are not accompanied by an α-decay and thus cannot be tagged in the TPC.</footnote>
<table><caption>**Table 36.5:** Selected experiments using large TPCs for rare event searches. Shown are experiments that operated until recently, as well as current, soon-to-be-operating and proposed experiments. UAr stands for underground argon; HP-GXe stands for high-pressure gaseous xenon. For some of the proposed experiments, the location or the readout scheme is not yet decided (marked as "TBD").</caption><thead><tr><th>Experiment</th><th>Location</th><th>TPC type</th><th>Total (active) mass</th><th>Readout</th></tr></thead><tbody><tr><td colspan="5"><strong>Dark matter</strong></td></tr><tr><td>DarkSide-50</td><td>LNGS</td><td>Dual-phase, UAr</td><td>51.1 kg (46.4 kg)</td><td>3" PMTs, TPB</td></tr><tr><td>DarkSide-20k</td><td>LNGS</td><td>Dual-phase, UAr</td><td>50 t (50 t)</td><td>SiPMs, TPB</td></tr><tr><td>Argo</td><td>SNOLAB</td><td>Dual-phase*, UAr</td><td>~400 t (~400 t)</td><td>SiPMs, TPB</td></tr><tr><td>LUX-ZEPLIN</td><td>SURF</td><td>Dual-phase, Xe</td><td>10 t (7 t)</td><td>3" PMTs</td></tr><tr><td>PandaX-4T</td><td>CJPL</td><td>Dual-phase, Xe</td><td>5.6 t (3.7 t)</td><td>3" PMTs</td></tr><tr><td>PandaX-xT</td><td>CJPL</td><td>Dual-phase, Xe</td><td>47 t (43 t)</td><td>2" PMTs</td></tr><tr><td>XENONnT</td><td>LNGS</td><td>Dual-phase, Xe</td><td>8.6 (5.9 t)</td><td>3" PMTs</td></tr><tr><td>DARWIN/XLZD</td><td>TBD</td><td>Dual-phase, Xe</td><td>50-100 t (40-80 t)</td><td>3" PMTs</td></tr><tr><td colspan="5"><strong>0νββ decay</strong></td></tr><tr><td>EXO-200</td><td>WIPP</td><td> LXe, <sup>136</sup>Xe 81%</td><td>175 kg (110 kg)</td><td>LAAPDs, wires</td></tr><tr><td>nEXO</td><td>SNOLAB</td><td> LXe, <sup>136</sup>Xe 90%</td><td>4.8 t (3.65 t)</td><td>SiPMs, charge pads</td></tr><tr><td>NEXT-White</td><td>LSC</td><td> HP-GXe, <sup>136</sup>Xe 91%</td><td>5 kg (4.3 kg)</td><td>3" PMTs, SiPMs, TPB</td></tr><tr><td>NEXT-100</td><td>LSC</td><td> HP-GXe, <sup>136</sup>Xe 90%</td><td>100 kg (80 kg)</td><td>3" PMTs, SiPMs, TPB</td></tr><tr><td>NEXT-HD</td><td>TBD</td><td> HP-GXe, <sup>136</sup>Xe 90%</td><td>1.2 t (1 t)</td><td>Fibres + SiPMs, TPB</td></tr><tr><td>PandaX-III†</td><td>CJPL</td><td> HP-GXe, <sup>136</sup>Xe 90%</td><td>140 kg (100 kg)</td><td>Micromegas</td></tr></tbody></table>

emanation materials and new coating techniques to prevent radon emanation from surfaces.

Other challenges related to the liquid target are the continuous purification for electronegative impurities and water, to maintain high charge and light yields, while not introducing radon into the TPCs, as well as new solutions for reliable storage and recuperation at large scales. A dedicated single-closed-loop cryogenic system capable of handling 100 t of underground argon was designed and constructed for DarkSide-20k [182]. Liquid phase purification powered by a liquid xenon pump, as demonstrated in [183], was employed to achieve an electron drift lifetime above 15 ms in about 8.6 t of xenon in XENONnT. A system capable of handling 30 t of xenon in liquid phase, including long-term storage and and transfer of the cryogenic liquid between storage module and detectors was constructed for PandaX-xT [177, 184].

Regarding the detector design, electrodes with large (>2.5 m) diameters, with high transparency, minimal sagging and low spurious electron emission, as well as high-voltage feed-throughs that can safely deliver 50 kV or more to the cathode must be employed. DarkSide-20k will use for the first time anode and cathode plates made out of acrylic coated with a commercial conductive polymer and with TPB. LZ successfully built custom-woven wire-mesh grids with 1.5 m diameter, produced with an in-house built loom to weave the wire meshes [185]. Finally the cryostat design must ensure stability, while reducing as much as possible the amount of material, and thus gamma and neutron emitters in proximity to the TPCs.

Besides Ar and Xe TPCs, detectors using superfluid $^4$He, targeted at low-mass dark matter, are under development within the HeRALD [186] and DELight [187] programs, based on the basic principles demonstrated by the HERON solar neutrino project [188]. The detectors will be instrumented with transition edge sensors or magnetic micro-calorimeters to observe both atomic signals, such as scintillation light, and quasiparticle (phonon and roton) excitations. As in other noble elements, the $He_2$ dimers appear in a short-lived (<10 ns) singlet and long-lived (13s) triplet state. The former decay promptly, emitting photons with energies peaked around 16 eV, while the triplet states can propagate through the fluid and de-excite at surfaces. Liquid helium is transparent to its VUV photons, since the first excited state of atomic helium is at 20 eV. Quasiparticles will propagate ballistically through the liquid without decaying, and can also be detected via the evaporation of $^4$He atoms from the surface of the liquid, with the helium binding energy being ~0.7 meV.

Large volume, low-background TPCs are also developed for directional dark matter searches. An example is CYGNO [189] which aims to build a TPC with 50 cm drift, filled with a He:CF$_4$ gas mixture at room temperature and atmospheric pressure at LNGS. The liberated charge in a particle interaction is drifted towards an amplification stage consisting of a triple GEM structure, where the charge is multiplied and also light is produced. The readout will consist of light detectors, PMTs and scientific CMOS cameras, yielding the energy and z-position of events and the 2D track projections, respectively. The combined information thus allows for a 3D track reconstruction, with the goal being to achieve energy thresholds for electronic recoils around 1 keV.

### 36.4.2 0νββ Decay

Experiments built to search for the 0νββ-decay of $^{136}$Xe, at a Q-values of 2457.8 keV, are based on single-phase TPCs, filled either with liquid or gas xenon at high pressure. The drift region is horizontal (EXO-200, NEXT-100) or vertical (nEXO, NEXT-HD, PandaX-xT-enriched). For EXO-200 and nEXO, the TPCs are enclosed by radio-pure, thin-walled Cu vessels in cryofluid, hydro-fluoro ether, acting thermal bath and radiation shield. In EXO-200, which took data at the Waste Isolation Pilot Plant (WIPP) until 2018, the charge drifted to crossed-wire planes at each anode, while the light was collected by arrays of large area avalanche photodiodes placed behind the wire planes at both ends. In nEXO, the TPC vessel will be a vertical Cu cylinder with 130 cm height and diameter (for 118.3 cm drift), with the charge collected at the anode by 0.6 cm pitch and 9.6 m long electrode strips, and the scintillation light observed by SiPMs arranged in a barrel configuration. Unlike for dark matter TPCs, there are no reflector panels and the field rings and cathode are coated with reflective aluminium deposition. The design drift field is 400 V/cm and the goal for the relative energy resolution is 0.8%. EXO-200 set a lower limit on the half-life of 0νββ-decay of $3.5 \times 10^{25}$ y with a total exposure of 231.4 kg y [190]. The future nEXO aims for a sensitivity of $1.35 \times 10^{28}$ y with 5 t of enriched xenon and ten years of data taking [191].

TPCs using high-pressure xenon gas aim to reconstruct the tracks from the two electrons emitted in double beta decays, and the decay vertex, thus providing also a topological signature. In the NEXT project at the Laboratorio Subterráneo de Canfranc (LSC), the horizontal TPC, to be operated at 10-15 bar, features a single drift region. The primary (S1) and secondary (S2) scintillation light, the latter due to electroluminescence when the ion-

<footnote>*The option to build Argo as a single-phase detector is also under consideration.</footnote>

<footnote>†This is an R&D program for a future larger, enriched PandaX-xT detector.</footnote>
isation electrons cross a high-field region close to the anode, are
collected by arrays of PMTs and SiPMs placed behind the cathode
and anode, respectively, for energy measurements and tracking.
The surfaces facing the active volume are coated with TPB to
shift the VUV light to the visible spectrum. An inner Cu shield
absorbs radiation from the high-pressure vessel of the cryostat.

The NEXT-White experiment, a prototype for NEXT-100 and for the proposed tonne-scale NEXT-HD, has been operating a TPC with 20.8 cm radius and 53 cm drift, with 4.3 kg of xenon at 10 bar. It has shown excellent energy resolution (< 1% FWHM [161]) and demonstrated background rejection using the capability to reconstruct the trajectories of ionising charges in the gas, thus separating the two-electron signature of $\beta\beta$-decay from single electrons due to background sources [192, 193]. Using data collected with xenon enriched and depleted in $^{136}$Xe, it measured the half-life of the $2\nu\beta\beta$-decay and demonstrated clear Bragg peaks for the 2 electrons emitted in the decay [194]. NEXT-HD will operate a vertical-drift TPC, 2.6 m in diameter and height, to accommodate $\sim$1.1 t of enriched xenon at 15 bar [195]. An intense R&D programe for the *in situ* identification of the barium ions ($^{136}$Ba$^{2+}$, $^{136}$Ba$^{+}$) produced in the $0\nu\beta\beta$-decay (called B tagging) is ongoing [196–198]. PandaX-III, an R&D program for a future, enriched PandaX-xT detector, operates a high-pressure Xe gas TPC, where the xenon is mixed with 1% trimethylamine (TMA) to ensure stable operation of the Micromegas employed in the readout planes, and to minimise electron diffusion [199]. Experimental searches for $0\nu\beta\beta$-decay are discussed in more detail in Section 14.9.

Apart from enriched xenon detectors, large TPCs using xenon in its natural isotopic abundance are also sensitive to second-order weak decays, such as the double beta decay of $^{134}$Xe and $^{136}$Xe, and the double electron capture process in $^{124}$Xe and $^{126}$Xe. In its electronic recoil channel, XENON1T observed for the first time the $2\nu$ECEC process in $^{124}$Xe by detecting the simultaneously emitted K-shell X-rays/Auger electrons of the daughter atom $^{124}$Te with a combined energy of 64.33 keV, which is twice the K-shell binding energy. With a half-life of $(1.1 \pm 0.2)_{\text{stat}} \pm 0.1_{\text{sys}} \times 10^{22}$ y, this is the slowest process ever measured directly [145, 200]. The double electron capture in $^{124}$Xe can also be studied with high-pressure xenon gas TPCs, as demonstrated by NEXT [201]. LZ, PandaX-4T and XENONnT will improve upon existing results and will also search for the $2\nu\beta^+\text{EC}$ decay. This channel has a distinct signature due to the two 511 keV gammas emitted after the positron annihilates with an electron in the medium. With a predicted half-life around $1.6 \times 10^{23}$ y [202] its first observation is within reach of these running experiments, which will also measure the half-life and in particular also the shape of the $2\nu\beta\beta$-decay of $^{136}$Xe with high statistics and at low energies not previously accessed. The current generation of dark matter detectors will also set constraints on the $0\nu\beta\beta$-decays of $^{136}$Xe and $^{134}$Xe, as predicted or shown in [145, 203–205], delivering proof-of-principle methods towards higher sensitivity searches in DARWIN/XLZD and PandaX-xT. As an example, with 40 t of natural xenon in a TPC, a $^{136}$Xe half-life sensitivity of $3 \times 10^{27}$ y (90% C.L.) after ten years of operation can be reached [206], a number which increases by about a factor of 1.7 for an enlarged xenon mass of 60 t.

## 36.5 Sub-kelvin detectors

Revised August 2023 by O. Cremonesi (INFN, Milano-Bicocca), L. Hsu (FNAL) and G. Signorelli (Pisa U.; INFN, Pisa).

### 36.5.1 Motivation for Sub-kelvin Detectors

Detectors operating below 1 K are referred to as low-
temperature detectors (LTDs). The advantage of using LTDs
over conventional detectors resides in their better energy reso-
lutions, lower noise, and improved energy thresholds, which can
all be achieved with a versatile choice in materials. In certain
applications, these advantages outweigh the potential drawbacks
of cooling and reading out a detector payload at sub-kelvin tem-
peratures, and thus enable exploration of new frontiers in fun-
damental physics, astrophysics and cosmology. Among the en-
deavors enabled by LTDs are direct searches for dark matter over

a wide mass range, precision experiments to measure the elec-
tron neutrino mass, searches for neutrinoless double-beta decay,
and X-ray observation of the Universe. Large arrays of LTDs are
also employed to measure the properties of the cosmic microwave
background (CMB) spectrum whose parameters are determined
by fundamental physics. These include dark matter and dark en-
ergy densities, the sum of neutrino masses and the number of light
relativistic species, as well as probing the physics of inflation at
energy scales of $\sim 10^{16}$ GeV. This article presents a brief overview
of LTDs, their features, and several applications. More detailed
treatment of this subject is available in the literature [207–210].

The advantages of LTDs are enabled by the detection of very low energy excitations (e.g. phonons and quasiparticles). In a typical interaction, energy from an incident particle is dissipated through excitation of secondary particles such as electrons, ions, holes, photons, phonons etc. These particles will in turn produce their own secondaries. Thus there is a cascade down in energy until the original energy deposit is converted entirely into heat and the detector reaches thermal equilibrium. Prior to the equilibrium phase, the energy at any given moment is partitioned among multiple excitation modes. Conventional particle detectors work by sensing the higher energy excitation modes, such as ionization and scintillation, which require an average minimum energy of few eV to 10's of eV to produce. For such detectors, a large fraction of the deposited energy remains undetected in the form of heat. Furthermore, the measurements are subject to the fluctuations inherent in the partition of energy across different excitation modes. Secondaries that don't eventually escape the detector, will de-excite or recombine to dissipate their energy in the form of phonons and quasiparticles, which are characterized by energies in the range of meV down to $\mu$eV. These can be detected by LTDs at various stages of their final degradation towards thermal equilibrium. Thus LTDs allow for energy resolutions and operational thresholds much lower than detectors that only sense scintillation and ionization. Furthermore, LTDs provide a precise energy measurement owing to the relatively large number of excitation quanta that can be detected. In fact, LTDs designed to measure thermal phonons achieve the highest possible energy resolutions with optimal noise performance.

At thermal equilibrium, energy *E* deposited in an LTD causes a temperature rise *ΔT* = *E*/*C* where *C* is the heat capacity. Thermal equilibrium is characterized by the condition where the average heat flowing to an LTD equals the average heat flowing from the LTD (into a proper heat sink or bath). In this state, the ideal intrinsic energy resolution is determined by the statistical fluctuations in the phonon system. Fluctuations in the total number of phonons in the LTD absorber have variance *C*/*k*<sub>B</sub>, which yields a minimum resolution of *ΔE*<sup>2</sup> = *k*<sub>B</sub>*T*<sup>2</sup>*C* to the device energy resolution, where *k*<sub>B</sub> is Boltzmann's constant. Thus, the smaller the heat capacity, the more sensitive the response of the calorimeter and the better the energy resolution. The most relevant feature of this result is that the latter is independent of the energy deposition. The heat capacity itself is the product of the detector volume (V) and the specific heat (*c*<sub>p</sub>). Optimization of LTD response can be achieved by using small detector volumes and materials with low specific heat. Noise contributions from additional sources will increase the variance and are generally parameterized as a multiplicative factor ($\xi \gtrsim 1$) to the variance expression above.

Similarly, the power *P* from incident particles or radiation can be measured through a temperature rise given by $\Delta T = P/G$, where *G* is the thermal conductance to a weakly linked bath held at constant temperature. Power fluctuations are limited by *G* and have a spectral density of $S_P = N E P^2 = 4 k_B T^2 G$, where *N E P* is the noise equivalent power, defined as the power in a 1 Hz bandwidth that gives a response signal with an equal amplitude to the noise. Hence lower conductance yields better sensitivities. To minimize thermal conductance in precise power measurements, weak thermal links can be realized by using thin membranes or by decoupling the electron and phonon systems. However, a compromise must be made. While lower *G* yields better noise metrics, conversely, larger *G* is needed to dissipate all incident power (which can be large in the case of CMB detectors) or to have a
faster detector response (the characteristic response time being $\tau = C/G$).

LTDs that measure power are sometimes referred to as bolometers in literature, as opposed to calorimeters that measure energy, generating some confusion. In principle, there is no clear distinction between a calorimeter and a bolometer. The operation mode is generally determined by the ratio of the characteristic time constant and the average time between the arrival of incident particles or quanta [211]. Yet another convention is to refer to non-equilibrium LTDs as those detectors that measure incident energy or power by counting excitations that have energy $\gg k_B T$. In such detectors, energy resolution is determined by the statistical fluctuations of the energy partition, similar to conventional ionization detectors but with a much lower average excitation energy and hence a larger number of excitation quanta.

<table><caption>**Table 36.6:** Low temperature dependence on temperature (T) for specific heat, based on different material classes. In the table below $\Theta_D$ is the Debye temperature and $T_C$ is the transition temperature of the superconductor.</caption><thead><tr><th>Heat Capacity</th><th>Material</th></tr></thead><tbody><tr><td>α (T/Θ<sub>D</sub>)<sup>3</sup></td><td>Dielectric and diamagnetic</td></tr><tr><td>α T</td><td>Conductor</td></tr><tr><td>α exp(-2T<sub>C</sub>/T)</td><td>Superconductor</td></tr><tr><td>α (μ<sub>B</sub>B/k<sub>B</sub>T)<sup>2</sup> sech<sup>2</sup>(μ<sub>B</sub>B/k<sub>B</sub>T)</td><td>Paramagnet<br>(in magnetic field <b>B</b>)</td></tr></tbody></table>

A variety of possible detector materials and sensor technologies makes LTDs very versatile and highly customizable. Dielectric, superconducting and paramagnetic materials are often used owing to the fact that at very low temperatures, the specific heat decreases strongly as a function of $T$ (see table 36.6). Superconductors offer additional advantages: the abrupt change in resistance when a material transitions from its normal to superconducting state enables highly sensitive measures of temperature changes. Additionally, the existence of a small (less than a meV) but distinct energy gap that is required to break a Cooper pair, provides a means to measure energy deposits by counting the resulting quasiparticles (QP). QP relaxation processes are typically faster than thermal processes making these detectors suitable for high-rate photo-counting. In summary, both the sensitivity and energy resolution of an LTD benefit greatly from low temperature operation.

### 36.5.2 Detector Types

A generalized LTD calorimeter consists of an absorber in thermal contact with a phonon or quasiparticle sensor, and a thermal link to a heat bath at a constant temperature (see figure 36.10). The absorber provides the mass necessary for the interaction of the particle and a fast and complete thermalization of the deposited energy. The sensor accomplishes the task of translating the particle interaction into measurable parameters. It is generally sensitive to equilibrium phonons (e.g. thermistors and MMCs) and thus provides a precise measurement of the temperature. However, non-equilibrium (e.g. STJ's) and mixed (e.g. TES) phonon sensors have been devised and implemented in many applications as well. The goal of the thermal link is to cool the absorber down to its equilibrium temperature after the absorption of a particle. In monolithic detectors the thermometer and absorber are identical, while in composite detectors the thermometer is attached to a separate absorber. This basic design applies to single-event particle detection as well as for continuous radiation measurement devices. In the case of the latter, a suitable absorber whose mass is irrelevant, e.g. an antenna at the end of a waveguide, collects the incident power and dissipates it onto a resistive (e.g. Au) film, which is put in contact with a sensor capable of detecting tiny temperature changes (e.g. semiconduc-

tor thermistors, transition-edge sensors, and kinetic inductance detectors, to name a few).

Superconducting Tunnel Junctions (STJs) and Kinetic Inductance Detectors (KIDs) are examples of non-equilibrium detectors. STJs exploit Josephson tunnelling of particles and QPs between two superconductors. The superconductors act as radiation absorbers, and are separated by a thin insulating layer. When such a junction is DC biased at a voltage just below the gap voltage, the excess quasiparticles generated by the incoming radiation are detected as a tunneling-current proportional to the incoming energy. Statistical fluctuations in the tunnelling process limit the energy resolution which is given by:

$$ \sigma_E = \sqrt{\varepsilon(F + G)E_0}, \qquad (36.5) $$

where $\varepsilon \sim \Delta$, the band-gap, while $F \sim 0.2$ and $G > 1$ are the Fano factor and tunnelling fluctuation respectively. STJs have been proven to be excellent single photon and UV-VIS spectroscopic detectors with near theoretical energy resolutions, high detection efficiencies and excellent time resolution. In astrophysics they are used as mixers to detect radiation in the 100 GHz to 1 THz range by exploiting the non-linear behaviour of their current versus voltage characteristic curve. STJs share similar design elements to charge qubits, which are being used for the development of quantum computers. Such qubits have also recently been used in dark matter searches as single photon detectors to evade the standard quantum limit in measurement noise [212]. Despite their extremely good energy resolutions, STJs cannot be scaled-up to produce sensors with large observing volumes due to readout complexity and the difficulty in uniformly suppressing the superconducting Josephson current, which is superimposed on the QP current.

KIDs exploit the variation of the kinetic energy $T$ stored in a superconductor by Cooper pairs whose inertia acts as an effective inductance, given by:

$$ T = \frac{1}{2}nm^*v^2 = \frac{1}{2}LI^2 \qquad (36.6) $$

where $n$ is the number density of Cooper pairs, $m^* = 2m_e$ is the Cooper pair mass and $I = 2nev$ is the Cooper pair current. $L = m_e/2ne$ is defined as Kinetic Inductance and is inversely proportional to the number of Cooper pairs [213]. When a KID is placed in series with a superconducting capacitor, the resonance frequency of the circuit will be temporarily shifted by incident radiation, which converts Cooper pairs to QPs, thus changing the effective inductance. The presence and amount of radiation is observed as a change in amplitude or phase of a tuned sinusoidal signal that is sent through the circuit. In practice the change in $L$ is small, and very high $Q$ microwave resonance circuits are needed to sense this variation (hence the name MKIDs, for Microwave-KIDs). Furthermore, only areas of the film where large currents are flowing will be sensitive to pair breaking, thus making the response of a distributed KID position dependent. To overcome this issue, QP trapping (by coupling two superconductors with different band-gaps) is used for absorbing optical photons and X-rays. To detect lower frequencies (e.g. in the 100-1000 GHz range for CMB) a lumped element resonator (LEKID), with little current variation across the device, is used. The device itself, based on a series LC circuit inductively coupled to a microstrip feed line, can act as the absorber as well as the sensing element in a detector system. Macroscopic devices (few mm$^2$) can be fabricated by shaping the inductor in the form of a meander coupled to an inter-digited capacitor [214]. The theoretical noise limit of these devices is governed by generation-recombination noise and takes the form:

$$ NEP_{QP} = 2\Delta\sqrt{\frac{n_{QP}}{\tau_{QP}}}, \qquad (36.7) $$

where $n_{QP}$ and $\tau_{QP}$ are the QP number and lifetime respectively. KIDs are easy to fabricate, very sensitive, broad band and easily multiplexable: they can be coupled with a single microstrip that simultaneously reads 1000s of detectors resonating at different frequencies. They provide therefore a promising solution
<figure><img src="image_250.png" /><figcaption>**Figure 36.10:** A generalized LTD consists of an absorber, a sensor and a thermal link to a stable-temperature bath. Biasing schemes and readout is described in detail in the text for individual sensor types.</figcaption></figure>

for deploying large arrays of detectors with applications to high-energy physics, astronomy or CMB measurements, although there are still some challenges, especially at frequencies below 100 GHz, related to their worse noise performance when compared to other LTDS, and to the choice of materials with a sufficiently small energy-gap.

Semiconductor thermistors are resistive elements characterised by a strong dependence of the resistance on the temperature. Usually, they consist of small crystals of germanium or silicon with a dopant concentration slightly below the metal-to-insulator transition. However, they can also be realized in the form of amorphous films such as NbSi. At low temperatures, their resistivity ($ρ$) is governed by variable range hopping (VRH) conduction and is described by the expression $ρ(T) = ρ_0 \exp((T/T_0)^γ)$, where $T_0$ and $ρ_0$ are parameters controlled by the doping level, while $γ$ depends on the compensation level K (ratio of acceptor to donor concentrations). For low values of K, $γ$ is well approximated by $1/4$ while it converges to $1/2$ as K increases.

Semiconductor thermistors are high impedance devices (1–100 MΩ) whose performance is usually parameterized in terms of the logarithmic sensitivity $α = d \log R/d \log T$, typically in the range of 1–10. Silicon thermistors are fabricated using a multiple ion implantation process in high purity silicon wafers to produce a thin and uniformly doped box-like volume. The best germanium thermistors are fabricated starting from bulk, high-purity germanium crystals doped by means of neutron irradiation in the core of a nuclear reactor, referred to as nuclear transmutation doping (NTD). Individual sensors are then produced by dicing the irradiated samples and finishing them by hand. The great advantage of NTDs is the highly uniform doping level over large volumes which results in a better signal to noise ratio with respect to other doping techniques. The doping level depends on the isotopic composition of the starting material and the irradiation time.

The weak coupling to the heat sink can be provided by the electrical leads used for the read-out. However, nowadays microelectronic planar technologies and silicon micromachining are

more commonly preferred, and sensors are suspended on thin silicon nitride membranes or thin silicon beams. Thermistors are read-out in an approximately constant current biasing configuration obtained by inserting large load resistors in the bias circuit, which allows for direct conversion of the thermal signal ($ΔT$) into a voltage signal ($ΔV$).

Semiconductor thermistors are very practical to use with some drawbacks. One of these is related to their high impedance which requires a JFET front-end placed as close as possible to the device in order to minimize the signal integration on parasitic electrical capacitances. This can represent a technical challenge, because JFETs must be maintained at significantly higher temperatures ($\gtrsim$100 K). Furthermore, deviations from the exponential behaviour of the conductivity have been observed at low temperatures. They are usually described in terms of a finite thermal coupling between electrons and phonons which results in an intrinsic limit to the signal rise times, which is of the order of hundreds of milliseconds at temperatures below 100 mK. Nevertheless, semiconductor thermistors are an established and robust technology, and arrays of detectors based on these devices have been widely used for neutrinoless double beta decay searches, neutrino mass measurements and X-ray spectroscopy. Energy resolutions lower than 5 eV have been achieved with Sn or HgTe absorbers.

Superconducting Transition Edge Sensors (TESs) exploit the sharp transition between superconducting and normal conducting phases, yielding a high sensitivity to temperature variations. Temperature perturbations, and hence resistance changes, are sensed as modulations in the current through the TES. TESs are operated in a constant voltage biasing configuration where Joule heating, arising from the current flowing in the TES, decreases with a rise in resistance, which then brings the TES back to its nominal operating temperature. This electrothermal feedback (ETF) is achieved by providing a TES with a voltage bias whose power, $P_J = V_{bias}^2/R(T)$, heats the TES to its nominal operation point, the superconducting transition temperature. Operation in ETF mode improves linearity, speeds up response (to
faster than $\tau = C/G$), and in some cases it provides tolerance for $T_C$ (critical temperature) variation between multiple TESs in a large array. The low impedance in this configuration makes them well-suited for readout by SQUID (Superconducting Quantum Interference Device) based amplifiers. Logarithmic sensitivities $\alpha = d \log R/d \log T$ of the order of several hundreds can be achieved. By using different superconductors, or superconductor-metal pairs patterned in suitable shapes, a wide range of resistances, transition temperatures and time constants are obtainable to meet the requirements of the desired application [215].

Nano-TESs are fabricated by lithographic techniques in the form of long (few $\mu$m) and narrow (nm) wires that exhibit extremely small NEPs due to their reduced C and G, enabling single-photon sensing. Superconducting Nanowire Single-Photon Detectors (SNSPDs) are similarly patterned superconductors or superconducting bilayers maintained at a temperature well below their $T_C$. When a DC current just below the critical current is driven through the nanowire, the absorption of a single photon causes the formation of a hot spot that drives the superconductor to a normal conducting state, resulting in a very fast (tens of picoseconds) current pulse through a shunt resistor. For this reason, nano-TESs and SNSPDs are used as single photon detectors for light dark matter and axion searches in applications where large detecting mass is not critical [216].

Magnetic Metallic Calorimeters (MMC) exploit paramagnetic sensors exposed to a weak magnetic field with a weak thermal link to a heat bath. A temperature rise causes a change in the sensor magnetization, which is sensed by a SQUID magnetometer. A common material is an Au:Er mixture, with the addition of a few hundred ppm of enriched $^{166}$Er, which is needed to reduce the unwanted contribution of nuclear magnetic moments of other Er isotopes. The read-out is non-dissipative and avoids the noise sources common to the dissipative devices. The use of a metallic host ensures relatively fast time response, since the typical spin-electron relaxation times are of the order of 0.1 microseconds at ~50 mK [217]. For an optimized MMC, the energy resolution is given by $\Delta_E = \sqrt{2k_B T^2 C (\tau_0/\tau_1)^{1/4}}$, where $\tau_0$ (order of micro second) and $\tau_1$ (order of milli second) denote the signal rising and decay times respectively [207]. In order to obtain a fast and efficient energy thermalization, MMC are typically fabricated from gold. The intrinsically large heat capacity of the paramagnet does not spoil the temperature sensitivity and allows the use of relatively large gold absorbers without degrading the device performance. Furthermore, thermal isolation from the heat sink is not generally an issue. Owing to the simple concept of these devices, MMC can be precisely customized and fabricated by employing standard microtechnology. Planar MMC arrays characterized by an excellent energy resolution, large dynamic range and good linearity have been successfully used for the detection of soft X-rays.

Performance and technological constraints limit the maximum size of LTEDs. To improve overall experimental sensitivities, a large number of sensors must be deployed, typically at temperatures of a few tens of mK, where cooling power is limited to a few $\mu$W. To reduce the readout complexity and the heat load at the colder stages, multiplexing (MUX) techniques are often employed. Multiplexing consists of reading multiple detectors out through a limited number of lines that traverse room temperature to cryogenic temperatures [218]. In frequency-domain multiplexing (FDM), a tuned superconducting LC circuit is placed in series with each sensor, and a frequency comb of AC biases (usually in the MHz range) is sent to a group of sensors in parallel. A synchronous demodulation of the amplified current signal allows the recovery of the resistance variation of each detector. Microwave-multiplexing ($\mu$MUX) represents a variation of this concept, based on the usage of rf-SQUIDs, where the frequency comb is in the GHz range. Alternatively, the signal from a single detector can be recovered by readout of one detector at a time (time-domain multiplexing, TDM). KIDs have been gaining popularity owing to the fact that they naturally form resonant circuits, hence multiplexing in the frequency domain is readily achieved by adjusting their capacitance.

### 36.5.3 Experimental Applications

LTDs are sensitive over a wide range of energy, from centimetre wavelength (~ meV) through the visible spectrum (~ eV) up to the X-ray domain (~ keV) and beyond. Several broad categories of LTD applications towards measurements of fundamental physics are described in more detail in the text below and summarized in tables 36.7 and 36.8.

Bolometric detectors are favored as microwave detectors owing to their nearly constant response over frequency, playing an important role in far-infrared astronomy and in the survey of the cosmic background radiation. The high-frequency instrument of the Planck satellite (HFI) used spiderweb bolometers read by NTD-Ge thermistors, but current experiments use mainly TESs or, more recently, KIDs. Depending on the objective of the experiment, antenna coupling or absorber coupling is used. In the former case, the bolometer detects one polarization and one (or a few) modes of the radiation, while absorber-coupled bolometers do not distinguish between polarizations. In order to avoid the absorption or emission from Earth's atmosphere, many (CMB) instruments are operated by observatories located at high altitude, dry places (such as the Atacama desert or Antarctica), balloon-borne platforms, or from space. In Table 36.7, we list a subset of the ongoing or planned CMB experiments (see Section 29 of this Review for the details on present challenges). In the Atacama desert in Chile, CLASS is taking data, POLARBEAR is being upgraded to Simons Array and ACTPol is being upgraded to AdvancedACT-Pol, the next big step being the deployment of the Simons Observatory. At the South Pole, SPTPol has been upgraded to SPT-3G, while BICEP3 and BICEP array will constitute the South Pole Observatory. The most powerful upgrade in terms of both size and sensitivity will be CMB-S4, a consortium of telescopes both at the Pole and in Chile. In the Canary islands, QUIJOTE and GroundBIRD are operating and LSPE/STRIP is in preparation. QUBIC has recently started operations in Argentina and AliCPT is in preparation in Tibet. Regarding balloon projects, SPIDER and EBEX were already launched while LSPE/SWIPE and PIPER will be in the near future. Finally from space, after the success of Planck, LiteBIRD has been selected by the Japan Aerospace Exploration Agency (JAXA) as the next strategic large mission to be launched in the 2020s.

The incoming radiation couples directly to the antenna probes (as in BICEP/Keck) or through micro-machined horn waveguides (AdvancedACT-Pol, CLASS) or lenslets (Simons Array, SPT-3G), depending on the frequency range. All of these experiments have focal planes with hundreds to hundreds of thousands of sensors. To optimize focal plane occupancy, multi-mode or multi-chroic, dual polarization sensitive detectors are used. In the former case, the sensitivity is enhanced by collecting power from a larger number of modes at the expense of angular resolution. In the latter, one single mode of the radiation is focused on a broad band antenna, and on-chip polarization separation and band-pass filters split the signal in different frequency bands directing the power to different absorbers and sensors.

Experimental design is driven by a trade-off between the sensitivity and the complexity of the production processes and readout. On the one front, single-sensor NEP at the level of $10^{-21}$ W/√Hz has been achieved in laboratories and research centers. Meanwhile, efforts are in place for the industrialization of the fabrication processes, which is essential for scaling up production for the large number of detectors needed for future experiments.

Massive cryogenic calorimeters have been proposed since the 1980's as particle detectors for the search of rare processes (e.g. dark matter, neutrinoless double beta decay) [219]. Almost simultaneously, the use of arrays of small mass calorimeters was suggested for X-ray astrophysics [220] and precision measurements of the neutrino mass [221, 222]. Although essential to understanding the nature of neutrinos, neutrinoless double beta decay (NDBD) has eluded discovery (or definitive exclusion) for over 50 years. Calorimeter techniques provide the best sensitivities to NDBD. However, before the advent of low temperature calorimeters (LTC), only a few isotopes ($^{48}$Ca, $^{136}$Xe and $^{76}$Ge) could be utilized for NDBD studies with the calorimetric approach. This limitation was removed by the advancement of LTC's, and in par-
<table><caption>**Table 36.7:** Some selected experiments using LTDs to measure the CMB. These experiments constrain the physics of inflation and the absolute mass, hierarchy, and number of neutrino species. The experiment location determines the part of the sky that is observed. The size of the aperture determines the angular resolution. The table also indicates the type of sensor used, the number of sensors, the frequency range, and the number of frequency bands. Data for planned upgrades or future experiments are provided in parentheses.</caption><thead><tr><th>Sub-K CMB<br>Experiment</th><th>Location</th><th>Aperture</th><th>Sensor<br>type</th><th># Sensors<br>(planned)</th><th>Frequency<br>(planned)</th><th>Bands<br>(planned)</th></tr></thead><tbody><tr><td colspan="7"><strong>Ground-based</strong></td></tr><tr><td>Atacama Cosmology<br>Telescope (2007–)</td><td>Chile</td><td>6 m</td><td>TES</td><td>5,614</td><td>30–230 GHz</td><td>5</td></tr><tr><td>BICEP/Keck (2006–)</td><td>South Pole</td><td>26/68 cm</td><td>TES</td><td>2,500</td><td>95–270 GHz</td><td>6</td></tr><tr><td>CLASS (2015–)</td><td>Chile</td><td>60 cm</td><td>TES</td><td>3,488</td><td>40–220 GHz</td><td>4</td></tr><tr><td>GroundBIRD<br>(2021–)</td><td>Canary<br>Island</td><td>30 cm</td><td>MKID</td><td>322</td><td>145–220 GHz</td><td>2</td></tr><tr><td>POLARBEAR /<br>Simons Array (2012–)</td><td>Chile</td><td>3.5 m</td><td>TES</td><td>1,274<br>(22,764)</td><td>150 GHz<br>(90–280 GHz)</td><td>1<br>(4)</td></tr><tr><td>South Pole<br>Telescope (2007–)</td><td>South<br>Pole</td><td>10 m</td><td>TES</td><td>16,260</td><td>90–220 GHz</td><td>3</td></tr><tr><td>Simons Observatory<br>(2022–)</td><td>Chile</td><td>6 m/0.5 m</td><td>TES</td><td>(60,000)</td><td>(27–280 GHz)</td><td>(6)</td></tr><tr><td>CMB-S4<br>(2024–)</td><td>Chile +<br>South Pole</td><td>21<br>telescopes</td><td>TES</td><td>(500,000)</td><td>(20–280 GHz)</td><td>(11)</td></tr><tr><td colspan="7"><strong>Balloon</strong></td></tr><tr><td>EBEX (2013–)</td><td>McMurdo</td><td>1.5 m</td><td>TES</td><td>~1,000</td><td>150–410 GHz</td><td>3</td></tr><tr><td>PIPER (2016–)</td><td>New Mexico</td><td>2 m</td><td>TES</td><td>5,120</td><td>200–600 GHz</td><td>4</td></tr><tr><td>SPIDER (2014–)</td><td>McMurdo</td><td>30 cm</td><td>TES</td><td>1,959</td><td>90–280 GHz</td><td>3</td></tr><tr><td>LSPE (2022–)</td><td>Longyearbyen</td><td>60 cm</td><td>TES</td><td>(326)</td><td>(140–270 GHz)</td><td>(3)</td></tr><tr><td colspan="7"><strong>Satellite</strong></td></tr><tr><td>Planck HFI<br>(2003-2013)</td><td>L2</td><td>1.5 m</td><td>NTD</td><td>52</td><td>100-857 GHz</td><td>9</td></tr><tr><td>LiteBIRD (2028–)</td><td>L2</td><td>20–40 cm</td><td>TES</td><td>(4,508)</td><td>(34–448 GHz)</td><td>(15)</td></tr></tbody></table>

ticular by CUORE, which takes advantage of the naturally high abundance of $^{130}$Te in TeO$_2$ crystals. Additionally, the operation of CUORE at LNGS [223] has demonstrated that the technical challenges of operating ton-sized LTD detectors in a deep, underground location are surmountable. Currently, the most promising future approach is based on the hybrid approach of scintillating LTCs, which unfortunately cannot be used for $^{130}$Te. Now, new projects are being proposed based on different scintillating compounds. In particular $^{100}$Mo is the choice of CUPID [224] (NTD thermistors glued to Li$_2$$^{100}$MoO$_4$ crystals), which will use the same infrastructure of CUORE and follows from the successful operation of several demonstrators (CUPID-0 [225] and CUPID-Mo [226]), and AMORE (MMC sensors on Ca$^{100}$MoO$_4$ or Li$_2$$^{100}$MoO$_4$ crystals) [227]. With an energy resolution comparable to germanium diodes and a mass of the order of a ton, these experiments aim to probe the inverted hierarchy of neutrino masses. The slow response of these detectors is still a dominant limitation because pile-up may prove to be a serious background. Extremely pure materials, careful assembly procedures, and deep underground laboratories are therefore necessary.

In the 1980's, the calorimetric technique was recognized as a feasible approach to make a direct measurement of the neutrino mass from the end-point of a beta spectrum. Thus, LTCs were proposed as a possible alternative to the standard spectrometric measurements [228]. Calorimetric measurements offer a number of advantages: i) a weak dependence on the final excited states, ii) no source effects (e.g. self-absorption), and iii) lack of backscattering from the detector. Therefore LTCs provide a faithful reconstruction of the beta spectral shape over a broad energy range below the end-point. However, the difficulty in resolving a small fraction of the spectrum near the end-point is a serious limitation that strongly constrains the source strength and the statistics that need to be accumulated. Such an inconvenience can be mitigated by selecting beta emitters with a small Q value, owing to the fact that the fraction of counts in an interval, $\delta$ close to Q, scales as $(\delta/Q)^3$. However, this is generally at the cost of choosing decays with more complex nuclear transitions. In addition, LTCs may be affected by specific systematics (e.g. solid state effects). Ultimately it is recognized that spectrometers and

calorimeters have complicated but different systematic effects. It is therefore critical to develop complementary experiments exploiting both techniques.

LTCs were initially proposed as perfect calorimeters to measure the energy spectrum of a low Q beta emitter embedded in an absorber. However, the requirements of excellent energy resolution and a low rate (to avoid pileup) requires a very large number, $O(10^4 - 10^6)$, of small mass devices (micro-calorimeters). Early experiments used $^{187}$Re, which is a long-lived beta emitter that is naturally abundant in rhenium samples and is characterised by a very low Q value (2.4709 keV [229]). A large number of $^{187}$Re based experiments have been developed over the years (MANU [230], MIBETA [231], MARE [232]). Nowadays a different approach is preferred and is based on the measurement of the atomic radiation following electron capture, typically in $^{163}$Ho which is also characterized by a very low Q (2.837 keV [233]). Different experiments have been proposed to face the challenge: ECHo in Germany [234] (using MMC sensors), HOLMES in Italy [235] and NUMECS [236] in the US (using TESs). The very large number of microcalorimeters needed to obtain sensitivities comparable to spectrometric measurements is a serious challenge, both for the readout and the thermal heat load. An alternative readout based on the use of KIDs, for their multiplexing capability, has been proposed and is presently under development.

Traditional searches for WIMP-like dark matter aim to measure the scatter of a massive dark matter particle off of a target nucleus. Similar to detectors employed for neutrinoless double beta decay, these searches benefit from large-mass absorbers for the target because the dark matter interaction rate scales directly with the number of nuclei in the target and hence its mass. Among the most successful experiments to date, are those that combine the detection of phonons with another channel such as ionization energy (EDELWEISS and SuperCDMS) or scintillation light (CRESSST). This simultaneous, dual measurement takes advantage of the fact that the energy deposited in the absorber is partitioned into these channels differently depending on whether the initial particle interaction produces electron or nuclear recoils (or both). This particle identification allows for the rejection of background from natural sources of radiation, which most commonly