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1 ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ MEASUREMENT OF NEUTRINO FLUX FROM THE PRIMARY PROTONÄPROTON FUSION PROCESS IN THE SUN WITH THE BOREXINO DETECTOR O. Yu. Smirnov 1,, M. Agostini 2, S. Appel 2, G. Bellini 3, J. Benziger 4,D.Bick 5, G. Bonˇni 6,D.Bravo 7, B. Caccianiga 3, F. Calaprice 8, A. Caminata 9, P. Cavalcante 6, A. Chepurnov 10, K. Choi 11, D. D'Angelo 3,S.Davini 12,A.Derbin 13, L. Di Noto 9, I. Drachnev 12,A.Empl 14,A.Etenko 15, K. Fomenko 1, D. Franco 16, F. Gabriele 6, C. Galbiati 8, C. Ghiano 9, M. Giammarchi 3, M. Goeger-Neff 2, A. Goretti 8, M. Gromov 10, C. Hagner 5, E. Hungerford 14, Aldo Ianni 6, Andrea Ianni 8, K. Jedrzejczak 17,M.Kaiser 5, V. Kobychev 18, D. Korablev 1, G. Korga 6,D.Kryn 16, M. Laubenstein 6, B. Lehnert 19, E. Litvinovich 15, 20, F. Lombardi 6, P. Lombardi 3, L. Ludhova 3, G. Lukyanchenko 15, 20, I. Machulin 15, 20, S. Manecki 7, W. Maneschg 21, S. Marcocci 12, E. Meroni 3, M. Meyer 5, L. Miramonti 3, M. Misiaszek 6, 17, P. Mosteiro 8, V. Muratova 13, B. Neumair 2, L. Oberauer 2, M. Obolensky 16, F. Ortica 22, K. Otis 23, L. Pagani 9, M. Pallavicini 9, L. Papp 2, L. Perasso 9, A. Pocar 23, G. Ranucci 3,A.Razeto 6, A. Re 3, A. Romani 22, R. Roncin 6, 16, N. Rossi 6, S. Schéonert 2, D. Semenov 13,H.Simgen 21, M. Skorokhvatov 15, 20, A. Sotnikov 1, S. Sukhotin 15, Yu. Suvorov 15, 20, R. Tartaglia 6, G. Testera 9, J. Thurn 19, M. Toropova 15, E. Unzhakov 13, R. B. Vogelaar 7, F. von Feilitzsch 2, H. Wang 24,S.Weinz 25, J. Winter 25,M.Wojcik 17,M.Wurm 25,Z.Yokley 7, O. Zaimidoroga 1, S. Zavatarelli 9, K. Zuber 19,G.Zuzel 17 (The Borexino Collaboration) 1 Joint Institute for Nuclear Research, Dubna 2 Physics Department and Excellence Cluster Universeª, Technische Universitéat Méunchen, Garching, Germany osmirnov@jinr.ru

2 MEASUREMENT OF NEUTRINO FLUX Dipartimento di Fisica, Universita degli Studi e INFN, Milano, Italy 4 Chemical Engineering Department, Princeton University, Princeton, NJ, USA 5 Institut féur Experimentalphysik, Universitéat, Hamburg, Germany 6 INFN Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy 7 Physics Department, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA 8 Physics Department, Princeton University, Princeton, NJ, USA 9 Dipartimento di Fisica, Universita degli Studi e INFN, Genova, Italy 10 Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 11 Department of Physics and Astronomy, University of Hawaii, Honolulu, HI, USA 12 Gran Sasso Science Institute (INFN), L'Aquila, Italy 13 St. Petersburg Nuclear Physics Institute National Research Center Kurchatov Instituteª, Gatchina, Russia 14 Department of Physics, University of Houston, Houston, TX, USA 15 National Research Center Kurchatov Instituteª, Moscow 16 AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cite, Paris Cedex 13, France 17 M. Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 18 Kiev Institute for Nuclear Research, Kiev 19 Department of Physics, Technische Universitéat Dresden, Dresden, Germany 20 National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 21 Max-Planck-Institut féur Kernphysik, Heidelberg, Germany 22 Dipartimento di Chimica, Biologia e Biotecnologie, Universita e INFN, Perugia, Italy 23 Amherst Center for Fundamental Interactions and Physics Department, University of Massachusetts, Amherst, MA, USA 24 Physics and Astronomy Department, University of California Los Angeles (UCLA), Los Angeles, California, USA 25 Institute of Physics and Excellence Cluster PRISMA, Johannes Gutenberg-Universitéat Mainz, Mainz, Germany Neutrino produced in a chain of nuclear reactions in the Sun starting from the fusion of two protons for the ˇrst time has been detected in a real-time detector in spectrometric mode. The unique properties of the Borexino detector provided an opportunity to disentangle pp-neutrino spectrum from the background components. A comparison of the total neutrino ux from the Sun with solar luminosity in photons provides a test of the stability of the Sun on the 10 5 yr time scale and sets a strong limit on the power production in the unknown energy sources in the Sun of no more than 4% of the total energy production at 90% C.L. PACS: t INTRODUCTION The solar photon luminosity (a total power radiated in the form of photons into space) is determined by measuring the total solar irradiance by spacecrafts over the wide subrange of the electromagnetic spectrum, from X-rays to radio

3 1820 SMIRNOV O. YU. ET AL. wavelengths; it has been accurately monitored for decades. The luminosity L = W is measured for a precision of 0.4% with the largest uncertainty of about 0.3% due to disagreements between the measurements of different satellite detectors [1,2]. The energy lost by neutrinos adds L ν =0.023L to this value [3]. The solar luminosity constraint on the solar neutrino uxes can be written as [4] L 4π(1 a.u.) 2 = α i Φ i, (1) where 1 a.u. is the average EarthÄSun distance, the coefˇcient α i is the amount of energy provided to the star by nuclear fusion reactions associated with each of the important solar neutrino uxes, Φ i. The numerical values of the α's are determined to an accuracy of 10 4 and better. The estimated uncertainty in the luminosity of the Sun corresponds to less than 3% uncertainty in total solar neutrino ux. The Sun is a weakly variable star, its luminosity has short-term uctuations [2, 5]. The major uctuation occurs during the eleven-year solar cycle with an amplitude of about 0.1%. Long-term solar variability (such as the Maunder minimum in the 16th and 17th centuries) is commonly believed to be less than the short-term variations. Because of the relation (1) between the solar photon and neutrino luminosity, the measurement of the total neutrino luminosity will provide a test of the stability of the Sun at the time scale of yr [6], the time needed for the radiation born at the center of the Sun to arrive to its surface. Finding a disagreement between L and L ν would have signiˇcant long-term enviromental implications, and in the case of an agreement of two measurements it would be possible to limit the unknown sources of the solar energy, different from the known thermonuclear fusion of light elements in the pp-chain and CNO-cycle. The main neutrino sources in the Sun are the pp- and 7 Be reactions, providing roughly 91 and 7% of the total neutrino ux, respectively. Borexino already measured 7 Be neutrino ux with 5% precision [7], but till recent time the pp-neutrino ux was derived in a differential measurement using the data of solar detectors. Solar pp-neutrino measurement is a critical test of stellar evolution theory, discussion of the physics potential of the pp solar neutrino ux measurement can be found in [8Ä10] (at the moment of the discussion the parameters space for MSW solution were not established yet, thus the authors gave priority to this part of the physical potential). A number of projects aiming to perform pp-neutrino detection have been put forward in past two decades, but with all the time passed since the proposals, none of them started the operation facing the technical problems with realization. The principal characteristics of the proposals are presented in Table 1. The

4 MEASUREMENT OF NEUTRINO FLUX 1821 Table 1. Key characteristics of the solar neutrino projects sensitive to the pp-neutrino. The number of expected neutrino is calculated for the fraction of the neutrino spectrum above the threshold, but the region of sensitivity (limited, i.e., by signals-to-backgrounds ratio of 1) could be stricter Project, Threshold, pp events, Method Resolution Mass, t Reaction reference kev d 1 LENS 176 Yb, 301(ν) 7% Yb +νe 0.5 [13] MeV (8% nat. 176 Yb) 176 Lu +e INDIUM 115 In 118(ν) 5Ä10% In +νe 1.0 [14] MeV 115 Sn (613) + e GENIUS 76 Ge 11(e ) 0.3% 1 ν + e ν + e 1.8 [15] scatt. kev HERON Superuid 4 He 50(e ) 8.3% 10 ν + e ν + e 14 [16, 17] protons/phonons + uv kev XMASS Liquid Xe 50(e ) 17.5% 10 ν + e ν + e 14 [18] scintill. kev CLEAN Liquid Ne 20(e ) 135 ν + e ν + e 7.2 [19] 82(ν) HELLAZ He (5 atm), 100(e ) 6% 2000 m 3 ν + e ν + e 7 [20] TPC kev MOON Drift 168(ν) 12.4% FWHH 3.3 νe+ 100 Mo 1.1 [21] MeV 100 Tc +e MUNU TPC, CF4 100(e ) 16% FWHH 0.74 ν + e ν + e 0.5 [22] direction MeV (200 m 3 ) NEON He, Ne 20(e ) 16% FWHH 10 ν + e ν + e 18 [23] scintill. kev 10 t LS LS 170(e ) 10.5 kev 10 ν + e ν + e 1.8 [24, 25] kev Borexino LS 165(e ) 5% 75.5 ν + e ν + e 13.6 [26] MeV (ˇducial)

5 1822 SMIRNOV O. YU. ET AL. radiochemical experiments sensitive to the solar pp-neutrinos (SAGE [11] and GALLEX [12]) are not cited in the table, the combined best ˇt of the radiochemical and other solar experiments gives solar pp-neutrino ux of (6.0 ± 0.8) cm 2 s 1 [11] in a good agreement with expected value of 6.0 (1.000 ± 0.006) cm 2 s 1. A possibility to use ultrapure liquid organic scintillator as a low-energy solar neutrino detector for was for the ˇrst time discussed in [24, 25]. The authors come to the conclusion that a liquid scintillator detector with an active volume of 10 t is a feasible tool to register the solar pp-neutrino if operated at the target level of radiopurity for Borexino and good energy resolution (5% at 200 kev) is achieved. 1. BOREXINO DETECTOR The Borexino detector has a dome-like structure (see Fig. 1), 16 m in diameter, ˇlled with a mass of 2,400 t of highly puriˇed water which acts as the shield against the external radioactive emissions of the rocks and the environment that surrounds the facility. The water buffer acts also as an effective detector of residual cosmic rays. Within the volume of water a steel sphere is mounted which hosts 2,200 looking inward photomultiplier tubes providing 34% geometrical coverage. On the outer side of the stainless sphere 200 PMTs of the outer muon veto detector are mounted, these PMTs detect the Cherenkov light caused by muons passing through. The sphere contains one thousand tonnes of pseudocumene. Finally, the innermost core of the facility contains roughly 280 t of the scintillating liquid bounded within a 100-μm-thick nylon transparent bag with 4.2 mradius. The water and the pseudocumene buffers, as well as the scintillator itself, have a record-low level of radioactive purity. The energy of each event is measured using light response of the scintillator, and the position of the interaction is Fig. 1. Schematic view of the Borexino detector

6 MEASUREMENT OF NEUTRINO FLUX 1823 determined using timing information from the PMTs. The latter is important for the selection of the innermost cleanest part of the detector within 3 m radius, as only the internal 100 t of scintillator have the radioactive background low enough to allow the solar neutrino detection; the scintillator layer close to the nylon serves as an active shield against the γ originating from the nylon trace radioactive contamination. The threshold of the detector is set as low as possible to exclude triggering from the random dark count of PMTs. The Borexino has an excellent energy resolution for its size, this is the result of the high light yield of 500 p.e./mev/2000 PMTs. The energy resolution is as low as 5% at 1 MeV. 2. DATA PROCESSING The low-energy range, namely 165Ä590 kev, of the Borexino experimental spectrum has been recently carefully analyzed with a purpose of the pp-neutrino ux measurement [27]. The data were acquired from January 2012 to May 2013 and correspond to 408 live days of data taking. These data were collected at the beginning of the second phase of Borexino which had started after the additional puriˇcation of the liquid scintillator following the calibration campaign of 2010Ä 2011 [28]. The main backgrounds for the solar neutrino studies were signiˇcantly reduced in Phase 2, the content of 85 Kr is compatible with zero, and background from 210 Bi reduced by a factor of 3 to 4 compared to the values observed at the end of Phase 1 just before the puriˇcation. The experimental spectrum is presented in Fig. 2. The main features of the experimental spectrum can be seen in the ˇgure: the main contribution comes from 14 C decays at low energies (below 200 kev), the monoenergetic peak corresponds to 5.3 MeV α-particles from 210 Po decay. The statistics in the ˇrst bins used in the analysis is very high, of the order of events, demanding development of the very precise model for the studies Å the allowed systematic precision at low-energy part should be comparable with the statistical uctuations of 0.14% Data Analysis. The Borexino spectrum in the low-energy range is composed mainly of the events from β decays of 14 C present in liquid organic oscillator in trace quantities, its measured abundance with respect to 12 Cis(2.7 ± 0.1) g/g. The β decay of 14 C is an allowed ground-state to ground-state ( ) GamowÄTeller transition with an endpoint energy E 0 = ( ± 0.004) kev. In Borexino the amount of the active PMTs is high ( 2000), demanding setting of the high acquisition threshold in order to exclude detector triggering from random coincidence of dark count in PMTs: hardware trigger was set at the level of 25 PMTs in coincidence within 30-ns window, providing negligible random events count. The acquisition efˇciency corresponding to 25 triggered

7 1824 SMIRNOV O. YU. ET AL. Fig. 2 (color online). Borexino energy spectrum between 165 and 590 kev. The pp-neutrino component is shown in red (1), the 14 C spectrum in dark purple (7), and the synthetic pile-up in light purple (8). The large green peak is 210 Po α decays (6). 7 Be (dark blue, (2)), pep (3) and CNO (light blue (4)) solar neutrinos, and 210 Bi (orange (9)) spectra are almost at in this energy region

8 MEASUREMENT OF NEUTRINO FLUX 1825 PMTs is roughly 50% and corresponds to the energy release of 50 kev. In present analysis, the same as in the ppª analysis, the threshold was set at the lowest possible value at 60 triggered PMTs ( 160 kev). In independent measurement with laser the trigger inefˇciency was found to be below 10 5 for energies above 120 kev [26] Energy Resolution. The most sensitive part of the analysis is the behavior of the energy resolution with energy. The variance of the signal is smeared by the dark noise of the detector (composed of the dark noise from individual PMTs). In order to account for the dark noise, the data were sampled every two seconds forcing randomly the ˇred triggers. Some additional smearing of the signal is expected because of the continuously decreasing number of PMTs in operation. The amount of live PMTs is followed in real time and we know precisely its distribution, so in principle this additional smearing can be precisely accounted for. It was found that the following approximation works well in the energy region of interest: σn 2 = N(p 0 p 1 v 1 )+N 2 (v T (N)+v f ), where N = N 0 f(t) T is an average number of working PMTs during the period of the data taking; f(t) is a function describing the amount of working PMTs in time with f(0) = N 0. The last parameter here is v f (N) = f 2 (t) T f(t) 2 T,it is the variance of the f(t) function over the time period of the data taking. An additional contribution to the variance of the signal was identiˇed, it is the intrinsic width of the scintillation response. From the simple consideration this contribution reects the additional variations due to the uctuations of the delta electrons production and the energy scale nonlinearity. It should scale inversely proportional to the energy loss. Because of the limited range of the sensitivity to this contribution, basically restricted to the very tail of the 14 C spectrum, the precise energy dependence could be neglected and we used a constant additional term in the resolution. Taking it all together, the variance of the energy resolution (in terms of the used energy estimator) is σn 2 = N(p 0 p 1 v 1 )+N 2 (v T (N)+v f )+σd 2 + σint, 2 where σ d is a contribution of the dark noise (ˇxed) and σ int is a contribution from the intrinsic line shape smearing. The probability p 1 is linked to the energy estimator with relation n = Np Scintillation Line Shape. The shape of the scintillation line (i.e., the response of the detector to the monoenergetic source uniformly distributed over the detector's volume) is another sensitive component of the analysis. A common approximation with a normal distribution is failing to describe the tails of the MC-generated monoenergetic response already at the statistics of the order of 10 3 events. This was notiˇed already in the ˇrst phase of Borexino and the approximation of the scintillation line shape with generalized gamma function [29]

9 1826 SMIRNOV O. YU. ET AL. have been used to ˇt monoenergetic 210 Po peak in the solar 7 Be neutrino analysis [7, 30, 31]. The generalized gamma function (GGC) was developed for the energy estimator based on the total collected charge, but it provided a reasonable approximation for the energy estimator based on the number of triggered PMTs given the moderate statistics corresponding to the total amount of the events in 210 Po peak. The ˇt quality of the 210 Po peak is rather insensitive to the residual deviations in the tails. This is not the case for the precise 14 C spectrum modeling, as all the events in the fraction of the 14 C spectrum above the energy threshold originate from the spectral smearing. An ideal detector's response to the point-like monoenergetic source at the center is a perfect binomial distribution and it would be well approximated by the Poisson distribution. When dealing with a real response one should adjust the base distributionª width to take into account at least the additional smearing of the signal due to various factors. The problem with binomial base functionª (or with its Poisson approximation) is that its width is deˇned by the mean value. In case of Poisson the variance of the signal coincides with mean μ. A better approximation of the response function was tested with MC model, namely, the scaled Poisson (SP) distribution: f(x) = μxs (xs)! e μ, (2) featuring two parameters that could be evaluated using expected mean and variance of the response: s = σ2 n n n2 and μ = σn 2. (3) The agreement of the approximation and the detector response function was tested with Borexino MC model and it was found that at low energies (2) better reproduces the scintillation line shape compared to the generalized gamma function up to the statistics of 10 8, while at energies just above the 14 Ctail both distributions give comparable approximation. The quality of the ˇt was estimated using χ 2 criterion, for example, with 10 7 total statistics (these events are uniformly distributed in the detector and then the FV is selected) for n =50 (approximately 140 kev) we found χ 2 /n.d.f. =88.0/61 for the GGC compared to χ 2 /n.d.f. =59.3/61 for the SP distribution. As proven by MC tests, the SP distribution as a base function works well in the energy region of interest despite of the additional smearing due to the factors enlisted in the previous paragraph. This is a result of the absorptionª of the relatively narrow nonstatistical distributions by the much wider base function; as follows from MC, such an absorption results in the smearing of the total distribution without changing its shape. As was noted above, the ˇt was performed in n scale. All the theoretical spectra involved in the ˇt were ˇrst translated into the n scale and then smeared

10 MEASUREMENT OF NEUTRINO FLUX 1827 using resolution function (2) with μ and scale factor s calculated using (3). As is clear from the discussion above, the detector's response has the shape described by (2) only in the naturalª n scale. If the measured values of n were converted into the energy, the shape would be deformed because of the nonlinearity of the energy estimator scale with respect to the energy, complicating the construction of the precise energy response Standard Fit. The standardª options of the spectral ˇt are: number of triggered PMTs in a ˇxed time window of 230 ns (npmts) used as energy estimator; 62Ä220 npmts ˇt range; (75.5 ± 1.5) t ˇducial volume (deˇned by the condition R<3.02 mand Z < 1.67 m). The rate of the solar neutrinos is constrained either at the value found by Borexino in the different energy range (R( 7 Be) =(48± 2.3) cpd [7]) or ˇxed at the prediction of the SSM in the SMW/LMA oscillation scenario (R(pep) = 2.80 cpd, R(CNO) = 5.36 cpd). All counts here and below are quoted for 100 t of LS. The 14 C rate was constrained at the value found in independent measurement with the second cluster R( 14 C)=(40± 1) Bq (or R( 14 C)=(3.456 ± ) 10 6 cpd). The synthetic pile-up rate was constrained at the values found with the algorithm. The normalization factors for other background components were mainly left free ( 85 Kr, 210 Bi, and 210 Po) and the ˇxed rate of 214 Pb (R( 214 Pb) = 0.06 cpd) was calculated on the base of the amount of identiˇed radon events. The light yield and two energy resolution parameters (v T and σ int ) are left free. The position of 210 Po is also left free in the analysis, decoupling it from the energy scale Systematics Study. An evident source of systematics is the uncertainty of the FV. The FV mass is deˇned using position reconstruction code, residual bias in the reconstructed position is possible. The systematic error of the position reconstruction code was deˇned during the calibration campaign, comparing the reconstructed source position with the nominal one [27, 28]. At the energies of interest the systematic error on the FV mass is 2%. The stability and robustness of the measured pp-neutrino interaction rate was veriˇed by performing ˇts varying initial conditions, including ˇt energy range, method of pile-up construction, and energy estimator. The distribution of the central values for pp-neutrino interaction rates obtained for all these ˇt conditions was then used as an estimate of the maximal systematic error (partial correlations between different factors are not excluded). The remaining external background in the ˇducial volume at energies relevant for the pp-neutrino study is negligible. In the particular case of the very lowenergy part of the spectrum, the ˇt was repeated in ˇve smaller ˇducial volumes (with smaller radial and/or z-cut), which yields very similar results, indicating the absence of the inuence of the external backgrounds at low energies.

11 1828 SMIRNOV O. YU. ET AL. 3. RESULTS AND IMPLICATIONS The solar pp-neutrino interaction rate measured by Borexino is pp = (144 ± 13(stat.) ± 10(syst.) cpd/100 t, compatible with the expected rate of pp theor = (131 ± 2) cpd/100 t. The corresponding total solar pp-neutrino ux is φ pp (Borex) =(6.6 ± 0.7) cm 2 s 1, in a good agreement with the combined best ˇt value of the radiochemical and other solar experiments φ pp (other) = (6.0 ± 0.8) cm 2 s 1 [11]. Both are in agreement with the expected value of 6.0 (1.000 ± 0.006) cm 2 s 1. The survival probability for electron neutrino from pp-reaction is P ee (Borex) =0.64 ± This is the fourth energy range explored by Borexino, all the Borexino results on the electron neutrino survival probability are presented graphically in Fig. 3. Taking into account that measurements of Borexino and other experiments are independent, the results can be combined: φ pp =(6.37 ± 0.46) cm 2 s 1. The electron neutrino survival probability measured in all solar but Borexino experiment is P ee (other) =0.56 ± 0.08, combining it with Borexino one, we obtain P ee =0.60 ± 0.07, well compatible with theoretical prediction of the MSW/LMA model All available measurements of the solar neutrino uxes are shown in Table 2. The total energy production in the solar reactions observed till now (by detecting corresponding neutrino uxes) is (4.04±0.28) W s 1 in a good agreement with a Fig. 3. Survival probabilities for electron neutrino (Borexino only data from [7,27,32,33])

12 MEASUREMENT OF NEUTRINO FLUX 1829 Table 2. The Standard Solar Model predictions (for high metallicity and low metallicity abundances) and current experimental status of the solar neutrino ux measurement. The limits are given for 90% C.L. The corresponding energy release is calculated in the last column Units L, Reaction GS98 [34] AGS09 [35] Measurement MeV/1ν cm 2 s W s ± 0.8 [11] pp 5.98 ± ± ± 0.7 [26] ± ± 0.28 pep 1.44 ± ± ± 0.3 [33] ± Be 5.00 ± ± B 5.58 ± ± ± 0.24 [7] ± ± 0.16 [36] ± hep 8.0 ± ± < 23 [37] 13 N 2.96 ± ± CNO: 15 O 2.23 ± ± < 7.4 [33] 17 F 5.52 ± ±

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