Detecting the Upturn of the Solar $^8$B Neutrino Spectrum with LENA

LENA (Low Energy Neutrino Astronomy) has been proposed as a next generation 50 kt liquid scintillator detector. The large target mass allows a high precision measurement of the solar $^8$B neutrino spectrum, with an unprecedented energy threshold of 2 MeV. Hence, it can probe the MSW-LMA prediction for the electron neutrino survival probability in the transition region between vacuum and matter-dominated neutrino oscillations. Based on Monte Carlo simulations of the solar neutrino and the corresponding background spectra, it was found that the predicted upturn of the solar $^8$B neutrino spectrum can be detected with 5 sigma significance after 5 y.


Introduction
The MSW-LMA prediction for the survival probability of solar electron neutrinos P ee (E ν ) has been confirmed in the energy region of vacuum (E ν 1 MeV) [1] and matter dominated oscillations (E ν 5 MeV) [2,3,4]. Nevertheless, the predicted upturn of the 8 B neutrino spectrum in the transition region between vacuum and matter dominated oscillations could not be detected, as Water-Cerenkov detectors (WCDs) have a too high energy threshold and current liquid scintillator detectors (LSDs) are too small. A test of the MSW-LMA prediction in the transition region is important as new physiscs, like non-standard neutrino interactions [5] or light sterile neutrinos (m ν1 < m ν0 < m ν2 , where the sterile neutrino ν s is mainly present in the mass eigenstate ν 0 ) [6], could influence P ee in this region.
Compared to current solar neutrino detectors, the advantage of the proposed LENA detector [7] is the combination of a ∼200 keV energy threshold as well as a huge target mass. Thus, the external gamma background, which currently prevents a measurement of the solar 8 B spectrum below 3 MeV in Borexino [2], can be suppressed by self-shielding. This enables the measurement of the 8 B spectrum with an unprecedented threshold of 2 MeV. Hence, LENA can probe the MSW-LMA prediction over a large part of the transition region.
The present work discusses the sensitivity of LENA to detect the predicted upturn of the 8 B spectrum at low energies. In Sec. 2 the planned detector setup is briefly presented. The simulation of the expected solar neutrino and background spectra is discussed in Sec. 3 and Sec. 4. The analysis of the simulated data is presented in Sec. 5. Finally, the detection potential for the upturn of the solar 8 B spectrum is discussed in Sec. 6.

The LENA Detector
The neutrino target consists of ∼50 kt of liquid scintillator based on linear-akyl-benzene (LAB), that is enclosed in a cylinder with 14 m radius and 96 m height [8]. The emitted light is detected by photomultiplier tubes (PMTs) that are mounted with non imaging light concentrators (LCs) inside individual pressure encapsulations that are filled with a non-scintillating buffer liquid. The apertures of these optical modules are located at the boundary of the target volume at a radius of 14 m. The corresponding effective optical coverage is ∼ 30 %. The radius of the cylindrical concrete tank is 16 m, so that the target volume is shielded by 2 m of liquid scintillator. A muon veto formed by gas detectors is placed above the detector tank and provides auxiliary information for the reconstruction of cosmic muon tracks. In order to identify and reconstruct inclined muon tracks, an instrumented water volume surrounding the tank serves as an active Water-Čerenkov muon veto and shields the target volume from fast neutrons.
The preferred location for the detector is the Pyhäsalmi mine in Finland. The detector cavern is shielded by 1400 m of rock coverage, corresponding to ∼4000 m water equivalent (w.e.). Hence, the cosmic muon flux will be reduced to ∼ 0.2 m −2 h −1 [9], which is about five times less than in Borexino.

Simulation of the Solar Neutrino Spectra
There are two possible detection channels for solar 8 B neutrinos in LENA. The elastic neutrino electron scattering (ES) channel and charged current reactions of ν e 's on 13 C ( 13 C channel).

Elastic Neutrino Electron Scattering
In the ES channel, a neutrino scatters elastically off an electron, which is subsequently detected. As the energy of the recoil electron depends on the scattering angle, the measured recoil spectrum is a convolution of the solar neutrino spectrum and the electron recoil spectrum at a given neutrino energy.
The simulation of the electron recoil spectra was split into two parts. First of all, the differential events rates for neutrinos from different fusion reactions were calculated acording to the BS05(AGS, OP) standard solar model [10]. Using these differential events rates, 10 6 electron events were simulated with a GEANT4 [11] based Monte Carlo (MC) simulation of the LENA detector [12]. The events were homogeneously distributed over the target volume, so that possible position dependent effects are considered. Afterwards, the visible energy was reconstructed from the event position and the number of detected photons [12]. Figure 1 shows the resulting electron recoil spectra. At low energies, the 7 Be and the pep neutrinos have the largest event rate, preventing a detection of 8 B neutrinos below ∼ 1.4 MeV. Above

Charged Current Reaction on 13 C
The charged current reaction of electron neutrinos on 13 C (ν e + 13 C → 13 N + e − ) has a threshold of 2.2 MeV. Thus, it is another possible detection channel for solar 8 B neutrinos. Due to the kinematics of the reaction, the recoiling 13 N nucleus has only a few keV kinetic energy. Hence, the neutrino energy can be reconstructed on an event-by-event basis by measuring the electron energy. The subsequent β + decay of the 13 N nucleus (τ = 862 s) causes a delayed coincidence signal, which can be used to distinguish signal from background events. Hence, 13 C events will be selected by the spatial and timing coincidence between prompt and delayed signals. Although the cross section is about 10 times larger than the cross section of the ES channel [17], the event rate is almost two orders of magnitude lower due to the low isotopic abundance of 13 C (1.07 %). Nevertheless, the measurement of the unconvoluted shape of the solar 8 B neutrino spectrum with the 13 C channel allows an energy dependent measurement of P ee , as the unoscillated solar 8 B flux is known from the NC measurements of the SNO experiment [18].

Simulation of the Background Spectra
There are three different types of background present in the ES channel: external gamma rays that are emitted by the tank, the PMTs and the LCs, cosmogenic radioisotopes produced in-situ by traversing muons and intrinsic radioactive background. A background for the 13 C channel is caused by the accidental coincidences of these backgrounds and of ES interactions of solar neutrinos. Based on the assumed radiopurity of the tank [8], PMTs and LCs [19] (see Table 1), the external gamma ray background was simulated with the GEANT4-based LENA Monte Carlo simulation [12]. It was found that no external gamma background is present above 3.5 MeV. For lower energies, the rate can be reduced to a negligible level by applying a fiducial volume cut. The correspindig fiducial volume is 48 kt above and 19 kt below 3.5 MeV.
Cosmogenic radioisotopes are produced inside the target volume by spallation reactions of cosmic muons on carbon nuclei. The majority of the produced radioisotopes have a lifetime of less than ∼ 1 s [2,20]. Hence, the decays can easily be identified by the time coincidence to the parent muon, without introducing a large dead time. The remaining cosmogenic isotopes with a longer lifetime are 11 C (β + ), 10 C (β + ) and 11 Be (β − ) (see Table 2). The spectral shapes of these isotopes were obtained from the GEANT4-based LENA Monte Carlo simulation. Afterwards, the measured rates of the Borexino experiment [2,1] have been scaled to the Pyhäsalmi location, using the muon flux of the two sites 1 . Below 2 MeV, the 11 C background is about two orders of magnitude larger than the solar 8 B neutrino signal. Hence, the end of the 11 C spectrum defines the energy threshold for the detection of solar 8 B neutrinos. As 10 C and 11 Be have a much shorter lifetime than 11 C, it is possible to reduce the background from these isotopes by vetoing a cylinder with 2 m radius around each traversing muon for ∆t = 4 · τ ( 10 C) = 111.2 s. As the muon rate in the fiducial volume is ∼ 135 h −1 ,    Besides cosmogenic isotopes, there is also a background from intrinsic radioimpurities in the scintillator. As the amount of radioimpurities in the LENA detector is not known at the moment, it was assumed in the following that the radiopurity levels of the Borexino experiment 2 (c( 232 Th) = (6.5 ± 1.5) · 10 −18 g/g) [2] are reached. The only intrinsic beta-emitting 3 radioisotopes in the Borexino detector with a Q-Value above 2 MeV are 214 Bi ( 238 U chain, Q=3.3 MeV) and 208 Tl ( 232 Th chain, Q=5.0 MeV) [2]. 214 Bi can be tagged by the subsequent decay of 214 Po and is thus neglected in the following [2]. 208 Tl is produced by the alpha decay of 212 Bi which also decays into 212 Po (τ = 0.4µs) with 64 % branching ratio. Hence, the amount of 208 Tl can be determined from the observed number of 212 Bi-212 Po concidences. Figure  2 shows the resulting cosmogenic and intrinsic radioactive background spectra.
The accidental background for the 13 C channel has been calculated (see Figure 3) based on these spectra. Due to the relatively long life time of the 13 N nucleus, a large amount of background is present below 5 MeV reconstructed neutrino energy. Above 5 MeV, the accidental background is at least one order of magnitude below the solar 8 B signal. Thus, the energy threshold for the 13 C channel is set to 5 MeV neutrino energy.

Analysis Procedure
In order to determine the sensitivity for the detection of the upturn of the solar 8 B neutrino spectrum, the potential to distinguish the MSW-LMA prediction from a simple test model with P ee (E ν ) = const was investigated. Using the previously simulated neutrino and background spectra, 10 5 five year long measurements of the 8 B neutrino spectrum were simulated with the ROOT package [21]. Afterwards, the MC data sets were analyzed independently for the 13 C channel and the ES channel. The accidental background was subtracted from the 13 C channel to retrieve the oscillated solar 8 B spectrum. Afterwards, this spectrum was divided by the unoscillated solar 8 B spectrum to determine P ee (E ν ). Note that the accidental background spectrum can be precisely determined from the measured total spectrum of the ES channel. Finally, P ee (E ν ) was fitted with the MSW-LMA pre-diction and with the P ee (E ν ) = const model, using a χ 2 minimization. The normalization was treated as a free nuisance parameter in both cases. Hence, this analysis is only sensitive to the shape of P ee (E ν ) and is thus unaffected by the uncertainty of the solar 8 B flux. Figure 4 shows the result for one example measurement. While the MSW-LMA prediction is preferred one, the statistical significance is not enough to exclude the P ee (E ν ) = const model. Overall, the average exclusion significance in the 13 C channel is below 1 σ.  Figure 4: The measured electron neutrino survival probability after 5 years, using the 13 C channel. Furthermore, a fit with the MSW-LMA prediction (depicted in green) and with Pee = const (depicted in red) is shown.
For the ES channel, it is not possible to directly calculate P ee from the measured 8 B spectrum, as the neutrino energy can not be reconstructed on an event-by-event basis. Thus, the simulated spectrum was fitted with the expected spectrum according to the MSW-LMA prediction and the P ee (E ν ) = const hypothesis, using a χ 2 minimization with free parameters for the solar neutrino and the corresponding background rates. In order to maximize the statistics, the full 48 kt fiducial volume was used above 3.5 MeV, as no external gamma background is present at these energies, while the 19 kt fiducial volume was used below 3.5 MeV. As the contributions of the cosmogenic and intrinsic radioactive background can be measured independently, pullterms were added to the χ 2 function to maximize the sensitivity [22]: where k is the number of parameters with prior information, λ j is the fit value of the parameter j and µ j is the expected value of the parameter j, with σ λj uncertainty. The uncertainty for the cosmogenic backgrounds were taken from the Kam-LAND ( 10 C and 11 Be) [20] and the Borexino experiment ( 11 C) [1], while the uncertainty for the 208 Tl rate was estimated from the expected number of 212 Bi-212 Po coincidences. Figure 5 shows the results of the fit for one example measurement. Above ∼ 3 MeV visible energy, the data is consistent with both the MSW-LMA prediction and with the P ee = const hypothesis. But below ∼ 3 MeV, the MSW-LMA prediction is clearly favored, which shows the importance of measuring the 8 B spectrum below 3 MeV, which is not possible with current WC and LS detectors.  The total spectrum for the ES channel after 5 y measuring time. Furthermore, a fit according to the MSW-LMA prediction (depicted in green) and according to Pee = const (depicted in red) is shown.
In the last step, the results from the 13 C and the ES channel were combined by adding the χ 2 values of the corresponding fits. Using these values and the number of degrees of freedom, the probability that the MC data sample is consistent with the MSW-LMA prediction or the P ee (E ν ) = const model was calculated. In order to suppress statistical fluctuations, this process was repeated for each data sample. Finally, the probability that the P ee (E ν ) = const model can be excluded with 5 σ significance, which is equivalent to a detection of the upturn of the 8 B spectrum, was calculated, assuming that the MSW-LMA prediction is correct.  Table 3: The probability to detect the upturn of the solar 8 B spectrum, for measuring times ranging from 2 y to 5 y. Table 3 shows the probability for a 5 σ detection of the upturn of the solar 8 B neutrino spectrum, as a function of the measurement time. After 2 years, the upturn can be detected at 5 σ significance for over 40 % of all MC data sets, assuming that the MSW-LMA prediction is correct. After 5 y, the upturn was detected for each data set. Hence, in case that the upturn is not detected after 5 y, the MSW-LMA prediction would be ruled out and new physics must be present that reduce P ee (E ν ) in the transition region. Comparing the two detection channels, it was found that the sensitivity of the ES channel is much larger than the 13 C channel, due to the larger statistics. Nevertheless, the 13 C channel still provides an important cross check of the results.

Results
While the amount of cosmogenic background can be precisely estimated for the assumed rock coverage, it is much harder to estimate the intrinsic radioactive background. Hence, the analysis was repeated for a 100 times larger instrinsic radioactive background than in Borexino. Table 4 shows the detection potential for the upturn of the solar 8 B neutrino spectrum in this pessimistic scenario. While the detection potential is of course decreased, the effect of the increased background is not very strong and the upturn can still be detected at 5 σ significance after 5 y. The reason for this behaviour is that the important energy region below 3 MeV is not affected by the larger 208 Tl background. Hence, a precision test of the MSW-LMA prediction is possible with LENA even if radiopurity conditions are substantially worse than in Borexino.

Conclusions
Present-day experiments lack the capability for a precision measurement of the electron neutrino survival probability P ee in the transition region between vacuum and matter dominated oscillations measuring time prob. for a 5 σ det.
2 years 34.6 % 3 years 86.7 % 4 years 99.4 % 5 years > 99.9 % Table 4: The probability to detect the upturn of the solar 8 B spectrum, for measuring times between 2 y and 5 y and for a 100 times larger intrinsic radioactive background than in Borexino.
(1 MeV E ν 5 MeV). LENA will offer an excellent opportunity to close this gap in the determination of P ee by a high-statistics, low-energythreshold measurement of the solar 8 B neutrino spectrum. Due to its large target mass, the external gamma background, that currently prevents a measurement below 3 MeV electron recoil energy in Borexino, can be efficiently suppressed by a stringent fiducial volume cut. This allows a measurement of the solar 8 B neutrino spectrum with an unprecedented energy threshold of 2 MeV. In the present work, the detection potential for the spectral upturn of the solar 8 B spectrum that is predicted by the MSW-LMA solution was analyzed. It was found that the spectral upturn can be detected at 5 σ significance after 5 y measuring time, even if the intrinsic radiopurity level of the scintillator is two orders of magnitude worse than achieved in Borexino. In case that the upturn of the solar 8 B neutrino spectrum is not found, the measurement would rule out the MSW-LMA prediction and show that new physics decrease P ee in the transition region between vacuum and matter dominated oscillations.