1.0 Introduction and Assumptions

This preliminary report has been written under the assumption that the reader is somewhat familiar with the general goals of the project, the work accomplished by the KamLAND experiment, and some relevant particle and nuclear physics. In short, we are using the design and experience with the KamLAND detector as a baseline to consider what size and location of detector is needed to approach two goals:

The first, a guaranteed source, is the electron anti-neutrino flux from the mantle and core of the earth due to Uranium and Thorium decays. For locations near or on a continental crust, this “geonu” flux is dominated by the U/Th in the crust, not as interesting as the amount in the mantle and core. These values are only known very poorly at present and speculated upon by geologists (typically based upon the content of meteorites), so the geological community will welcome any information from the inaccessible inner earth.

The second measurement to be made is a search for a reactor at the earth’s core. As discussed elsewhere, this hypothetical power source could be the driver of the deep earth plumes, and ultimately responsible for the motion of landmasses as well as the earth’s magnetic field. The putative georeactor flux is very hard to measure in a location anywhere near the electrical power reactors in places such as Japan, Europe and North America (it is at most a small background to the georeactor flux in KamLAND).

1.1 Neutrino Oscillations

In the following discussion, all processes that involve neutrino production and subsequent detection assume that neutrino oscillations occur, with the oscillation parameters chosen to be the best fit values from global fits to all solar and reactor neutrino experiments. Since the baseline of neutrino propagation considered in this context is much larger than the oscillation lengths for the energy scale under consideration, the neutrinos can be considered to a good approximation to be fully mixed. The effect of oscillations can be accounted for by reducing the event rate by 0.6 compared to the rate without oscillations.

The energy window for the geo-neutrino analysis is 1.7 – 3.5 MeV, while that for the georeactor analysis is 3.4 MeV to 9.3 MeV. The spectra of the contributions to the signal are as illustrated in Figure 1.

1 Figure 1: The visible energy spectrum of geo-neutrino and commercial nuclear reactor neutrino detected by the KamLAND detector1. The shape of the geo-neutrino spectrum in Hano Hano is the same as in KamLAND, whereas that of the georeactor is somewhat different due to differences in the effect of neutrino oscillations. Also, the size of the reactor component in Hano Hano is expected to be comparable to the geo-neutrino components.

2.0 Geo-neutrino Detection Sensitivity

Hanohano’s location in the middle of the Pacific Ocean makes it sensitive primarily to geo-neutrinos originating from the earth’s mantle. The nominally expected event rate of geo-neutrinos of mantle origin based upon a simple Bulk Silicate Earth ModelError: Reference source not found is 4.5 events / kiloton / year, compared to 1.1 events / kiloton / year for geo-neutrinos from the oceanic and continental crust. This is illustrated in Figure 2, which shows the integrated neutrino flux out to various distances from the detector located near Hawaii. The situation is reversed at a continental location, with the same mantle/core flux, but about ten times the crustal flux (see Figure 3). For this document we shall take the “signal” to be the mantle geo-neutrino event rate. The crustal geo-neutrinos will be considered part of the background. Figure 4, which shows a map of the geo-neutrino flux at different positions on the earth’s surface, demonstrates the clear difference between Hano Hano and similar land-based detectors.

2 Figure 2: The cumulative flux of geo-neutrinos as a function of neutrino source distance from the detector at Hawaii. Figure adopted from Enomoto’s Ph. D. thesisError: Reference source not found.

3 Figure 3: Comparison of relative geo-neutrino contributions from the mantle and the continental and oceanic crusts at oceanic (Hawaii) and continental (Kamioka) locations. Figure adopted from Enomoto’s Ph. D. thesisError: Reference source not found.

4 Figure 4: The predicted geo-neutrino flux at different positions on the earth’s surface. Figure adopted from Fiorentini et al.2 (some cosmetic changes made by authors).

Likely backgrounds for geo-neutrinos (based upon KamLAND experience) are:  9Li produced by cosmic rays traversing the detector  Fast neutrons from cosmic rays passing near the detector   decay of 210Po followed by 13C(,n)16O in the scintillator  Accidental coincidence events  Antineutrinos from commercial nuclear reactors  Antineutrinos from a georeactor

We assume that the fast neutrons can be ignored since they occur at the edge of the fiducial volume, so that they can be removed by a fiducial volume cut. The estimated event rate (based upon KamLAND data) from each process is shown in Table 1.

Table 1: Background sources and rates for the mantle geo-neutrino analysis for energies between 1.7 and 3.5 MeV. The 210Po rate assumes 20 times purity compared to KamLAND’s liquid scintillator.

Background Source Rate (1/kt-yr) 9Li (2.15 km depth) 0.40 ± 0.07 9Li (3 km depth) 0.10 ± 0.02 9Li (4 km depth) 0.03 ± 0.01 210Po 2.5 ± 0.7 Accidentals <3.0 ± 0.3 Commercial Reactors 0.5

(Georeactor 1.9 per TWth) Crustal Geonus 1.1

5 In arriving at detector parameters for geoneutrino measurement, we shall assume that the georeactor power is zero, or at least that we know it perfectly from the measurements above 3.4 MeV neutrino energy. The total “background” rate at 4 km depth is 7.1 / kt-yr, compared to a signal rate of 4.5 / kt-yr. The signal significance for 1 kt-yr is S / S + B = 1.3. Thus, with 4 kt-yr a significance of 2.6 sigma (99% confidence level detection) can be obtained. In a 4 year exposure with 4 kilotons this would amount to a background of 113.6 events with expected geonu signal of 72 events. If we have estimated the background perfectly, then the background subtracted mantle geonu signal would be 72 +/- 14, or a 5 standard deviation, 20% measurement.

In order to confirm the above conclusion, we performed simulations where the combined energy spectrum of the signal and background are varied randomly and a multi- component fit is done for the number of signal events. We found that if the scintillator were contaminated at the level observed in KamLAND (2.0 ± 0.2  10-20 g/g with a background rate of about 46.6 events / kt-yr), positive detection of the mantle geonu signal at even 68% level would not be possible. Positive detection at 99% level for several kt-yr exposure is possible only when the 210Po background level is reduced from the KamLAND levels, which we believe to be possible, as will be discussed elsewhere (it is believed that KamLAND was contaminated by Radon during the initial filling process due to faulty pipe connections).

We note that the 9Li background is a relatively minor background component even at the depth of 2.15 km. This low background, however, is achieved at the cost of applying tight cuts to the data, which results in the removal of significant amount of good data. These cuts, moreover, introduce systematic errors that obscure the signal. For these reasons, the most favorable strategy is to go as deep as possible so that the cosmic ray background rate is so low that the application of cuts to remove 9Li events becomes unnecessary. Greater depth alleviates a multiplicity of background problems, including entering fast neutrons and significant dead time around muon transits.

We have been conservative in the “accidentals” estimate as yet, taking this to be the same as for KamLAND per unit volume. Much of the accidentals come from the region near the outside of the fiducial volume, the balloon material and supporting ropes in the case of KamLAND. We expect this to be better in the present design due to larger volume (better surface to volume ratio) and due to having the barrier further outside the fiducial volume. Until we have a detector more specified we cannot refine this estimate, so we take the conservative assumption of the accidentals being equivalent to KamLAND. Note that on the optimistic side of the balance, with 4 years and 4 kilotons, reducing the Po background to negligible levels and the accidentals by a factor of ten, we could make a detection of the mantle/core geonus at the 20 sigma level over background, and a measurement to around 12% precision. Hence there is strong motivation to pursue methods to minimize low energy backgrounds. 3.0 Georeactor Neutrino Detection Sensitivity

6 The energy spectrum of antineutrinos produced in a nuclear fission reactor spans the range of ~0 to about 10 MeV, much wider than the 0 to 3.4 MeV span of geo-neutrinos. In the energy region 1.8 MeV (threshold energy for neutrino interaction with target) to 3.4 MeV, geo-neutrinos are a background to the georeactor. We decided to set a lower energy threshold of 3.4 MeV in order to completely remove this background. We also set an upper bound of 9.3 MeV for convenience (the probability that a georeactor neutrino has greater energy is very low). In this energy range, the georeactor neutrino event rate is 3.8 events / TWth / kiloton / year.

The background sources for georeactor neutrino detection are the same as for geo- neutrino detection. The event rates, however, differ because of the different energy window and analysis cuts. We summarize them in Table 2. If we take the depth to be 4 km, the total background rate is 5.6 / kt-yr, compared to the signal for a 1 TWth georeactor of 3.8 / kt-yr. The signal detection significance after one year is S / S + B = 1.2 sigmas. An exposure of 4 kt-yr increases this to 2.4 sigma, nearly 95% confidence level.

Table 2: Background sources and corresponding rate for mid-ocean georeactor neutrino detection. The 210Po background is assumed to be 20 times purer than the level for KamLAND’s liquid scintillator.

Background Rate (1/kt-yr) 9Li (2.15 km) 6.3 ± 1.2 9Li (3 km) 1.6 ± 0.3 9Li (4 km) 0.4 ± 0.1 210Po 0.7 ± 0.5 Accidentals 3.5 Commercial Reactors 1

As with geo-neutrino detection, we performed simulation studies of Hanohano’s sensitivity to the georeactor assuming various signal and background levels and an initial 1 kiloton-year exposure. If the 210Po level in the scintillator is as high as observed in KamLAND, and assuming a depth of 2.15 km, a 99% confidence level upper limit of 2 TWth can be set in the event that a georeactor does not exist. If one does exist, positive detection at the 99% level is possible only if the power is greater than 2.5 TWth. By reducing the 210Po rate to near-zero levels and by setting the depth at 4 km, the 99% upper limit can be reduced to 0.5 TWth. If a georeactor exits, the minimum power required for 99% confidence level detection is about 0.5 TWth.

Thus, the georeactor measurement is easier than the mantle/core geonu measurement. Under the same assumptions of 4 kilotons and 4 years operation, and dropping the accidentals by a factor of ten, the measurement of a 1 TWt georeactor would be achieved at 20 sigma over background, and to a precision of 13%.

7 4.0 Recommended Detector Specifications

Based on the foregoing results, we recommend that the detector fiducial volume be 4 kilotons and the total live time to be at least one year. We recommend that the depth be as large as possible, with 4 kilometers being sufficiently deep to comfortably accomplish physics goals. The liquid scintillator must be as free of 210Po as possible, with a goal of twenty times less than the initial KamLAND Radon contamination. This goal should be easily attainable since the high contamination level observed in KamLAND is almost certainly due to high radon levels in the mine environment in which the scintillator was placed for many months. Minimization of Radon levels at all stages of scintillator handling after purification is a high priority engineering goal.

In sum we find that a 4 kiloton deep ocean detector can achieve the physics goals of this experiment, and measure the low energy neutrino backgrounds to levels between one and two orders of magnitude better than past attempts.

8 1 Ph. D. thesis, Sanshiro Enomoto, Tohoku University (2005). 2 G. Fiorentini, M. Lissia, F. Mantovani, and R. Vannucci, hep-ph/0401085.