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Physics prospects of the Jinping neutrino experiment
View the table of contents for this issue, or go to the journal homepage for more 2017 Chinese Phys. C 41 023002
(http://iopscience.iop.org/1674-1137/41/2/023002)
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Physics prospects of the Jinping neutrino experiment
*John F. Beacom1 Shaomin Chen (¯)2;1) Jianping Cheng (§ï²)2 Sayed N. Doustimotlagh2
Yuanning Gao (pw)2 Guanghua Gong (÷1u)2 Hui Gong (û)2 Lei Guo (H[)2
Ran Han (¸,)3 Hong-Jian He (Ûùï)2 Xingtao Huang (57)4 Jianmin Li (o¬)2
Jin Li (o7)2 Mohan Li (o%º)2 Xueqian Li (oÆd)5 Wei Liao ( U)6
Guey-Lin Lin (B)7 Zuowei Liu (4)2 William McDonough8 Ondˇrej ˇSr´amek9
Jian Tang (/è)10 Linyan Wan (ö)2 Yuanqing Wang ( )11 Zhe Wang ( ))2;2)
Zongyi Wang ( nâ)11 Hanyu Wei (¢)2 Yufei Xi (S)12 Ye Xu (Mw)13
Xun-Jie Xu (NÊ#)2 Zhenwei Yang ( )2 Chunfa Yao (Su)14 Minfang Yeh15
Qian Yue (°)2 Liming Zhang (Üi²)2 Yang Zhang (Ü)2 Zhihong Zhao (ë÷)11
Yangheng Zheng (xð)16 Xiang Zhou (±)17 Xianglei Zhu (ÁX)2 Kai Zuber18 1Dept. of Physics, Dept. of Astronomy, and CCAPP, The Ohio State University, Columbus, OH 43210
2 Department of Engineering Physics, Tsinghua University, Beijing 100084 3 Science and Technology on Reliability and Environmental Engineering Laboratory,
Beijing Institute of Spacecraft Environment Engineering, Beijing 100094
4 School of Physics, Shandong University, Jinan 250100 5 School of Physics, Nankai University, Tianjin 300371
6 Institute of Modern Physics, East China University of Science and Technology, Shanghai 200237 7 Institute of Physics, National Chiao-Tung University, Hsinchu
8 University of Maryland, College Park, Maryland 20742
9Department of Geophysics, Faculty of Mathematics and Physics, Charles University in Prague, Prague 10School of Physics, Sun Yat-Sen University, Guangzhou 510275
11Department of Civil Engineering, Tsinghua University, Beijing 100084
12Institute of Hydrogeology and Environmental Geology, Chinese Academy of Geological Sciences, Shijiazhuang 050061 13Fujian University of Technology, Fujian 350118
14Department of Structural Steels, China Iron & Steel Research Institute Group 100081 15Brookhaven National Laboratory, Upton, New York 11973
16School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049 17School of Physics and Technology, Wuhan University, Wuhan 430072 18Institut f¨ur Kern- und Teilchenphysik, Technische Universit¨at Dresden, Dresden 01069
Abstract: The China Jinping Underground Laboratory (CJPL), which has the lowest cosmic-ray muon flux and the lowest reactor neutrino flux of any laboratory, is ideal to carry out low-energy neutrino experiments. With two detectors and a total fiducial mass of 2000 tons for solar neutrino physics (equivalently, 3000 tons for geo-neutrino and supernova neutrino physics), the Jinping neutrino experiment will have the potential to identify the neutrinos from the CNO fusion cycles of the Sun, to cover the transition phase for the solar neutrino oscillation from vacuum to matter mixing, and to measure the geo-neutrino flux, including the Th/U ratio. These goals can be fulfilled with mature existing techniques. Efforts on increasing the target mass with multi-modular neutrino detectors and on developing the slow liquid scintillator will increase the Jinping discovery potential in the study of solar neutrinos, geo-neutrinos, supernova neutrinos, and dark matter.
Keywords: CJPL, Jinping neutrino experiment, solar neutrino, geo-neutrino, supernova neutrino PACS: 95.85.Ry, 14.60.Pq, 26.65.+t DOI:10.1088/1674-1137/41/2/023002
Received 13 September 2016, Revised 26 October 2016
∗ Supported by the National Natural Science Foundation of China (11235006, 11475093, 11135009, 11375065, 11505301, and 11620101004), the Tsinghua University Initiative Scientific Research Program (20121088035, 20131089288, and 20151080432), the Key Laboratory of Particle & Radiation Imaging (Tsinghua University), the CAS Center for Excellence in Particle Physics (CCEPP), U.S. National Science Foundation Grant PHY-1404311 (Beacom), and U.S. Department of Energy under contract DE-AC02-98CH10886 (Yeh).
1) E-mail: [email protected] (corresponding author) 2) E-mail: [email protected] (corresponding author)
©2017 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of
In this paper, we present the physics prospects of the Jinping neutrino experiment [1]. Section 1 briefly introduces the underground laboratory. Section 2 de-scribes the detector concept. Sections 3–7 give the sensitivity studies for solar neutrinos, geo-neutrinos, supernova burst neutrinos, supernova relic neutrinos and dark matter, respectively. Section 8 gives a brief summary.
1
Experimental site
1.1 OverviewThe China Jinping Underground Laboratory (CJPL) [2] is located in Sichuan province, China, 28.2◦N,
101.7◦E and 2400 meters under Jinping mountain.
The first phase of the Jinping laboratory (CJPL-I) was constructed in the middle of the traffic tunnels at the end of 2009. Two dark matter experiments, CDEX [3] and PandaX [4] are now running at CJPL-I. The sec-ond phase of the Jinping laboratory (CJPL-II) started at the end of 2014. Four 150-m long tunnels have been constructed to provide space for more underground ex-periments [5].
We propose to build two neutrino detectors in CJPL-II, with a total fiducial target mass of 2000 tons for solar neutrino physics and, equivalently, 3000 tons for geo-neutrino and supernova geo-neutrino physics. The initial plan is to adopt the liquid-scintillator technique as the baseline design, with the capacity of extension to a slow scintillator detector.
1.2 Rock radioactivity
The radioactivity of the rock in Jinping tunnel was measured [6] and the results are shown in Table 1 to-gether with the measurements from Sudbury [7], Gran Sasso [8], and Kamioka [9] underground laboratories.
Table 1. Radioactivity contamination in Bq/kg for some underground laboratories.
site 238U 232Th 40K
Jinping 1.8±0.2 (226Ra) <0.27 <1.1
Sudbury 13.7±1.6 22.6±2.1 310±40 Gran Sasso hall A 116±12 12±0.4 307±8 Gran Sasso hall B 7.1±1.6 0.34±0.11 7±1.7 Gran Sasso hall C 11±2.3 0.37±0.13 4±1.9
Kamioka ∼12 ∼10 ∼520
1.3 Cosmic-ray muon flux
According to the in-situ measurement [10], the muon flux is as low as (2.0± 0.4) × 10−10/(cm2· s). A
com-parison with other underground labs can be seen in Fig. 1 [10, 11]. Cosmic-ray muon induced radioactive
isotopes are extremely dangerous backgrounds for low-energy neutrino experiments and are therefore expected to be significantly suppressed at Jinping.
Fig. 1. (color online) Muon flux vs reactor neutrino background flux for various underground labs in the world.
1.4 Reactor neutrino background
Jinping is also far away from all the nuclear power plants [12] in operation and under construction. A world map with all nuclear power plants and SNO, Gran Sasso, Kamioka, and Jinping laboratories is shown in Fig. 2. A reactor background flux comparison with these laborato-ries is shown in Fig. 1. The reactor electron antineutrino background at Jinping is rather low and will be explained in detail in later sections.
Fig. 2. (color online) World map with all the nu-clear power plants in operation and under con-struction. SNO, Gran Sasso, Kamioka and Jin-ping laboratory locations are also marked.
2
Detector concept
With the primary physics goals for low-energy neu-trinos, the Jinping detector design follows the struc-ture adopted by the recent underground neutrino exper-iments, and it will also consider the unique features of the low environmental backgrounds and the tunnel struc-ture.
Target mass is a key factor of the proposed neutrino experiment and a few constraints must be considered to
reach the level of target mass requirement. In addition, graded shielding is necessary to reach a radioactive clean central region.
1) The deep overburden limits both the tunnel size and shape, putting a constraint on the target vol-ume for a single detector. A thin and long detector is very poor for physics performance.
2) The attenuation length is about 20 meters for liq-uid scintillators. A detector should not have a di-mension significantly larger than this length. 3) Water shielding in the outer layer was used in
pre-vious experiments to detect cosmic-ray muons and shield the detector from neutrons and radiative gammas in the surrounding rock, steel structure, and PMTs. The minimal thickness is around 1–2 meters.
4) A central fiducial volume is necessary to reject background events in the outer layer of the tar-get region, which is usually from the gamma back-grounds on the target material vessel.
5) Cost and risk for any large amount of civil con-struction and detector concon-struction.
In this section, we give a preliminary plan for the neu-trino detectors. A preliminary study from a test-stand is also shown to demonstrate the possible separation be-tween Cherenkov and scintillation light. Considering the current level of technology and expected development, we also give some thought to the electronics used to pre-cisely read out the waveform from photomultiplier tubes (PMTs).
2.1 Experimental hall layout and neutrino de-tector
At CJPL-II, two cylindrical caverns have already been planned, each around 20 m in diameter and 24 m in height.
A conceptual design for a cylindrical neutrino detec-tor can be seen in Fig. 3. A spherical inner vessel is also an option. The central vessel is made of acrylic, and the height and diameter of the cylinder are both 14 meters. The vessel is filled with the target material, which can be either a regular liquid scintillator or a slow liquid scin-tillator. The fiducial volume is defined by a cylinder of 11.2 m diameter and 11.2 m height, and the fiducial mass is 1 kiloton assuming the target material density is 0.9 g/cm3.
The central vessel will be sealed and surrounded with pure water. Scintillation and Cherenkov light originat-ing from neutrino interactions with the target material in the central region will be collected by the PMTs.
These PMTs will be mounted on a supporting stain-less steel structure, and will be kept 2–3 m away from the central vessel to shield from gammas. The outer-most layer of the detector is a low radioactive stainless steel tank 20 m in both diameter and height, which hosts the central vessel, PMTs, supporting structure, and pure water.
Fig. 3. (color online) The conceptual design for a cylindrical neutrino detector at Jinping. Two de-tectors are needed to reach the desired mass re-quirement.
With two neutrino detectors, the total fiducial vol-ume will be about 2 kilotons for the solar neutrino stud-ies, in which the detection process is neutrino-electron scattering. For the geo-neutrino and supernova neutrino studies, the equivalent fiducial mass can be extended to 3 kiloton, because the signal is from the inverse beta de-cay process, i.e. a prompt-delayed coincidence, and has a better rejection of background.
Such a design is considered as the most economic op-tion when balancing the need of the fiducial mass and the dimensions of the CJPL-II tunnel. However, contin-uing studies incorporated with scintillator performance are ongoing to finalize the detector design.
2.2 Target material
We will use a liquid scintillator with sufficient light yield for our baseline design. We also consider using a slow liquid scintillator aiming at the separation between Cerenkov and scintillator light. Redundant measure-ments of a particle can be possible in this option. The prompt Cherenkov light can be used for the directional reconstruction of charged particles while the slow scintil-lation light can be used for the energy reconstruction of particles. Furthermore, Cherenkov light yield and scin-tillation light yield have different dependencies on parti-cle momentum and can be exploited to identify gammas, electrons, muons, and protons.
2.2.1 Liquid scintillator
The light yield of liquid scintillator can be as high as (1− 2) × 104 photons/MeV, which is sufficient for the
energy resolution required in later sections. 2.2.2 Slow liquid scintillator
Slow liquid scintillator could be water based or oil based, which is still under development. Linear alkyl benzene (LAB) is one important ingredient for the water-based liquid scintillator (WbLS) [13, 14]. With a 20 liter container in a small test-stand [15], we measured the time profile of scintillation light in the LAB and tested the waveform separation between Cherenkov and scin-tillation light. As shown in Fig. 4, a clear separation between the Cherenkov (prompt component) and scin-tillation (slow component) light can be achieved. The yield of scintillation light was estimated to be 1×103
pho-tons/MeV. More effort is needed to balance the fast and slow components with increasing light-yield.
Fig. 4. (color online) Average waveforms of the Cherenkov+scintillation (red) and scintillation-only (blue) light in LAB.
2.3 Electronics
Because of the different fine timing structures in the slow liquid scintillator detector, a dedicated electronics system is needed to record the waveform output from the PMTs. This new feature can consequently be exploited to perform particle identification between gammas, elec-trons, and protons, for instance.
Waveform sampling with 1 GHz FLASH ADC (FADC) will be applied as the baseline technology for the Jinping neutrino experiment. Multi channels with different gains will be used to cover the dynamic range from 1 photon-electron (PE) to 100 PE.
For each PMT, a separate electronics module with a High Voltage generator, a base divider, an FADC sam-pler and a processing circuit will be installed at the end of each PMT in a water tight housing. The signal from a PMT does not need to pass through any coaxial cable
which may degrade the signal quality and timing res-olution. The reliability of the circuit and the housing structure is a major design challenge.
Each PMT works in self-trigger mode: whenever a signal level goes beyond a given threshold, the sample data in a designed readout window around the over-threshold points will be stored and transferred. The win-dow size is adjustable up to a few micro-seconds. All the electronics contain synchronized time-tick counters for aligning sample fragments among PMTs.
Out of the water, the back-end electronics will pro-vide the data acquisition, clock synchronization and con-trol service. The PMT electronics and back-end elec-tronics will be connected via multi-pair twist cables which will carry the low voltage power supply, dedicated clock/time signal, upstream and downstream data links. An encoding algorithm with variable lengths will be ap-plied to the data stream to reduce the bandwidth re-quirement.
Fig. 5. (color online) An event display of a 7 MeV electron simulation in a cylindrical detector filled with LAB. Each circle indicates a PMT with at least one photo-electron (PE) detected. The red circles are for prompt Cherenkov radiation, and the blue ones are for the scintillation light, where the Cherenkov or scintillation identification is based on MC truth. The bottom-left panel is for the distribution of the number of PEs for all the PMTs, and the bottom-right panel is for the time distribution. A Cherenkov ring is visible in this plot.
2.4 Simulation studies
Preliminary simulation studies have been started to optimize the detector design to take the advantage of the Jinping laboratory environment and achieve the
physics goals. The following work was done with the Geant4 [16, 17] simulation package together with the cus-tomized geometry, light emission model, PMT response, etc. Figure 5 shows an event display for a 7 MeV elec-tron, which can be produced via the neutrino-electron scattering in LAB according to our measurement. For demonstration purposes, we use different colors for the Cherenkov and Scintillation light.
3
Solar neutrinos
3.1 IntroductionParticles from sources at cosmic distances are of great interest. Neutrinos, as a stellar probe, have extremely low interaction cross sections. Unlike gammas, optical photons and protons, neutrinos can easily reach our de-tectors without being interrupted by matter on their paths. The original status, i.e. energy and direction, can therefore be maximally maintained, except that the neutrino flavors will oscillate among the three families of neutrinos, and consequently information about the ini-tial interactions of neutrino productions can be probed. The attributes of neutrinos make them powerful probes of the deep interiors of sources like the Sun, providing ways to test models of solar evolution along with neu-trino oscillation.
3.1.1 Solar models
Solar models, neutrino theories, and solar neutrino experiments have developed rapidly over the past half a century. This remarkable history has been docu-mented in Refs. [18–21] and references therein. Nowa-days the Sun is described by the Standard Solar Model (SSM) [22, 23], which relies on about 20 parameters.
• The first group of parameters are the current solar age, luminosity, mass, and radius.
• The primordial abundances of key elements, He, C, N, O, Ne, Mg, Si, S, Ar, and Fe.
• The cross-sections of nuclear reactions, includ-ing p(p, e+ν
e)d, d(p, γ)3He, 3He(3He, 2p)4He, 3He(4He, γ)7Be,3He(p, e+ν
e)4He,7Be(e−, νe)7Li,
p(e−p, ν
e)d,7Be(p, γ)8B,14N(p, γ)15O.
The evolution starts with a cluster of homogeneous gas of H, He, C, N, etc. Nuclear fusion reactions burn H, He to heavier elements and emits gammas, electrons, positrons, etc. The Sun fuels itself by both the pp and CNO fusion processes, in which the pp-cycle con-tributes 99% of the total for energy production. The whole processes are constrained by the boundary condi-tions of the current solar status. The transport of energy in the central region is primarily through the inverse bremsstrahlung process of photons, and the calculated
radiative opacity depends upon the chemical composi-tion and the modeling of complex atomic processes. In the outer region, the energy is brought to the surface by convective motion. The interior of the Sun is assumed to be spherical symmetric and to be at the balance of gravity, radiation, and particle pressure.
The present composition of the solar surface is pre-sumed to reflect the initial abundances of all of the el-ements that are as heavy as carbon [24]. These metal elements are assumed to be chemically homogeneous throughout the Sun, except for a minor correction due to diffusion. Suggestions have been made to argue the assumption of composition. CNO neutrino measure-ment could be a direct test of the solar-core metallicity [25, 26].
The nuclear reaction cross-sections are from theoreti-cal theoreti-calculations and/or terrestrial measurements [27, 28]. For example, the cross-section for the initial p(p, e+ν
e)d
process is too low to be measured in a laboratory, and has to be calculated with nuclear physics theory. The
3He(4He, γ)7Be cross-section is measured in the
labo-ratory, and the result must be extrapolated to the so-lar Gamow peak with correct theoretical consideration. More experimental efforts on this regard can be found in LUNA [29], JUNA [30], and [31] etc.
Electron neutrinos can oscillate to muon and tau neu-trinos in the three-flavor framework in vacuum or low electron-density material [32, 33]. However, this quan-tum ability of neutrinos is changed in the high electron-density environment in the Sun’s interior, also known as the matter, Mikheyev-Smirnov-Wolfenstein (MSW) ef-fect [34, 35].
The SSM describes the whole life of the Sun from the pre main-sequence time to the current day, even into the future. The study of solar neutrinos directly tests the theory of stellar evolution, nuclear energy genera-tion, and neutrino oscillation. The knowledge of the Sun is critical to further understand stars in distant space.
3.1.2 Solar neutrino experiments
The first triumph of solar neutrino flux measurement was for the νe component detected using a 37Cl
detec-tor at Homestake [36], but it was a big surprise that the measurement was only about 50% of the prediction. The following steady experimental efforts by SAGE (71Ga
de-tector) [37], GALLEX (71Ga detector) [38], GNO (71Ga
detector) [39], Kamiokande (water Cherenkov detec-tor) [40], and Super Kamiokande (water Cherenkov de-tector) [41] all confirmed the Homestake measurement. Later the SNO [42] experiment used a heavy water de-tector to make a measurement sensitive to all the fla-vors, whose neutral current scattering result agrees with the SSM prediction. Today we understand that electron neutrinos, νe, generated through the fusion processes
oc-curring inside the Sun may oscillate to other flavors, νµ
or ντ, and this process is affected by the MSW effect in
the surrounding dense materials in the Sun.
Recently the Borexino experiment successfully iden-tified the low energy 7Be, pep and pp solar neutrinos,
and measured the fluxes in agreement with the SSM pre-diction when taking the oscillation into account [43]. A new era of precision measurement of the solar neutrino has begun.
3.1.3 Helioseismology
Solar oscillation was first found in Ref. [44] by study-ing the velocity shifts in absorption lines formed in the solar surface. The surface of the Sun is divided into patches which oscillate with velocity amplitudes of order 0.5 km s−1 and periods of order 5 minutes. This
phe-nomenon can be used to deduce a precise sound speed profile in the Sun and correspondingly the density and pressure profile. Helioseismology is the other method that can be used to study the interior of the Sun. 3.1.4 Open Problems
The remaining issues for the properties of neutrinos and the solar model [45–47] are summarized below.
• Discovery of the missing solar neutrino compo-nents is expected from a more precise measure-ment [19, 25, 48]. CNO neutrinos are believed to dominate the fueling processes inside high temper-ature massive stars, but have not yet been observed by any neutrino experiment. Searching for CNO neutrinos from the Sun is the first practical ap-proach, despite its relatively small flux. The hep neutrinos are also still missing from any experimen-tal measurements.
• Precise measurements of all the solar neutrino com-ponents will provide not only a tighter constraint on the solar model, but also a high statistics obser-vation of pp and others in real time, all of which might give completely new insights into the energy production and fluctuation of stars. In addition, a precise measurement of the solar neutrino flux could play a key role in the study of the following problems.
• Solution of the metallicity problem. As discussed in Ref. [49, 50], an improved solar model predic-tion is available with the input of the most up-to-date photospheric abundance of metals, which is 30% lower than earlier results. The new cal-culation based on the low metallicity assumption predicts lower fluxes for several neutrino compo-nents than those based on the previous high metal-licity assumption. The next generation of solar neutrino experiments are expected to resolve the conflict.
A precise measurement of the CNO neutrino is especially important for the metallicity problem [25, 26]. The relation of the solar neutrino fluxes and helioseismology can be seen in Fig. 6. The CNO neutrino flux predicted by the SSM has a di-rect dependence on the abundance of the metal el-ements than other components. The variance of metallicity will change the temperature, density and pressure profile and affect the fluxes of oth-ers indirectly.
Fig. 6. (color online) The relation of solar neutrino fluxes and sound speed measurement of helioseis-mology.
• A full picture of the MSW effect in the solar elec-tron neutrino oscillation. The oscillation of low energy νe, < 1 MeV, likely occurs in vacuum.
As the neutrino energy increases, the MSW effect on solar neutrino oscillation emerges and becomes dominant due to the high electron density envi-ronment of the Sun’s interior, and the transition of νe to the other flavors will eventually reach a
maximum. However, this transition region from vacuum to matter is still poorly constrained by ex-periments [51–54].
• Precise measurements of θ12 and ∆m221. There is
currently a 2σ tension in the ∆m2
21 measurement
between solar [55] and reactor measurements [56]. The Sun emits electron-neutrinos, while reactors emits electron-antineutrinos. Better measurements can be used to improve the measurement of the PMNS matrix and matter effect, and provide a test of CPT invariance as well. A more precise value of θ12 will help to define a better lower edge of the
inverted neutrino mass hierarchy, and is thus im-portant for neutrinoless double beta decay experi-ments in the future.
• Observation of νe regeneration inside the Earth.
The Earth should in principle have a terrestrial matter effect on solar neutrinos. A regeneration of these neutrinos will give rise to a flux asym-metry for electron flavor solar neutrinos during the daytime and the nighttime [57, 58]. An in-dication of the day-night asymmetry has already been observed with a 2.7σ significance at Super Kamiokande [59].
• Probing the sub-leading effects in addition to neu-trino oscillation [51, 54]. The Sun serves as an ideal neutrino source to probe for new physics, es-pecially for those through a secondary effect of the standard scheme. In addition, the expected upturn behavior has not been observed yet for the solar neutrino oscillation from the matter to the vacuum effect. This has left a lot of space for non-standard neutrino interactions. Other interesting topics can also be studied with solar neutrinos, such as new neutrino states, sterile neutrinos, effects of vio-lation of fundamental symmetries, new dynamics of neutrino propagation, and probes of space and time.
The rest of the section is arranged as follows. Sec-tion 3.2 introduces the simulaSec-tion setup for the sensitiv-ity study, including neutrino oscillation probabilsensitiv-ity, solar neutrino model, detector configuration, etc. Section 3.3 addresses the systematics which can affect the studies of the solar model and MSW effects. Section 3.4 gives the sensitivity for identifying each solar neutrino com-ponent. Sections 3.5, 3.6 and 3.7 discuss the potentials for studying the transition of vacuum-matter oscillation, day-night asymmetry, and the test of high and low metal-licity models, respectively.
3.2 Simulation study
A simulation study was done with some default set-tings for Jinping, including the expected signal and back-ground levels, energy resolution, target mass, and live time, in order to evaluate the sensitivity for each physics topic.
3.2.1 Solar neutrino model
The neutrino energy spectra for all the solar neutrino components were taken from Ref. [22]. The average neu-trino flux predictions on Earth without the oscillation
Fig. 7. (color online) Solar neutrino energy spec-tra and fluxes with the high metallicity hy-pothesis, where the unit for continuous spec-tra is 1010/MeV/cm2/s, and for discrete lines is
1010/cm2/s.
effect are from Ref. [50, 60] for the high and low metal-licity hypotheses, respectively. The correlations between the neutrino components estimated in Ref. [61] were used in the study. The spectra with the high metallicity flux prediction are shown in Fig. 7 and all the numerical val-ues are listed in Table 2.
Table 2. Theoretical predictions for solar neutrino fluxs and errors without oscillation based on the high and low metallicity hypotheses [50, 60]. The production branching ratios for the 0.38 and 0.86 MeV7Be lines are 0.1052 and 0.8948, respectively.
EMax flux (GS98) flux (AGS09)
or ELine/ high metallicity/ low metallicity/
MeV (×1010s−1cm−2) (×1010s−1cm−2) pp 0.42 5.98(1 ± 0.006) 6.03(1 ± 0.006) 7Be 0.38 0.053(1 ± 0.07) 0.048(1 ± 0.07) 0.86 0.447(1 ± 0.07) 0.408(1 ± 0.07) pep 1.45 0.0144(1 ± 0.012) 0.0147(1 ± 0.012) 13N 1.19 0.0296(1 ± 0.14) 0.0217(1 ± 0.14) 15O 1.73 0.0223(1 ± 0.15) 0.0156(1 ± 0.15) 17F 1.74 5.52 × 10−4(1 ± 0.17) 3.40 × 10−4(1 ± 0.17) 8B 15.8 5.58 × 10−4(1 ± 0.14) 4.59 × 10−4(1 ± 0.14) hep 18.5 8.04 × 10−7(1 ± 0.30) 8.31 × 10−7(1 ± 0.30) 3.2.2 Oscillation probability
The propagation path of solar neutrinos from the Sun to the Earth can be divided into three parts: 1) from the inner core to the surface of the Sun; 2) from the sur-face of the Sun to the sursur-face of the Earth; 3) the path through the Earth during the nighttime.
The survival probability of solar electron neutrinos with energy Eνfrom the inner core to the surface of the
Sun must include the matter effect [34, 35] and can be approximated by the following formula [62, 63],
P ee= cos4θ13 1 2+ 1 2cos2θ M 12cos2θ12 , (1) where the mixing angle in matter is
cos 2θM 12= cos 2θ12−β p(cos2θ12−β)2+ sin22θ12 , (2) with β =2 √ 2GFcos2θ13neEν ∆m2 12 , (3)
where GF is the Fermi coupling constant and ne is the
density of electrons in the neutrino production place of the Sun. The calculation is done under the assumption
of adiabatic evolution [64], so that the density of elec-trons varies slowly and does not cause any exchange among the mass eigenstates after being created. For the solar case initially only νe’s are produced by the
fusion processes. With sin2θ
12=0.307, sin2θ13=0.0241,
∆m2
12= 7.54× 10−5 eV
2, and n
e= 6× 1025/cm3 [65] in
the inner core of the Sun, the survival probability of νe
as a function of neutrino energy was obtained, without considering the generation of radius distribution of each component. Correspondingly the appearance probability of νµ and ντ is
P
eµ(τ)= 1−P
ee. (4)
The second part is the disappearance probability for the propagation from the surface of the Sun to the surface of the Earth. The mass eigenstates of neutrinos emerging from the surface of the Sun are treated as decoherent [66] due to the sizable width of the energy spectrum of each neutrino component, even for 7Be neutrinos [67]. The
amplitudes of all the mass eigenstates keep unchanged and decoherent all the way to the Earth. The fluxes per unit area only decrease by a factor of the Earth-Sun distance squared with a percent-level annual modulation effect due to the eccentric orbit of the Earth. The above oscillation probability P
ee is sufficient for most studies
[68].
3.2.3 Elastic scattering cross section
The neutrino electron elastic scattering process will be used to detect solar neutrinos. The scattered elec-tron’s energy and direction can be measured and used to derive the incoming neutrino energy and direction. The differential scattering cross-sections as a function of the kinetic energy of the recoil electron, Te, and neutrino
en-ergy, Eν, in the electron rest frame can be written, for
example, in Ref. [69] as: dσ(Eν, Te) dTe = σ0 me " g2 1+ g22 1−Te Eν 2 −g1g2 meTe E2 ν # , (5) with σ0= 2G2 Fm 2 e π ' 88.06×10 −46cm2, (6)
where me is the electron mass. Depending on the flavor
of the neutrino, g1 and g2 are:
g(νe) 1 = g (¯νe) 2 = 1 2+ sin 2θ W' 0.73, g(νe) 2 = g (¯νe) 1 = sin2θW' 0.23, (7)
where θWis the Weinberg angle, then for νµ,τthey are
g(νµ,τ) 1 = g (¯νµ,τ) 2 =− 1 2+ sin 2θ W' −0.27, g(νµ,τ) 2 = g (¯νµ,τ) 1 = sin2θW' 0.23. (8)
The differential cross-section for νe electron scattering
as a function of Te and the cosine angle between the
re-coiling electron and initial neutrino direction are shown in Fig. 8. The directional information will be less useful when the energy of solar neutrino becomes smaller.
kinetic energy of electron/MeV 0 2 4 6 8 10 0 2 4 6 8 (b) (a) 10 12 cosθ 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 ×10−45 ×10−45 cross section/(c m 2/MeV) cross section/(c m 2/0.01)
Fig. 8. (color online) (a) the differential cross sec-tion for the scattering as a funcsec-tion of the kinetic energy of recoil electron for a 10 MeV νe (blue)
and νµ,τ (black); (b) the distribution of the
co-sine angle between the recoiling electron and ini-tial neutrino direction for a 10 MeV νe(blue) and
a 1 MeV νe(black).
3.2.4 Detectable electron spectrum
Since the observed spectrum of electron kinetic en-ergy contains all the contributions from electron-, muon-and tau-neutrinos, the electron kinetic energy spectrum becomes Rν=NeΦν Z dEν dλ dEν Z dσ e(Eν, Te) dTe Pee(Eν) +dσµ,τ(Eν, Te) dTe [1−Pee(Eν)] dTe, (9)
where Ne is the number of electrons in the target, Φνis
the neutrino flux of the Sun, dλ/dEν is the differential
energy spectrum of the solar neutrinos, dσe dTe
dσµ,τ
dTe
is the differential scattering cross section as a function of electron kinetic energy for νe (νµ,τ), and Pee is the νe
Fig. 9. (color online) Kinetic energy distribution of recoil electrons for each solar neutrino compo-nent, in which the MSW oscillation and the high metallicity hypotheses are both considered.
Table 3. Expected electron event rates for different thresholds and metallicity hypotheses. The uncertainties are all from the solar model prediction only.
electron event >0 keV (GS98) >0 keV (AGS09) >200 keV (GS98) >200 keV (AGS09) rate /day/100 ton high metallicity low metallicity high metallicity low metallicity
pp 132.59 ± 0.80 133.70 ± 0.80 4.557 ± 0.027 4.595 ± 0.028 7Be (0.38 MeV) 1.93 ± 0.13 1.76 ± 0.12 0.228 ± 0.016 0.208 ± 0.015 7Be (0.86 MeV) 46.9 ± 3.3 42.8 ± 3.0 31.6 ± 2.2 28.8 ± 2.0 pep 2.735 ± 0.033 2.792 ± 0.034 2.244 ± 0.027 2.291 ± 0.028 13N 2.45 ± 0.34 1.80 ± 0.25 1.48 ± 0.21 1.09 ± 0.15 15O 2.78 ± 0.42 1.95 ± 0.29 2.03 ± 0.31 1.42 ± 0.21 17F 0.069 ± 0.012 0.0426 ± 0.0072 0.0506 ± 0.0086 0.0312 ± 0.0053 8B 0.443 ± 0.062 0.364 ± 0.051 0.427 ± 0.060 0.351 ± 0.049 hep 0.0009 ± 0.0003 0.0009 ± 0.0003 0.0009 ± 0.0003 0.0009 ± 0.0003 survival probability. The recoiling electron spectra of the
solar neutrinos for all the fusion processes can be seen in Fig. 9. The number of electron candidates for the high and low metallicity hypotheses and the effective number of electron candidates with a 200 keV energy threshold are shown in Table 3, where the number of electrons per 100 tons was assumed to be 3.307×1031[43].
3.2.5 Fiducial target mass
In our sensitivity study the fiducial target masses are set to be 1000, 2000, and 4000 tons, respectively. 3.2.6 Detector response model
Three types of target materials were studied for the detection of the recoiling electrons through elastic neutrino-electron scattering.
Liquid scintillator, with its high light yield and low detecting threshold, has been successfully applied in many low-energy neutrino experiments. The liquid scin-tillator detector response can be approximated by a sim-ple characteristic resolution function. The non-uniform and non-linear detector energy responses can both be corrected, so they do not need to be included in this study. The SNO+ experiment inherited the almost doubled photocathode coverage from the SNO exper-iment [70] compared to Borexino [71], so a doubled light yield was considered possible in this study. Liq-uid scintillator was used as a reference material for this study.
Water is the second option under our consideration. The technique developed by the Super Kamiokande ex-periment [72] is very mature, but the light yield is low.
Slow scintillator is the third option, because of the attractive feature that it can separate scintillat-ing and Cherenkov light and provide additional in-formation for energy reconstruction and background suppression.
Three typical energy resolutions were tested in this study and their values in terms of photo-electron/MeV (PE/MeV) and corresponding resolution functions are
summarized in Table 4.
Table 4. Three types of light yields and resolution functions for the detector response.
light yield resolution function material (σE/E)
200 PE/MeV 1/p200E/MeV water (SK) 500 PE/MeV 1/p500E/MeV LS or Slow-LS 1000 PE/MeV 1/p1000E/MeV LS (SNO+)
3.2.7 Background assumption
There are mainly three categories of backgrounds. 1) Cosmic-ray muon induced spallation backgrounds. With the overburden of Jinping, these backgrounds will be a factor of 200 lower than those in Borexino and a factor of 2 lower than SNO. 2) Internal radioactive beta or gamma backgrounds. They are the residual background remain-ing in the detectremain-ing material regardless of the depth. We assume that these backgrounds can be reduced by purifi-cation down to the same level as Borexino. 3) Environ-ment radioactive background. This presents as external gammas for a central detector volume. Borexino back-ground rates were applied in our study, and were scaled according to the surface area.
For simplicity, no quenching effect was considered in the following study, so that for sequential beta and gamma decays, all the gamma energies and beta kinetic energies were added linearly without considering the de-cay structure of excited states. For the positrons from the beta+ decays, twice the electron mass was added to the detected energy for the positron annihilation.
The external gamma background was modeled by an exponential distribution, motivated by Ref. [43]. The major external208Tl is assumed to have an exponential
energy tail with a decay constant of 0.4 MeV, which is related to the gamma ray attenuation length and fiducial volume buffer dimension.
A summary of the event rates for all the backgrounds can be found in Table 5. Details are given below.
the phase-I 7Be measurement at Borexino [43, 73, 74],
from which the fiducial volume mass, live time, and back-ground rates of14C,85Kr,210Bi, and11C were extracted.
The values for 14C and 11C were used for the Jinping
study. Other background values, 10C, 208Tl, 11Be, and
Ext-208Tl were extracted in a similar way as discussed
below.
The Borexino-I pep refers to the analysis result of the phase-I pep measurement at Borexino [43, 75], where the data of 598.3 live days was scaled down by 48.5% for the final selection efficiency. With the technique of three-fold coincidence (TFC), the background rate of10C was
suppressed. The10C background rate without the TFC
technique was taken as a standard value of the Borexino experiment, and then scaled to Jinping. The most sig-nificant and representative external gamma background,
Ext-208Tl, as a major background was extracted from
this analysis and used for the Jinping study.
Borexino-I8B is for the phase-I8B analysis at
Borex-ino [76], where the energy beyond 3 MeV was dis-cussed. The reported rates of the high energy back-grounds208Tl and11Be were taken to be the standard
val-ues for the Borexino experiment, and used for the Jinping study.
The second phase of the Borexino experiment has a much lower85Kr and210Bi background rates [77]. A
sample with double the live days of data was assumed, in order to compare the phase one analysis. The measured background rates of85Kr and210Bi of the second phase
were used for the Jinping study.
For comparison purposes, the background situation of the SNO+ experiment [78] is also listed.
Table 5. A summary of the fiducial mass, live time, and backgrounds for all the known running or planned solar neutrino experiments. See the text in Sec. 3.2.7 for the references and calculation methods for each experiment or analysis. Jinping’s fiducial mass and resolution will be scanned in the study.
mass/ time/ resolution/ 14C 85Kr 210Bi 11C 10C 208Tl 11Be Ext-208Tl
100 ton day PE/MeV /counts/day/100 ton
Borexino-I7Be 0.7547 740.7 500 3.46 × 106 31.2 41.0 28.5 0.62 0.084 0.032 2.52 Borexino-I pep 0.7130 290.2 500 3.46 × 106 31.2 41.0 2.48 0.18 0.084 0.032 2.52 Borexino-I8B 1 345.3 500 3.46 × 106 31.2 41.0 28.5 0.62 0.084 0.032 2.52 Borexino-II7Be 0.7547 1480 500 3.46 × 106 1 25.0 28.5 0.62 0.084 0.032 2.52 Borexino-II pep 0.7130 580 500 3.46 × 106 1 25.0 2.48 0.18 0.084 0.032 2.52 Borexino-II8B 1 690 500 3.46 × 106 1 25.0 28.5 0.62 0.084 0.032 2.52 SNO+ 5 1500 1000 3.46 × 106 1 25.0 0.29 0.0062 0.084 0.00032 1.47
Jinping scan 1500 scan 3.46 × 106 1 25.0 0.15 0.0031 0.084 0.00016 1.17
3.2.8 Total spectrum
Simulation samples were constructed with solar sig-nals and backgrounds. They were fitted and analyzed for each physics topic below and the corresponding discovery sensitivities will be reported.
3.3 Systematics of the flux measurement Two systematic uncertainties were considered for the measurement of the solar neutrino flux. One is the fidu-cial volume definition, which is only related to the bias of vertex reconstruction rather than the resolution. A 1% systematic uncertainty was assumed for the fiducial vol-ume cut. The other is from the energy response of the detector. With the experience of the Borexino experi-ment and the recent Daya Bay experiexperi-ment [79, 80], we believe that the uncertainty from the non-linearity and non-uniformity effect in the energy reconstruction can be controlled down to the level of 1%. With a large data sample expected at Jinping, we assumed there was no fitting procedure error as introduced by Borexino analy-sis. In total, 1.5% systematic uncertainty is assigned to all the flux measurements.
3.4 Precision for each component measurement Simulations with the inputs from Table 3 and var-ious target masses and energy resolutions were done to evaluate the expected precisions. A fitting example is shown in Fig. 10. The 0.38 MeV to 0.86 MeV ratio
Fig. 10. (color online) Fit results for the simula-tion sample with a 2000-ton target mass and 500 PE/MeV energy resolution.
of the 7Be lines was fixed according to Table 2. Since
the characteristic line shapes for the15O and 17F were
not distinguishable, only the15O component was
consid-ered in the fitter. The hep neutrino contribution was not significant in the fit, and was ignored. Table 6 lists the relative statistical precisions for all the solar neutrino components with the high and low metallicity models.
Table 6. Relative statistical precision of solar neu-trino fluxes for three different target masses and energy resolutions. The default results are for the high metallicity assumption and the ones in the parentheses are for low metallicity if significantly different. NA is marked when the relative uncer-tainty is greater than 50%.
energy resolution/PE/MeV 200 500 1000 pp 0.02 0.007 0.005 fiducial 7Be 0.007 0.006 0.005 mass pep 0.07 0.05 0.04 1000 ton 13N NA 0.5 (NA) 0.3 (0.4) 15O 0.3 0.2 (0.4) 0.1 (0.2) 8B 0.02 0.02 0.02 pp 0.01 0.005 0.004 fiducial 7Be 0.005 0.004 0.004 mass pep 0.06 0.03 0.03 2000 ton 13N 0.4 0.3 0.2 (0.3) 15O 0.2 0.1 0.08 (0.1) 8B 0.02 0.02 0.02 pp 0.01 0.004 0.003 fiducial 7Be 0.004 0.003 0.003 mass pep 0.04 0.03 0.02 4000 ton 13N 0.3 0.2 (0.3) 0.2 (0.3) 15O 0.1 (0.2) 0.07 (0.1) 0.06 (0.09) 8B 0.01 0.01 0.01
3.4.1 Improvement on the known neutrino components pp neutrino: As shown in Fig. 10, the electron en-ergy from the elastic pp neutrino scattering is slightly higher than that from the main background 14C, and
the best signal region for detecting the pp neutrinos is around 0.2–0.3 MeV. The statistical uncertainty on the pp neutrino flux is very sensitive to the energy resolu-tion of the detector, which can reach 1% with the 500 PE/MeV light yield. The total uncertainty will be dom-inated by the systematic uncertainty. We hope to control the dominant systematic uncertainty and reduce the to-tal uncertainty down below 1%, and this will help to explore the expected difference between the neutrino lu-minosity and the optical lulu-minosity.
7Be neutrino: The7Be and8B neutrinos are critical
to distinguish the high and low metallicity hypotheses.
The 7Be neutrino flux can be measured statistically to
better than 1%, which is less dependent on the energy resolution due to the characteristic sharp turn. The total flux uncertainty is dominated by the systematic uncer-tainty.
8B neutrino: The 8B neutrinos suffer the largest
matter effect, which makes them sensitive to the vaccum-matter transition phase and the day-night flux asymme-try. The relatively high energy of 8B neutrinos makes
them less contaminated by other backgrounds, and be-cause of the broad energy spectrum, the study of 8B
neutrinos does not rely on the energy resolution much. The statistical precision of the flux of 8Be neutrinos is
expected to be about 1%–2% , which is limited by the target mass, and is comparable to the systematic uncer-tainty.
pep neutrino: The distinguishable structure of the pep neutrino spectrum, like the 7Be neutrinos, makes
them easily identifiable. With the three energy resolu-tion opresolu-tions considered, the sensitivities can all reach 7% and even 3% if the target mass can be increased to 2000 tons. The pep neutrinos are one of the key ingredients in the study of the solar model and the vacuum-matter oscillation transition.
3.4.2 Discovery of the CNO neutrinos
CNO neutrino: The flux of CNO neutrinos strongly depends on the metallicity hypotheses and itself is a very interesting subject since the CNO neutrinos are from the main fueling process of high temperature stars, while the pp process is dominant in the Sun because of the rela-tively low temperature. The major backgrounds for the
13N and15O neutrino detection are the7Be and pep
neu-trinos, and85Kr and210Bi decays. An effective
identifi-cation of the other neutrinos and backgrounds will help to resolve the CNO neutrinos, and this relies on the en-ergy resolution. With a resolution of 500 PE/MeV or better, discovery of the 15O neutrinos at Jinping will
be possible (the relative error is better than 30%) for the high metallicity assumption. With a larger tar-get mass, for example 2000 tons, the discovery poten-tial will be significant for both high and low metallicity assumptions.
3.5 Matter-vacuum transition phase
The transition of oscillation probability from the matter-governed region to the pure vacuum-like region is a very interesting phenomenon of the MSW effect. This effect has been studied by Borexino [43, 76], Super Kamiokande [72], SNO [78], and previous experiments. Experimentally, however, the oscillation in the transi-tion region is still loosely constrained, giving chances for non-standard effects enhanced by an MSW-like reso-nance, for example as described in Refs. [53, 81–84]. The current status is shown in Fig. 11. With the Jinping
simulation, the expected flux measurements are com-pared with the predictions with neutrino energy and re-coil electron kinetic energy, which are shown in Fig. 11 and 12, respectively. For Fig. 12, the uncertainty of each bin is assigned as the square root of the full statistics of each bin including all the backgrounds and signals, and, for a better demonstration, the bin ranges were ad-justed according to the statistics of each individual signal region.
Fig. 11. (color online) The transition of oscillation probability from the vacuum to matter effect as a function of neutrino energy. The central line is for the theoretical prediction, while the shaded area is obtained by marginalizing θ12, θ13, and ∆m212
with the present experimental uncertainty. Top plot: Data points plotted are the present mea-surements [74, 75, 77]. Bottom plot: We assume a 2000-ton target mass, 1500-day exposure, a res-olution of 500 PE/MeV, and the low metallicity hypothesis. The five points with error bars are the simulation results for pp,7Be, pep,15O and8B, in
which the central values are set to the true ones, the y-error bars include both statistical and sys-tematic uncertainties and the x-error bars corre-spond to the range of energy measurement, while the15O x-error is omitted for a clear view.
Fig. 12. (color online) The ratio of the detected kinetic energy spectrum of recoil electrons after background subtraction over the non-oscillation truth. Here we assumed a 2000-ton target mass, 1500-day exposure, a resolution of 500 PE/MeV, and the low metallicity hypothesis. The solid line is for the theoretical prediction and the points are simulated data with statistical errors. Because of the large correlation among the points, the sys-tematic uncertainties are not included.
3.6 Day-night asymmetry
After solar neutrinos pass through the Earth, elec-tron neutrinos may be regenerated because of the MSW matter effect [57], which leads to a slightly higher sur-vival probability during the night than during the day time. The average survival probability is very sensitive to ∆m2
21 and the density profile at the nearby surface
of the Earth [58, 59]. The latter can cause a day-night asymmetry varying around 1%–3% for the rate of so-lar neutrinos. With 5 years of data-taking and a 2000-ton detector, the total statistics of8B could reach 10000
events, which is insufficient to have a conclusive mea-surement of the day-night asymmetry.
3.7 Metallicity problem
With the expected improvements in the measurement of solar neutrino fluxes, we have carried out a study of the hypothesis test for the solar models with the high and low metallicities. The study is focused on the experimen-tal capability with given oscillation parameters, because the theoretical uncertainties of the solar neutrino flux predictions are difficult to quantify currently [23]. The evaluation was done assuming 2000-ton target mass and 1500-day exposure.
The ability to distinguish two hypotheses, separation S, is defined as S = " X i,j (Fh,i−Fl,i)(V−1)ij(Fh,j−Fl,j) #1/2 , (10) where Fh,i and Fl,i are the predicted neutrino fluxes
metallicities, respectively, and V is the covariance ma-trix, which follows the usual definition as
Vij= σiσjρij, (11)
where σi is the uncertainty of the i-th component and
ρij gives the correlation between the i-th and j-th
com-ponents.
Firstly, an optimistic calculation of the separation, Sopt, between the two hypotheses was done assuming all
of the flux measurements were independent. By simpli-fying Eq. (10), Sopt= " X i S2 opt,i #1/2 = " X i (Fh,i−Fl,i)2/σi2 #1/2 , (12) where Sopt,i gives the separation achieved for the i-th
component. Table 7 gives the inputs for calculating Sopt,
including the flux difference between the two hypotheses, the expected experimental uncertainties, σexp,i, Sopt,i,
and the theoretical uncertainties σtheory,i. The final
re-sult is
Sopt= 9.6, (13)
which can be treated as a 9.6 σ rejection to the high metallicity hypothesis and vice versa. The most power-ful separations are expected from the7Be, 15O, and8B
neutrinos.
Table 7. Details of the high and low metallicity hy-potheses test. The second column shows the flux difference, i.e. GS98-AGS09 [50, 60]. The third column gives the expected absolute experimental error, σexp,i, which is calculated according to the
GS98 flux estimation and the expected statisti-cal and systematic errors. The fourth column is the separation for the i-th component, |Sopt,i|, as
defined in Eq. 12. In the last column, the abso-lute theoretical uncertainty for the i-th compo-nent, σtheory,i, is presented for comparison. The
flux difference, σexp,i, and σtheory,i are in units
of 1010(pp), 109 (7Be), 108 (pep,13N,15O), 106
(8B,17F), and 103 (hep) cm−2s−1.
Fh,i− Fl,i σexp,i |Sopt,i| σtheory,i
pp 0.05 0.10 0.53 0.036 7Be −0.44 0.078 5.7 0.32 pep 0.03 0.048 0.62 0.018 13N −0.79 0.89 0.89 0.30 15O −0.67 0.23 3.0 0.28 17F −2.12 - - 0.76 8B −0.99 0.14 7.1 0.64 hep 0.27 - - 2.49
Secondly, a model separation quantity Sconswas
con-servatively evaluated taking into account the contribu-tion from the7Be,8B, and15O neutrinos, and the
exper-imental correlations among them. The correlations stem
from the fitting procedure to separate the 7Be and 8B
components, since the statistical precisions are relatively high, as listed in Table 6. The major sources of system-atic errors, target mass and energy response, might be fully correlated among all the neutrino components for the worst case. It should be noted that the relative sys-tematic uncertainty of 1.5% is dominant for the7Be
neu-trinos and significant for the 8B neutrinos. As a result,
the correlation between them is as high as 50%, degrad-ing the power to distdegrad-inguish the models. The correlation matrix between them is given below
ρ = 1 0.1581 0.5799 0.1581 1 0.1104 0.5799 0.1104 1 , (14)
where the rows and columns are arranged sequentially for the 7Be, 15O, and8B, respectively. The calculation
gives
Scons= 7.6. (15)
As a conclusion, the proposed Jinping neutrino ex-periment has the capability to resolve the high and low metallicity hypotheses in the given references with 7–10 σ with the fixed input of present mixing angles. We expect the uncertainties on these mixing angles will be improved with terrestrial experiments.
3.8 Conclusion and summary
Based on the discussion in this section, with 2000-ton fiducial mass and 500 PE/MeV light yield, the expected outcome for the proposed Jinping neutrino experiment running over 5 years is very promising to make a discov-ery of the CNO neutrinos and to significantly improve the measurements of the pp, 7Be, and pep neutrino fluxes.
The experiment can also provide a stronger constraint on the vacuum-matter transition to the MSW effect, and have the experimental capability to distinguish the high and low metallicity hypotheses in the given references. Due to the limited target mass, physics relying on the statistics of8B neutrinos cannot be precisely probed, for
example, the day-night asymmetry. In this study, we did not discuss the possible improvement of the measurement of neutrino mixing angles and the possibility to rule out other new physics.
4
Geo-neutrinos
4.1 IntroductionIdentifying and understanding the Earth’s energy budget is a fundamental question in geology, as it defines the power that drives plate tectonics, mantle convection, and the geodynamo [85]. The motivation for understand-ing geo-neutrinos starts with the wish to understand our planet.
The Earth’s total heat flow is currently estimated to be 46± 3 TW [86]. The driving power comes presum-ably from two sources: 1) the heat evolved from decay of radiogenic isotopes, and 2) primordial energy that re-sulted from the accretion of the planet and the gravita-tional differentiation of iron sinking to the center of the Earth [87, 88]. Estimates for the radiogenic heat pro-duction (from K, Th and U, >99%) in the Earth cover a continuum of compositional models that can be de-fined by three groups: (1) low Q models (10–15 TW of power), medium Q models (17–22 TW) and high Q models (>25 TW), which were previously classified as cosmochemical, geochemical, and geodynamical models, respectively [87]. The continents are estimated to ac-counts for 7 TW of the total budget of heat-producing elements, which translates to the mantle having insignif-icant (3 TW) to substantial (>18 TW) amounts of ra-diogenic power [89].
Geo-neutrinos are produced by radioactive decays from inside the Earth, with only those from the 232Th
and238U decay chains being detectable because their
en-ergies are >1.8 MeV, the threshold for initiation of in-verse beta decay (IBD). Quantifying the flux of these geo-neutrinos will place limits on the radiogenic power in the planet and provide authoritative insights into the building blocks of the Earth and the energy driv-ing plate tectonics. The field of neutrino geophysics only became practical recently by the advent of large under-ground neutrino detectors, i.e. the KamLAND [90–92] and Borexino [93–95] experiments.
The current experimental status can be seen in Ref. [88]. The fuel that drives the Earth’s engine comes from unknown proportions of primordial energy from as-sembling the planet and nuclear energy from the heat produced during natural radioactive decay. There is an order of magnitude uncertainty in present-day estimates of the amount of radiogenic power driving mantle dy-namics. The existing measurements of the Earth’s flux of geoneutrinos [90–95] reveal the amount of uranium and thorium in the Earth, and have excluded a fully ra-diogenic Earth, but regrettably, because of the consider-able uncertainty from these models, cannot discriminate between the three competing compositional models for the Earth. The most recent result from the Borexino experiment [95] reported a figure for the mantle flux of geo-neutrinos, although with about 75% uncertainty at the 1-sigma level.
The mantle neutrinos are of the most theoretical in-terest, but the corresponding fraction is only from 15% to 30% for any given continental experiments [96], and the distribution of heat producing elements is not pre-cisely known. The crustal geo-neutrino flux is the best known of the contributors to the total flux, as it the most accessible part of the Earth. Calculating the
geo-neutrino contribution from the continental crust is done by integrating data from geophysical [97–99] and geo-chemical [96] surveys of continents, with detailed regional studies for the first 500 km surrounding the detector [100] as this region typically contributes half of the total geo-neutrino signal. Critical constraints on the Earth models will come from precise measurements of the Earth’s geo-neutrino flux.
A natural nuclear fission reactor at the center of the earth with an estimated power output of 3–10 TW has been proposed as the energy source of the earth’s mag-netic field [101]. Experimental results may critically as-sess such assumptions and set limits on its presumed power contribution.
Due to its location far away from nuclear power plants, Jinping is an ideal site to precisely measure the neutrino flux and to probe for potential geo-reactors. Next we will introduce geo-neutrino signals in Section 4.2, the critical backgrounds from reactor neu-trinos and other contributors in Section 4.3, and the sen-sitivity to study geo-neutrinos at Jinping in Section 4.5. The sensitivity for geo-reactors will be briefly discussed in Section 4.6.
4.2 Geo-neutrino signal
This section discusses the spectrum and flux of the geo-neutrinos, together with their detection.
4.2.1 Geo-neutrino spectrum and flux
Natural decays from the 238U and232Th families and 40K produce heat: 238 92 U→ 206 82 Pb + 8α + 6β −+ 6¯ν e+ 51.698 MeV, 232 90 Th→ 208 82 Pb + 6α + 4β − + 4¯νe+ 42.652 MeV, 40 19K→ 40 20Ca+ β −+ ¯ν e+ 1.311 MeV (BR = 89.3%), 40 19K + β − →40 18Ar + νe+ 1.505 MeV (BR = 10.7%). (16) The predicted beta-decay spectra of the antineutrinos are from Ref. [102].
The neutrino flux prediction depends on the geo-models and locations. The recent flux prediction at the Jinping site in Ref. [89] was used for the sensitivity study in this section. The total neutrino flux is 58.5+7.4
−7.2 TNU
including both U and Th. 4.2.2 Geo-neutrino detection
In principle, neutrinos can be detected via either the elastic scattering process or the inverse beat decay (IBD) reaction. Owing to the low cross-section and the poten-tial solar neutrino background, we do not expect the first process can be used at Jinping. The electron antineutri-nos will be detected using the IBD reaction chain [103]
¯
Depending on the detector type, the energy of electron antineutrinos can be approximately calculated by either Te++ 1.8 MeV in water or Te++ 0.78 MeV in
scintilla-tor. Here, Te+ is the visible energy of the positron, and
the tiny energy of neutron recoil is neglected. The 1.0 MeV difference in scintillator is due to the fact that the visible energy of the positron is actually the sum of the positron kinetic energy and the annihilation γ energy. Because of the soft geo-neutrino spectra and the high Cherenkov threshold, the measurement of geo-neutrinos can only be performed in liquid scintillator detectors or water-based scintillator detectors.
4.3 Geo-neutrino backgrounds 4.3.1 Reactor antineutrino background
Reactor electron antineutrinos are an irreducible background to the detection of geo-neutrinos. The only way to reduce the reactor neutrino flux is to apply the 1/r2 law and place the detector far away from nuclear
power plants. Fortunately, the location of Jinping is at least 1200 km away from any nuclear power plant either operational or under construction, and is therefore the best site for geo-neutrino experiments of all the existing experiments. Below, we evaluate the reactor antineu-trino background at Jinping.
4.3.2 Differential neutrino flux of a single reactor Reactor antineutrinos are primarily from the beta de-cays of four main fissile nuclei 235U, 238U, 239Pu, and 241Pu. The differential ¯ν
e flux, φ(Eν), for a reactor is
calculated by [104] φ(Eν) = Wth P ifiei X i fiSi(Eν), (18)
where i sums over the four isotopes, Wth is the
ther-mal power of a reactor which can be found in the IAEA [105, 106], fi (
P
ifi= 1) is the fission fraction of
each isotope, ei is the average energy released per fission
of each isotope, and Si(Eν) is the antineutrino spectrum
per fission of each isotope. A set of typical fission frac-tions, fi, and the average energy released per fission, ei,
are listed in Table. 8.
Table 8. Fission fraction and average released en-ergy of each isotope [104].
isotope fi ei/MeV/fission 235U 0.58 202.36 ± 0.26 238U 0.07 205.99 ± 0.52 239Pu 0.30 211.12 ± 0.34 241Pu 0.05 214.26 ± 0.33
4.3.3 Total differential reactor neutrino flux
To get the total reactor neutrino background spec-trum at Jinping, φJinping(Eν), we used the thermal
pow-ers of all the currently running and under construction
nuclear power plants from the IAEA [105], and took into account the electron antineutrino survival probability.
φJinping(Eν) is expressed as φJinping(Eν) = Reactors X i φi(Eν)P¯νe→¯νe(Eν, L) 1 4πL2, (19) with Pν¯e→¯νe(Eν, L)≈ 1−sin 22θ 12sin2[1.267 ∆m2 21(eV)L(km) Eν(GeV) ], (20) where Eν is the neutrino energy, L is the distance from
each reactor to the Jinping site, and θ12 and ∆m221 are
neutrino oscillation parameters. L is calculated using the longitude and latitude coordinates for each nuclear power plant and Jinping site, and θ12 and ∆m221 are set
to be 0.586 and 7.58× 10−5 eV2, respectively. Table 9
lists the numerical results for the fluxes.
Table 9. Reactor neutrino flux at Jinping.
Jinping operation construction total China others China others φν/(105cm−2s−1) 3.71 2.73 6.20 0.35 12.99
4.3.4 Other non-¯νebackgrounds
Other possible backgrounds are the cosmic-ray muon induced 9Li and 8He, (α, n) background, and the
ac-cidental coincidence background. According to the re-cent publication by Borexino [95], the signal-to-non-¯νe
-background ratio is∼100, so these backgrounds were ig-nored in this study.
4.4 Fiducial mass for geo-neutrinos
The detection of ¯νe’s is through the IBD process in
Eq. (17). Since the delayed-coincidence technique is ap-plied to identify the prompt and delay signal pair, the ratio of signal to background can be significantly im-proved. Consequently, a lesser requirement on the fidu-cial volume can be applied, increasing the target mass from 2000 tons to 3000 tons.
4.5 Sensitivity for geo-neutrinos
The event rates of geo-neutrino signal, reactor neu-trino background, and the sensitivity of observing geo-neutrinos and determining the Th/U ratio are discussed in this section.
4.5.1 Signal and background rates and spectra
The detectable spectra from the IBD process can be calculated as
RJinping(Eν) = φJinping(Eν)×σ(Eν). (21)
With a modest setup, i.e. 1 kiloton fiducial volume and 1500 days’ data-taking, the total signal and reactor back-ground rates are summarized in Table 10. Within the
geo-neutrino signal region, <2.8 MeV, the reactor neu-trino background rate is less 30/kton/1500 day. The signal to background ratio is rather promising.
Table 10. Total geo-neutrino and reactor neutrino event rates at Jinping.
geo-neutrinos reactors
238U 232Th Total
rate/kton/1500 day 138 34 172 64
4.5.2 Sensitivity for geo-neutrino signals
According to the true signal and background spectra, and the exposure of 3 kiloton of target mass, 1500 days of data-taking, and 500 PE/MeV detector energy res-olution, we randomly sampled the spectra and performed
visible energy/MeV 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 20 40 60 80 100 χ2/ndf 57.21/58 reactor 0.973±0.085 geo 0.958±0.044 reactor geo
expected IBD events
visible energy/MeV 0 20 40 60 80 100 55.03/57 reactor 0.953±0.084 1.040±0.080 Th-232 U-238 0.72±0.18 reactor-Jinping geo-238U geo-232Th
expected IBD events χ2/ndf
events/(100 keV/3.0 kton/1500 days)
events/(100 keV/3.0 kton/1500 days)
Fig. 13. (color online) Fit result for both the geo-neutrino signals and backgrounds. The top plot is fitted with the Th/U ratio fixed to 3.9, while in the bottom plot Th and U components are fit-ted separately. Numbers shown in the corner are χ2/ndf and the ratios of the fit result to the
nom-inal value for the reactor background and geo-neutrinos.
a likelihood fit with both signals and background. One example fit with Th/U ratio fixed to the known value is given in Fig. 13. The precision of the total geo-neutrino flux can be determined down to 4%. The other fit with the Th and U fractions free is also shown in Fig. 13. The
238U fraction can be determined to 6%, and the 232Th
fraction’s precision can reach 17%. 4.5.3 Th/U ratio
With 5000 tests of random sampling and fitting, we estimated the expected precision to determine the ratio of U to Th components, i.e. how well we can determine the expected chondritic mass Th/U ratio of 3.9. The re-sult is that the Th/U ratio can be well measured, with a precision of 27%.
4.5.4 Sensitivity to geo-neutrino models
With the 4% precision in determining the total geo-neutrino flux, the result can be compared with the model predictions. Shown in Fig. 14 are two possible outputs with uncertainties overlaid on the model predictions of geo-neutrino flux as a function of heat production. The prediction has two main uncertainties. The first is a 10% uncertainty of the crust neutrino flux, and the other is the distribution of the mantle neutrinos, which could be uniform in the mantle or in the extreme case only concen-trate around the border of the mantle and the core. With the expected improvement of the geo-neutrino flux mea-surement, it should be possible to accept or reject some geo-neutrino predictions. But, certainly, a more precise geological survey of the near-by crust, and, if possible, a better understanding of the mantle neutrino distribution, are necessary to decrease the prediction uncertainty.
Fig. 14. (color online) The geo-neutrino sensitiv-ity vs geo-neutrino model predictions at Jinping. The three filled regions in the plot delimit, from the left to the right, low- medium- and high-Q models, respectively. The two horizontal bars are plotted at two possible geo-neutrino flux assump-tions with Jinping geo-neutrino measurement sen-sitivity.
![Table 2. Theoretical predictions for solar neutrino fluxs and errors without oscillation based on the high and low metallicity hypotheses [50, 60]](https://thumb-ap.123doks.com/thumbv2/9libinfo/7758629.149259/8.918.452.827.764.989/table-theoretical-predictions-neutrino-errors-oscillation-metallicity-hypotheses.webp)
