Reveal the Mantle and 40 K Components of Geoneutrinos with Liquid Scintillator Cherenkov Neutrino Detectors

In this article we present an idea of using liquid scintillator Cherenkov neutrino detectors to detect the mantle and 40K components of geoneutrinos. Liquid scintillator Cherenkov detectors feature both energy and direction measurement for charge particles. Geoneutrinos can be detected with the elastic scattering process of neutrino and electron. With the directionality, the dominant intrinsic background originated from solar neutrinos in common liquid scintillator detectors can be suppressed. The mantle geoneutrinos can be distinguished because they come mainly underneath. The 40K geoneutrinos can also be identified, if the detection threshold for direction measurement can be lower than, for example, 0.8 MeV. According to our calculation, a moderate, kilo-ton scale, detector can observe tens of candidates, and is a practical start for an experiment.


Introduction
The knowledge of geoneutrinos is crucial to understand our planet of Earth. Geoneutrinos have two components, crust and mantle, according to the generation region. The mantle component is a key to understand the power drives plate tectonics and mantle convection [1,2]. Its result is not very precise and relies heavily on the estimation of the crust neutrinos given by geology surveys. Geoneutrinos mainly come from three heat generation isotopes, 40 K, 232 Th and 238 U. 40 K is volatile and depleted in the Earth. A measurement of 40 K neutrinos will shed light on mantle composition, structure and thermal evolution [3]. However 40 K geoneutrinos have not been discovered.
The KamLAND [4] and Borexino [5] experiments have made the pioneer discovery on geoneutrinos. The detection is made by finding inverse-beta-decay (IBD) signals in liquid scintillator detectors. An IBD signal consists of a prompt positron signal and a delayed neutron capture signal, and the delay-coincidence presents a clear signature and the cross-section is high. The reaction energy threshold is 1.8 MeV, so only 232 Th and 238 U geoneutrino signals are accessible. The final state electron and neutron carry little information of the initial neutrino direction [6]. No result is reported through * Corresponding author: wangzhe-hep@mail.tsinghua.edu.cn neutrino-electron scattering process, because the intrinsic background, solar neutrino background, is 100-1000 times higher then geoneutrinos signals depending on energy.

Reveal the Mantle and 40 K Components with Liquid Scintillator Cherenkov Neutrino Detector
We propose to detect geoneutrinos with neutrinoelectron elastic scattering in a liquid scintillator Cherenkov detector. The technique can reveal the mantle and 40 K geoneutrinos by suppressing solar neutrino background with direction information. The concept is explained below.
A liquid scintillator Cherenkov neutrino detector can separate Cherenkov and scintillation lights. Cherenkov light can be used for direction reconstruction and scintillation light for energy reconstruction. The combination of them offer some capability for particle identification.
A liquid scintillator Cherenkov neutrino detector can be realized by two schemes, and both of which have some progress in experimental study. The first approach is to use a high light yield and fast liquid scintillator and fast photon sensors. The liquid scintillator emits about 10,000 scintillation photons per MeV, and has a emission time constant of a few nano seconds. The precision of the photon sensors is several pico seconds. The recent experimental development can be seen in references [7][8][9]. The second approach is to use a slow liquid scintillator and photomultiplier tubes (PMT). PMTs usually have a precision of about 2 nano seconds for timing, and the emission time constant of scintillation light in the slow liquid scintillator is much larger, for example, 10 nano seconds. Effort on this direction are reported in references [10,11].
The neutrino-electron scatter process has no theoretical threshold and a strong correlation between the initial neutrino direction and the scattered electron can be employed after a requirement on the kinetic energy of the recoiled electron is added. When the kinetic energy of the scattered electron is above the Cherenkov threshold, 0.178 MeV assuming the refractive index of the liquid is 1.49 [12], the most serious background, solar neutrino background, can be fully suppressed by the directionality.
We simulated a terrestrial detector located on the equator of the Earth to examine the detected neutrinos. The detector rotates along with the Earth. We define a solar z-axis, z , from the Sun to the detector, and an Earth z-axis, z ⊕ , from the Earth center to the detector (see figure 1 for the detail), and, correspondingly, define the angle between the scattered electron and z as θ and the angle with z ⊕ as θ ⊕ . Geoneutrinos and solar neutrinos are generated and the kinetic energy of scattered electrons is also recorded. Other backgrounds like radioactive background inside of the detector and external gammas are discussed later.
After requiring the electron kinetic energy to be greater than 0.8 MeV, solar neutrinos and geoneutrinos group in different clusters in the parameter space of cos θ and cos θ ⊕ as shown in figure 2. A course direction reconstruction, for example, positive or negative ⊕ θ cos  Figure 2: cos θ and cos θ ⊕ for solar, crust and mantle neutrinos. cos θ , is needed to distinguish solar background. The choice of 0.8 MeV is explained next. Figure. 3 shows the projection to cos θ ⊕ of crust neutrinos and mantle neutrinos of the events in figure. 2 after further requiring cos θ < 0.7. Their distributions are determined by the shell structure of the crust and mantle. The angle between geoneutrino direction and z ⊕ is in the range of [0 • , 90 • ], because of scattering, cos θ ⊕ is in the range of [-0.5, 1]. Mantle neutrinos and some of crust neutrinos come underneath the detector, and the directions overlap. With a fit of the cos θ ⊕ spectrum, the crust and mantle components can be estimated.
The kinetic energy of scattered electrons is shown in figure 4 with only the cut of cos θ < 0.7. The 40 K component has a much higher flux below 0.8 MeV and its also has a distinguishable structure caused by the 40 K decay beta-spectrum. They can be recognised since they all well above the Cherenkov threshold of electron.
We measured the signal statistics with a 2,000 tons liquid scintillator Cherenkov detector and 1,500 days data-taking, which is a moderate detector and a reasonable running time. The kinetic energy of electron sig-  nals are required to be higher than 0.8 MeV. The solar angle θ criterion is set to less than either 0 or 0.5. Table 1 summarizes the results. Tens of candidates are available and a 2,000 ton detector is a practical start. The neutrino-electron scattering and IBD processes may also offer a different way to study the neutrino oscillation in the Earth.

Simulation Scheme
We simulated a liquid scintillator Cherenkov detector with 30,000 tons target material [10] and 15,000 days for a better statistics to understand the features. The neutrino detector is placed on the equator. It rotates along the Earth with a period of 24 hours. The rotation axis tilt is ignored. The Sun is treated as a point source. The geoneutrinos come from the 3-dimension spherical shell structure of the crust and mantle, and a random sampling of the initial vertex is done according to the neutrino luminosity at each location. The Sun generates electron-neutrinos initially, and some of them can convert to muon-or tau-neutrinos on the path. The geo-neutrinos are initially electron-antineutrinos at generation, and they have a chance to oscillate to other flavors. Neutrino-electron elastic scattering is considered in the detector. The distribution of the scatted electron is calculated as: where dN dT is the number of scattered electrons N per unit electron kinetic energy T , N e is the number of target electrons, the integral goes though all region of neutrino energy E ν , the sum goes through all neutrino flavors ν, which is ν e , ν ν(τ) ,ν e , andν ν(τ) , dσ(E ν ,T e ) dT e is the differential cross-section with neutrino energy E ν and electron kinetic energy T e , P eν is the oscillation probability, and F(E ν ) is the flux of neutrinos. The kinetic energy of scattered electrons is sampled according to equation (1) and the scattering angle of electron is explained below.

Neutrino Electron Scattering
The differential scattering cross-sections with neutrino energy E ν and electron kinetic energy T e can be written, for example in reference [13], as: (2) where m e is the electron mass. For ν e andν e , g 1 and g 2 are: where θ W is the Weinberg angle, and then for ν µ,τ , g 1 and g 2 are: The constant σ 0 is With the condition and energy and momentum conservation, the cosine of the scattering angle between initial neutrino direction and scattered electron direction can be determined with:

Solar Neutrino Simulation
We used the Standard Solar Model (SSM) for the energy sampling of solar neutrinos. Reference [14] gives the neutrino energy spectra of all solar neutrinos. We used the neutrino flux predictions on Earth with the high metallicity assumption from reference [15] as the normalization. The characteristic energies and fluxes are summarized in table 2. 232 Th and 238 U neutrino overlap with O, F, N and B neutrinos, and 40 K mainly overlaps with pep neutrinos. Solar neutrinos are generated as pure electron neutrinos. Considering the oscillation in the Sun [16,17], the survival probability of electron neutrinos, P ee , is [18,19]: where the mixing angle in matter is Here G F is the Fermi coupling constant and n e is the density of electrons in the neutrino production place of the Sun, about 6 × 10 25 /cm 3 [20], and other constants are neutrino oscillation parameters, which are set to sin 2 θ 12 =0.307, sin 2 θ 13 =0.0241, ∆m 2 12 = 7.54 × 10 −5 eV 2 . The appearance probability of ν µ and ν τ is The range of P ee is from 0.3 to 0.6, and we didn't further consider the neutrino oscillation in the Earth, because the change in probability is less than 5%.

Geo Neutrino Simulation
We used a simplified Earth model to simulate geo neutrinos, since this study is only to demonstrate the power of liquid scintillator Cherenkov detector, and we did not adopt a sophisticated model like in refrence [21]. In the simple model, the Earth has 3 layers, the core, mantle and crust. The mantle and crust layers have uniform distributions of 40 K, 232 Th and 238 U, and no radioactivity from the core.
The whole volume of the Earth is divided into many small cells, and each of which has a coordinate of r. Electron antineutrinos are sampled from each cell. The differential flux of electron antineutrinos from each cell to the surface neutrino detector at d is described as [22,23]: where X is the natural isotopic mole fraction for each isotope, λ is their decay constants, N A is the Avogadro's number, µ is the atomic mole mass, n ν is the number of neutrinos per decay, P ⊕ ee is the average survival probability, A( r) is the abundance of each isotopes in kg/kg, ρ( r) is the local density at each location, and | r − d| gives the distance from each location r to our detector d.
The outer radii of the core, mantle and crust are set to 3480, 6321 and 6371 km [24], respectively, and their their densities are set to 11.3, 5.0 and 3.0 g/cm 3 . The element K, Th and U abundance values are set to match the detailed predictions as in [22,23], and they are summarized in table 3 . The neutrino spectrum of 40 K, 232 Th and 238 U are from reference [23]. The oscillation probability varies only 2% in [0, 3.5] MeV [23], so it is treated as a constant, i.e. P ⊕ ee = 0.553. The differential flux of ν µ(τ) components is calculated in the same way as the above equation, except that the P ⊕ ee is replaced by: The values of all the rest constants were taken from reference [22]. The integrated flux of each isotopes of the simplified model are consistent with the more detailed calculation in reference [23] within 30%.

Discussions on Technique and Backgrounds
The detection requires a good direction reconstruction resolution, since it will further smear the cos θ ⊕ distribution. This is especially more important to mantle neutrino study. In this paper, we haven't try to discuss the 40 K of the mantle component. These questions will investigated next.
This measurement brings up a rather stringent requirement on other backgrounds. The cosmic-ray muon induced backgrounds are 11 C and 10 C. At a deep site, for example, Jinping [25] at 2400 m underground, they are highly suppressed. For a 2000-ton detector and 1500day data-taking, the number of backgrounds are 4,500 and 930 for 11 C and 10 C, respectively. Their amounts are close to geoneutrino signals, a more detailed study for offline analysis with muon tagging and direction information are needed. Other contained natural radioactive backgrounds are 85 Kr, 210 Bi, and 208 Tl and their rates are rather high. Extra purification procedures and experimental studies are needed. Reactor neutrinos are dangerous, but a site can be chosen far away from commercial reactors, like Jinping, and it won't cause a problem. Random coincidence of real signals and PMT dark noise and 14 C signals is another issue, which all needs further experimental study.