First Simultaneous Precision Spectroscopy of pp, 7Be, and pep Solar Neutrinos withBorexino Phase-II

M. Agostini,1 K. Altenmuller,2 S. Appel,2 V. Atroshchenko,3 Z. Bagdasarian,4 D. Basilico,5 G. Bellini,5 J. Benziger,6

D. Bick,7 G. Bonfini,8 D. Bravo,9, 5 B. Caccianiga,5 F. Calaprice,10 A. Caminata,11 S. Caprioli,5 M. Carlini,8

P. Cavalcante,8, 9 A. Chepurnov,12 K. Choi,13 L. Collica,5 D. D’Angelo,5 S. Davini,11 A. Derbin,14 X.F. Ding,1 A. Di

Ludovico,10 L. Di Noto,11 I. Drachnev,1, 14 K. Fomenko,15 A. Formozov,15, 5, 12 D. Franco,16 F. Froborg,10

F. Gabriele,8 C. Galbiati,10 C. Ghiano,8 M. Giammarchi,5 A. Goretti,8 M. Gromov,12 D. Guffanti,1 C. Hagner,7

T. Houdy,16 E. Hungerford,17 Aldo Ianni†,8 Andrea Ianni,10 A. Jany,18 D. Jeschke,2 V. Kobychev,19 D. Korablev,15

G. Korga,17 D. Kryn,16 M. Laubenstein,8 E. Litvinovich,3, 20 F. Lombardi‡,8 P. Lombardi,5 L. Ludhova,4, 21

G. Lukyanchenko,3 L. Lukyanchenko,3 I. Machulin,3, 20 G. Manuzio,11 S. Marcocci,1, 11 J. Martyn,22 E. Meroni,5

M. Meyer,23 L. Miramonti,5 M. Misiaszek,18 V. Muratova,14 B. Neumair,2 L. Oberauer,2 B. Opitz,7 V. Orekhov,3

F. Ortica,24 M. Pallavicini,11 L. Papp,2 O. Penek,4, 21 N. Pilipenko,14 A. Pocar,25 A. Porcelli,22 G. Ranucci,5

A. Razeto,8 A. Re,5 M. Redchuk,4, 21 A. Romani,24 R. Roncin,8, 16 N. Rossi,8 S. Schonert,2 D. Semenov,14

M. Skorokhvatov,3, 20 O. Smirnov,15 A. Sotnikov,15 L.F.F. Stokes,8 Y. Suvorov,26, 3 R. Tartaglia,8 G. Testera,11

J. Thurn,23 M. Toropova,3 E. Unzhakov,14 A. Vishneva,15 R.B. Vogelaar,9 F. von Feilitzsch,2 H. Wang,26

S. Weinz,22 M. Wojcik,18 M. Wurm,22 Z. Yokley,9 O. Zaimidoroga,15 S. Zavatarelli,11 K. Zuber,23 and G. Zuzel18

(Borexino Collaboration∗)1Gran Sasso Science Institute (INFN), 67100 L’Aquila, Italy

2Physik-Department and Excellence Cluster Universe, Technische Universitat Munchen, 85748 Garching, Germany3National Research Centre Kurchatov Institute, 123182 Moscow, Russia

4Institut fur Kernphysik, Forschungszentrum Julich, 52425 Julich, Germany5Dipartimento di Fisica, Universita degli Studi e INFN, 20133 Milano, Italy

6Chemical Engineering Department, Princeton University, Princeton, NJ 08544, USA7Institut fur Experimentalphysik, Universitat Hamburg, 22761 Hamburg, Germany

8INFN Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy9Physics Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

10Physics Department, Princeton University, Princeton, NJ 08544, USA11Dipartimento di Fisica, Universita degli Studi e INFN, 16146 hGenova, Italy

12Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics, 119234 Moscow, Russia13Department of Physics and Astronomy, University of Hawaii, Honolulu, HI 96822, USA

14St. Petersburg Nuclear Physics Institute NRC Kurchatov Institute, 188350 Gatchina, Russia15Joint Institute for Nuclear Research, 141980 Dubna, Russia

16AstroParticule et Cosmologie, Universite Paris Diderot, CNRS/IN2P3, CEA/IRFU,Observatoire de Paris, Sorbonne Paris Cite, 75205 Paris Cedex 13, France17Department of Physics, University of Houston, Houston, TX 77204, USA

18M. Smoluchowski Institute of Physics, Jagiellonian University, 30059 Krakow, Poland19Kiev Institute for Nuclear Research, 03680 Kiev, Ukraine

20National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia21RWTH Aachen University, 52062 Aachen, Germany

22Institute of Physics and Excellence Cluster PRISMA, Johannes Gutenberg-Universitat Mainz, 55099 Mainz, Germany23Department of Physics, Technische Universitat Dresden, 01062 Dresden, Germany

24Dipartimento di Chimica, Biologia e Biotecnologie, Universita degli Studi e INFN, 06123 Perugia, Italy25Amherst Center for Fundamental Interactions and Physics

Department, University of Massachusetts, Amherst, MA 01003, USA26Physics and Astronomy Department, University of California Los Angeles (UCLA), Los Angeles, California 90095, USA

(Dated: December 4, 2017)

We present the first simultaneous measurement of the interaction rates of pp, 7Be, and pep solarneutrinos performed with a global fit to the Borexino data in an extended energy range (0.19-2.93) MeV. This result was obtained by analyzing 1291.51 days of Borexino Phase-II data, collected

† Also at: Laboratorio Subterraneo de Canfranc, Paseo de losAyerbe S/N, 22880 Canfranc Estacion Huesca, Spain

‡ Present address: Physics Department, University of California,San Diego, CA 92093, USA∗ Corresponding author: spokeperson-borex@lngs.infn.it

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between December 2011 and May 2016 after an extensive scintillator purification campaign. Wefind: rate(pp) = 134± 10 (stat) +6

−10 (sys) cpd/100 t, rate(7Be) = 48.3± 1.1 (stat) +0.4−0.7 (sys) cpd/100 t,

and rate(pep) =2.43 ± 0.36 (stat)+0.15−0.22 (sys) cpd/100 t. These numbers are in agreement with and

improve the precision of our previous measurements. In particular, the interaction rate of 7Be ν’s ismeasured with an unprecedented precision of 2.7%, showing that discriminating between the highand low metallicity solar models is now largely dominated by theoretical uncertainties. The absenceof pep neutrinos is rejected for the first time at more than 5σ.

An upper limit of 8.1 cpd/100 t (95% C.L.) on the CNO neutrino rate is obtained by setting anadditional constraint on the ratio between the pp and pep neutrino rates in the fit. This limit hasthe same significance as that obtained by the Borexino Phase-I (currently providing the tightestbound on this component), but is obtained by applying a less stringent constraint on the pep ν flux.

Solar neutrinos emitted by fusion reactions occurringin the Sun provide a unique and direct way to study theinterior of our star. The main contribution to the so-lar luminosity (∼99%) comes from reactions belongingto the pp chain, while the CNO cycle is expected to playa sub-dominant role [1]. The 50-year-long experimentaleffort to study solar neutrinos [2, 3] has been extremelyrewarding both in terms of solar physics, by confirmingthe Standard Solar Model (SSM) predictions [4], and interms of particle physics, by giving a substantial contri-bution to the discovery of neutrino flavour oscillations [5].

Precise spectroscopy of solar neutrinos (νe’s) aims atstudying the details of the solar-neutrino energy spec-trum by disentangling the contributions from differ-ent reactions (pp, 7Be, pep, 8B, and CNO neutrinos).The solar neutrino spectrum [4, 6] is dominated by thelow-energy νe’s coming from the primary pp reaction(Eν < 0.42 MeV) and extends up to ∼ 18.8 MeV (max-imum energy of the hep neutrinos). It also features twomono-energetic lines from 7Be ν’s (Eν = 0.384 MeV and0.862 MeV) and one mono-energetic line from pep ν’s(Eν = 1.44 MeV). Neutrinos from the CNO cycle are ex-pected to have a continuous energy spectrum extendingup to 1.74 MeV.

On the one hand, if SSM predictions of solar fluxesare assumed, measuring the solar neutrino rates for dif-ferent reactions helps to pin down the neutrino survivalprobability Pee for different energies, thus probing theconsistency of the MSW-LMA model [7] and can set con-straints on possible deviations, e.g. due to non standardinteractions (NSI) [8].

On the other hand, if oscillation parameters are as-sumed, the study of specific components can cross-checkthe SSM predictions. In particular, the experimentalmeasurements of 7Be, 8B or CNO neutrinos, which aresensitive to the solar metallicity, can help to settle thehigh (HZ) versus low (LZ) metallicity issue [4].

We present here the first simultaneous precision mea-surement of the interaction rates of pp, 7Be, and pepν’s, together with the best limit on the rate of CNO ν’s,obtained with Borexino. While our previous results con-cerning pp [9], 7Be [3], and pep ν’s [10] were obtainedseparately by analyzing data in restricted energy ranges,this work provides the first global analysis of several so-

lar neutrino components over an energy interval between0.19 MeV and 2.93 MeV (recoil-electron kinetic energy).In addition, we improve the precision of our previousmeasurements thanks to a larger exposure, a reductionof the most relevant backgrounds, and a more accuratedescription of the detector response.

The Borexino experiment is located at the LaboratoriNazionali del Gran Sasso in Italy. The core of the detec-tor [11] is 278 t of ultra-pure organic liquid scintillator,namely PC (pseudocumene, 1,2,4-trimethylbenzene) asa solvent and 1.5 g/l of fluor PPO (2,5-diphenyloxazole)as a solute, contained in a 125µm-thick nylon vesselof 4.25 m radius, surrounded by 2212 photomultipliers(PMTs). Neutrinos of any flavour interact by elasticscattering with electrons, whose recoil produces scin-tillation light (∼500 photoelectrons/MeV/2000 PMTs).The number of target electrons in the scintillator is(3.307 ± 0.003) × 1031/ 100 t. A non-scintillating bufferfills the space between the nylon vessel and a stainless-steel sphere (SSS) of 6.85 m radius, which supports thePMTs. The entire detector is enclosed in a cylindricaltank filled with ultra-pure water and instrumented with208 PMTs, acting as an active Cherenkov muon veto andas a passive shield against external γ’s and neutrons.

The analysis is based on data collected between De-cember 14th, 2011 to May 21st, 2016, which correspondsto an exposure of 1291.51 days × 71.3 t (∼ 1.6 times theexposure used in [3]). This period belongs to the so-calledBorexino Phase-II, which started after an extensive pu-rification campaign with 6 cycles of closed-loop water ex-traction, which has significantly reduced the radioactivecontaminants: 238U < 9.4× 10−20 g/g (95% C.L.), 232Th< 5.7× 10−19 g/g (95% C.L.), 85Kr, reduced by a fac-tor ∼ 4.6, and 210Bi, reduced by a factor ∼ 2.3 (see thiswork).

The expected solar ν’s interaction rate in Borexinoranges from ∼few counts to ∼100 counts per day (cpd)in 100 t depending on the neutrino component. Togetherwith the lack of directionality from the scintillation light,this demands a high radio-purity of the detector, a deepunderstanding of the backgrounds, and an accurate mod-elling of the detector response.

The energy, position, and pulse-shape of each eventare reconstructed by exploiting the number of detected

3

photons and their detection times. At 1 MeV, the energyand position reconstruction resolution are ∼ 50 keV and∼ 10 cm respectively. The analysis is performed using dif-ferent energy estimators: Np (total number of triggeredPMTs), Nh (number of detected photons, including mul-

tiple photons on the same PMT), Ndt1(2)p (number of trig-

gered PMTs within a fixed time interval of 230 (400) ns),or Npe (total charge of all collected hits). To accountfor the variation in the number of working channels asa function of time, all energy estimators are normalizedto 2000 PMTs [12]. The hardware energy threshold isNp> 20, which corresponds to ∼50 keV.

Events are selected using the same cuts described in [9]:we remove internal (external) muons [13] and we applya 300 (2) ms veto to suppress cosmogenic backgrounds.The total dead-time introduced by these vetoes is 1.5%.We remove 214Bi -214Po fast coincidences from the 238Uchain and unphysical noise events. The fraction of goodevents removed by these cuts, estimated using MonteCarlo (MC) simulations [14] and calibration data [15],is ∼ 0.1%. Background from sources external to the scin-tillator (nylon vessel, SSS, and PMTs) is reduced witha fiducial volume (FV) cut, which selects the innermostregion of the scintillator (71.3 t), contained within the ra-dius R<2.8 m and the vertical coordinate -1.8< z< 2.2 m.

The residual background is mainly due to radioac-tive isotopes contaminating the scintillator itself, suchas 14C (β− decay, Q = 156 keV), 210Po (α decay,E = 5.3 MeV quenched by a factor ∼10), 85Kr (β− decay,Q = 687 keV), and 210Bi (β− decay, Q = 1160 keV) from210Pb. The low energy region (below 300 keV), whichis most sensitive to pp ν’s, contains an additional back-ground due to the pile-up of uncorrelated events (mostly14C, external background, and 210Po [9, 14]). The energyregion sensitive to pep and CNO ν’s (between about 1.1and 1.7 MeV) is also affected by the cosmogenic isotope11C and by residual external background, mainly due toγ’s from the decay of 208Tl, 214Bi, and 40K.

The 11C isotope (β+ decay, τ = 29.4 min) is contin-uously produced by muons through spallation on 12C.In order to limit its effect on the sensitivity to pep ν’s,we exploit the so-called Three-Fold Coincidence (TFC)method, and e+/e− pulse-shape discrimination [10, 12].

The TFC takes advantage of the fact that 11C is oftenproduced together with one or even a burst of neutrons.The principle of the method is thus to tag events cor-related in space and time with a muon and a neutron.We have improved the TFC technique by implement-ing a new algorithm, which evaluates the likelihood L11C

that an event is a 11C candidate, considering relevantobservables such as distance in space and time from theparent muon, distance from the neutron, neutron mul-tiplicity, muon dE/dx and the number of muon clustersin an event. Based on this probability, the data-set isdivided in two samples: one depleted (TFC-subtracted)

and one enriched (TFC-tagged) in 11C. These two sets arefitted separately in the multivariate fit (see later). Thenew TFC algorithm has (92± 4)% 11C-tagging efficiency,while preserving (64.28± 0.01)% of the total exposure inthe TFC-subtracted spectrum.

The residual amount of 11C in the TFC-subtractedspectrum can be disentangled from the neutrino signalby exploiting the e+/e− pulse-shape discrimination vari-able [10, 12]. The probability density function (PDF) ofscintillation time profile is significantly different for e+

and e− events for two reasons: i) in 50% of the cases, e+

annihilation is delayed by ortho-positronium formation,which has a lifetime of τ ∼ 3 ns [16]; ii) the e+ energydeposit is not point-like, due to the two back-to-back511 keV annihilation γ’s. To exploit these differences,we use a novel discrimination parameter, called PS-LPR,based on the output likelihood of the position reconstruc-tion [12].

We obtain the interaction rates of solar neutrinosand background species by maximizing, through a mul-tivariate approach, a binned likelihood function builtas the product of 4 different factors coming from theTFC-subtracted energy spectrum, the TFC-tagged en-ergy spectrum, the PS-LPR and the radial distributions.The free parameters of the fit are the interaction ratesof neutrino and background species, and in the analyti-cal approach (see later), some of the response function-related parameters. Constraints on the values of the fitparameters are implemented (if not specified otherwise)as multiplicative Gaussian terms in the likelihood func-tion.

The PS-LPR reference shape for e+ is obtained froma pure TFC-selected 11C sample, while for e− eventsit is derived from simulations (and checked on dataagainst electron-like events selected from 214Bi-214Po co-incidences [12]). The reference radial distributions forexternal and internal events are built from simulations[14].

As done in previous Borexino analyses [12], the sig-nal and background reference spectral shapes used in thefit are obtained following two complementary strategies:one is based on the analytical description of the detectorresponse function, while the second one is fully based onMC simulations.

In the analytical approach, the details of the detectorenergy response are described with a model, which in-cludes ionization quenching and Cherenkov effects andspatial dependence of reconstructed energy and its reso-lution. The analytical model is derived from [12], withseveral improvements to extend the energy range of the

fit and uses the Ndt1(2)p variables. Most of the parameters

in the model are tuned with the MC or using indepen-dent measurements and calibrations and are fixed in thefit (Birks’ factor kB, geometrical correction, Cherenkovparameter). Other parameters are left free to vary in thefit, together with the neutrino and background interac-

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FIG. 1. Multivariate fit results (an example obtained with the MC method) for the TFC-subtracted (left) and the TFC-tagged(right) energy spectra, with residuals. The sum of the individual components from the fit (black lines) are superimposed onthe data (grey points).

R (m)0 0.5 1 1.5 2 2.5 3

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FIG. 2. An example of the multivariate fit showing the radial(top) and the PS-LPR (bottom) distributions of the events(black crosses).

tion rates: (i) the light yield, (ii) a resolution parameterwhich accounts for the non-uniformity of the responseand is relevant for the high-energy part of the spectrum,(iii) a resolution parameter which accounts for the intrin-sic resolution of the scintillator and effectively takes intoaccount other contributions at low energy, (iv) the posi-tion and width of the 210Po-α peak (to account for non-uniform and time-varying spatial distribution of 210Po

pp Be7

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FIG. 3. Results of the fit for TFC-subtracted energy spectrumzoomed in to the lowest energy region (an example obtainedwith the analytical method) and residuals.

in the detector), and (v) the starting point of the 11Cspectrum, corresponding to the annihilation of the two511 keV γ’s. Leaving the above listed parameters freegives the analytical fit the freedom to account for second-order unexpected effects or unforeseen variations of thedetector response in time.

The second method is based on the Borexino MC [14],a customized Geant4-based simulation package [17],

5

which can simulate all processes following the interac-tion of a particle in the detector (energy deposits includ-ing ionization quenching in the scintillator, scintillationand Cherenkov light production, photon propagation anddetection, response of the electronics chain) including allknown characteristics of the apparatus (geometry, prop-erties of the materials, number of working channels) andtheir evolution in time. All the MC input parametershave been chosen or optimized using samples of dataindependent from the ones used in the present analy-sis (laboratory measurements and Borexino calibrationswith radioactive sources [15]) and the simulation of thevariables relevant for the present analysis has reachedsub-percent precision [14].

Once the MC input parameters have been tuned,events are generated according to the theoretical sig-nal and background energy spectra and processed as realdata [18]. 210Po decays are simulated according to theiractual spatial and time distributions, obtained from ex-perimental data by tagging 210Po with a novel pulse-shape discrimination method based on a MultiLayer Per-ceptron (MLP) algorithm [19]. For every species, threedimensional histograms are built for each of the energy

estimators (Nh, Np and Ndt1(2)p ), the reconstructed ra-

dius, and the PS-LPR variable. When properly binnedand normalized, these histograms represent the PDF’sused in the fit. In the MC approach, there are no free fitparameters except for the interaction rates of all species.The goodness of the fit demonstrates simultaneously theaccuracy of the MC simulation as well as the stability ofthe detector response over the period of five years.

The interaction rates of pp, 7Be, and pep ν’s are ob-tained from the fit together with the decay rates of85Kr, 210Po, 210Bi, 11C, and external backgrounds (208Tl,214Bi, and 40K γ rays).

In the MC approach, the MC-based pile-up spec-trum [14] is included in the fit with a constraint of(137.5± 2.8 cpd/100 t) on the 14C-14C contribution basedon an independent measurement of the 14C rate [9]. Inthe analytical approach, pile-up is taken into accountwith the convolution of each spectral component with thesolicited-trigger spectrum [9]. Alternatively, the analyti-cal fit uses a synthetic pile-up spectrum [9] built directlyfrom data. The differences between these methods arequoted in the systematic error (see Table III).

In order to break the degeneracy between the 210Biand the CNO ν spectral shapes we constrain the CNOν interaction rate to the HZ-SSM predictions, includingMSW-LMA oscillations (4.92 ± 0.55 cpd/100 t) [4] [20].The analysis is repeated constraining the CNO ν rate tothe LZ-SSM predictions (3.52 ± 0.37 cpd/100 t) and incase of difference the two results are quoted separately.The contribution of 8B ν’s is small in the energy regionof interest for this analysis: it has been fixed to the HZ-metallicity rate 0.46 cpd/100 t.

The interaction rates of solar neutrinos and the decay

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FIG. 4. TFC-subtracted energy spectrum zoomed between800 keV and 2700 keV after applying stringent selection cutson the radial distribution (R< 2.4 m) and on the pulse-shape variable distribution (PS-LPR <4.8): the characteristicCompton-like shoulder in the electron-recoil spectrum visiblein the plot is due to pep ν interactions.

rates of background species, obtained by averaging theresults of the analytical and MC approaches, are sum-marized in Tables I and II, respectively.

An example of the multivariate fit (with the MC ap-proach) is shown in Fig. 1 (TFC-subtracted and TFC-tagged energy spectra), and in Fig. 2 (radial distributionand PS-LPR pulse-shape distribution).

The details of the fit at low energies (between ∼ 230and 830 keV) can be appreciated in Fig. 3. In this ex-ample, obtained with the analytical fit procedure, thepile-up is not present since it is taken into account withthe convolution method mentioned above.

To recognize the pep ν contribution to the measuredelectron-recoil spectrum, the TFC-subtracted spectrum,zoomed into the highest energy region (between 800 keVand 2700 keV), is shown after applying stringent selec-tion cuts on the radial distribution (R< 2.4 m) and onthe pulse-shape variable distribution (PS-LPR<4.8) (seeFig. 4): the characteristic Compton-like shoulder due topep ν interactions becomes clearly visible.

An extensive study of the systematic errors has beenperformed and the results are summarized in Table III.

Differences between the results of the analytical andthe MC fits are quoted as systematic errors. Furthersystematic uncertainties associated with the fitting pro-cedure were studied by performing the fit in many dif-ferent configurations (varying the energy estimator, thenumber and width of the bins, as well as the fit range).

6

Solar ν

Borexino experimental results B16(GS98)-HZ B16(AGSS09)-LZ

Rate Flux Rate Flux Rate Flux[cpd/100 t] [cm−2s−1] [cpd/100 t] [cm−2s−1] [cpd/100 t] [cm−2s−1]

pp 134± 10 +6−10 (6.1± 0.5 +0.3

−0.5)× 1010 131.1± 1.4 5.98 (1± 0.006)× 1010 132.2± 1.4 6.03 (1± 0.005)× 1010

7Be 48.3± 1.1 +0.4−0.7 (4.99± 0.11 +0.06

−0.08)× 109 47.9± 2.8 4.93 (1± 0.06)× 109 43.7± 2.5 4.50 (1± 0.06)× 109

pep (HZ) 2.43± 0.36 +0.15−0.22 (1.27± 0.19 +0.08

−0.12)× 108 2.74± 0.04 1.44 (1± 0.009)× 108 2.78± 0.04 1.46 (1± 0.009)× 108

pep (LZ) 2.65± 0.36 +0.15−0.24 (1.39± 0.19 +0.08

−0.13)× 108 2.74± 0.04 1.44 (1± 0.009)× 108 2.78± 0.04 1.46 (1± 0.009)× 108

CNO < 8.1 (95% C.L.) < 7.9× 108 (95% C.L.) 4.92± 0.55 4.88 (1± 0.11)× 108 3.52± 0.37 3.51 (1± 0.10)× 108

TABLE I. Borexino Phase-II results on pp, 7Be (862 +384 keV), pep and CNO solar ν’s: interaction rates and fluxes inferredassuming the MSW-LMA oscillation parameters [20]. The first error is the statistical derived by profiling the likelihood underWilk’s approximation. The interval extracted is coherent with the expectation from the toy-MC. The second error is thesystematic uncertainty. Different contributions to the systematic error are detailed in Table III. The result on pep ν’s dependson whether we assume HZ or LZ metallicity for CNO ν’s. The remaining columns show the theoretical interaction rates andfluxes predicted by the Standard Solar Model under the high (HZ) and low (LZ) metallicity assumptions [4].

Background Rate[cpd/100 t]

14C [Bq/100 t] 40.0± 2.085Kr 6.8± 1.8210Bi 17.5± 1.911C 26.8± 0.2210Po 260.0± 3.0

Ext. 40K 1.0± 0.6

Ext. 214Bi 1.9± 0.3

Ext. 208Tl 3.3± 0.1

TABLE II. Best estimates for the total rates of the back-ground species included in the fit with statistical and system-atic uncertainties added in quadrature.

pp 7Be pep

Source of uncertainty −% +% −% +% −% +%

Fit method (analytical/MC) -1.2 1.2 -0.2 0.2 -4.0 4.0

Choice of energy estimator -2.5 2.5 -0.1 0.1 -2.4 2.4

Pile-up modeling -2.5 0.5 0 0 0 0

Fit range and binning -3.0 3.0 -0.1 0.1 1.0 1.0

Fit models (see text) -4.5 0.5 -1.0 0.2 -6.8 2.8

Inclusion of 85Kr constraint -2.2 2.2 0 0.4 -3.2 0

Live Time -0.05 0.05 -0.05 0.05 -0.05 0.05

Scintillator density -0.05 0.05 -0.05 0.05 -0.05 0.05

Fiducial volume -1.1 0.6 -1.1 0.6 -1.1 0.6

Total systematics (%) -7.1 4.7 -1.5 0.8 -9.0 5.6

TABLE III. Relevant sources of systematic uncertainty andtheir contribution to the measured neutrino interaction rates.More details are in the text.

Systematic uncertainties related to the fit modelswere evaluated using a toy-MC. Ensembles of pseudo-experiments were generated from a family of PDF’s basedon MC simulations and fitted using both the MC andanalytical methods. The family of PDF’s includes defor-mations due to possible inaccuracies in the modelling ofthe detector response (energy scale, uniformity of the en-

ergy response, shape of PS-LPR) and uncertainties in thetheoretical energy spectra (210Bi). The magnitude of thedeformation was chosen to be within the range allowedby the available calibration data.

In an additional systematic study, the fit was repeatedtaking into account the upper limit on the 85Kr decayrate following the procedure described in [12] which ex-ploits the 85Kr-85mRb delayed coincidences (85Kr rate< 7.5 cpd/100 t at 95% C.L.) .

The three following lines of Table III list the uncertain-ties associated with the determination of the scintillatormass. The dominant uncertainty from the FV measure-ment is estimated using calibration sources of known po-sition and is the same as quoted in [3].

Fully consistent results are obtained when adoptinga larger FV (R<3.02 m, |z|<1.67 m). This FV containsmore external background (critical for the pep ν’s) whichis, however, properly disentangled by the multivariate fitthanks to its energy shape and radial distribution. Thepreviously published Borexino results regarding pp ν’s [9]and 7Be ν’s [3] were obtained in this enlarged fiducialvolume.

Finally, the analytical fit performed on a restricted en-ergy range (not sensitive to pp neutrinos) using the Npeenergy estimator gives consistent results (within 2σ) forthe interaction rates of 7Be and pep ν’s.

The 7Be solar ν flux listed in Table I is the sumof the two mono-energetic lines at 384 and 862 keV.It corresponds to a rate for the 862 keV line of46.3± 1.1+0.4

−0.7 cpd/100 t, fully compatible with the Borex-ino Phase-I measurement [3]. The 7Be solar ν flux isdetermined with a total uncertainty of 2.7 %, which rep-resents a factor of 1.8 improvement with respect to ourprevious result [3] and is two times smaller than the the-oretical error. The p-value of our measurement whencompared to the HZ-SSM predictions is 0.87, while it is0.11 for the LZ-SSM. This provides a weak hint towardsthe HZ hypothesis, which is however not statistically sig-nificant. The discrimination between the high and low

7

0.6 0.8 1.0 1.20.7

0.8

0.9

1.0

1.1

1.2

fB

f Be

HZ (GS98)LZ (AGSS09met)

B16 SSM (± 1σ):

Allowed regions:68.27% C.L.95.45% C.L.99.73% C.L.

FIG. 5. Allowed contours in the fBe-fB parameter space ob-tained by combining the new result on 7Be ν’s with solarand KamLAND data. The 1σ theoretical prediction for thelow metallicity (blue) and the high metallicity (red) SSMare also shown. The best fit (obtained fixing sin2θ13 to0.02 [20]) is found to be: Φ(7Be) = (5.00±0.15)× 109 cm2/s−1;Φ(8B) = (5.08± 0.10)× 106 cm2/s−1; tan2θ12 = 0.47± 0.03;∆m2

12 = 7.5×10−5± 0.2 eV2.

metallicity solar models is now largely dominated by the-oretical uncertainties.

Following the procedure described in [12], we combineour new result on the 7Be solar ν interaction rate with allthe solar and KamLAND data and obtain the regions ofallowed values for the reduced fluxes fBe and fB (fBe =Φ(7Be)/Φ(7Be)HZ, fB = Φ(8B)/Φ(8B)HZ). Fig. 5 showsthe allowed contours together with the 1σ theoretical pre-dictions for high metallicity and low metallicity SSM.

The pp interaction rate is consistent with our previ-ous result and its uncertainty is reduced by about 20 %.The combination of the Borexino results on pp and 7Be νfluxes can be used to measure experimentally for the firsttime the ratio R between the rates of the 3He-4He andthe 3He-3He reactions occurring in the pp chain insidethe Sun [21]. The value of R reflects the competitionbetween the two primary modes of terminating the ppchain and hence is a critical probe of solar fusion. By ne-glecting the pep and 8B ν contribution, R can be writtenas 2 Φ(7Be)/[Φ(pp)-Φ(7Be)] . We find R= 0.18± 0.03, inagreement with the most up-to-date predicted values forR= 0.180± 0.011 (HZ) and 0.161± 0.010 (LZ) [4].

The correlation between the CNO and pep ν interac-tion rates is broken by constraining the CNO one. The7Be and pp ν interaction rates are not affected by the hy-pothesis on CNO ν’s within our sensitivity. However, thepep ν interaction rate depends on it, being 0.22 cpd/100 thigher if the LZ hypothesis is assumed (see Table I).

The ∆χ2 profile obtained by marginalizing the pep rateis shown in Fig. 6 (left) for both the HZ and LZ assump-tions on CNO ν rate. Both curves are symmetric andallow us to establish, for the first time, that the absence

of pep reaction in the Sun is rejected at more than 5σ.

From the measured interaction rates of pp, 7Be,and pep neutrinos and assuming the HZ SSM fluxes,the calculation of the survival probability Pee yields:Pee(pp) = 0.57± 0.09, Pee(

7Be, 862 keV) = 0.53± 0.05,and Pee(pep) = 0.43± 0.11. Fig. 7 compares thesePee results with the expectations from the standardMSW-LMA oscillation scenario (taken from [20]).

The similarity between the e− recoil spectrum inducedby CNO neutrinos and the 210Bi spectrum makes it im-possible to disentangle the two contributions with thespectral fit. For this reason, we can only provide an up-per limit on the CNO neutrinos. In order to do so, weneed further to break the correlation between the CNOand pep contributions. In Phase-I, this was achieved byfixing the pep ν rate to the theoretical value [10]. Inthe current analysis, where pp ν’s are included in the ex-tended energy range, we place an indirect constraint onpep ν’s by exploiting the theoretically well known pp andpep flux ratio. The interaction rate ratio R(pp/pep) isconstrained to (47.8 ± 0.8) (HZ) [4], [20]. ConstrainingR(pp/pep) to the LZ hypothesis value 47.5 ± 0.8 givesidentical results.

We carried out a sensitivity study by performing theanalysis on thousands of data-sets simulated with a toyMonte Carlo tool: this study shows that under thecurrent experimental conditions the total expected un-certainty (statistical plus systematical) is 3.4 cpd/100 t.With this error, we expect the median 95% C.L. upperlimit for CNO to be ∼ 9 cpd/100 t and 10 cpd/100 t, forlow and high metallicity, respectively. On data, we ob-tain an upper limit on CNO ν rate of 8.1 cpd/100 t (95% C.L.) (see Table I), which is slightly stronger than themedian limit expected from the toy Monte Carlo study.The likelihood profile for the CNO rate is shown in Fig. 6(right). This result, using a weaker hypothesis on pep ν,confirms the current best limit on CNO ν’s previouslyobtained with Borexino Phase-I data [10].

In summary, we have reported the results of the firstsimultaneous measurement of the pp, 7Be, and pep com-ponents of the solar neutrino spectrum providing a com-prehensive investigation of the main pp chain in the Sun:we achieved a 2.7% precision on the 7Be ν flux and thestrongest evidence (higher than 5σ) of the pep reaction.Furthermore, by combining our new results on the 7Beand pp ν fluxes we obtain the first direct measurementof the ratio R between the 3He-4He and the 3He-3Hereactions which is a critical probe of solar fusion.

The Borexino program is made possible by fundingfrom INFN (Italy), NSF (USA), BMBF, DFG, HGF,and MPG (Germany), RFBR (Grants 16-02-01026 A,15-02-02117 A, 16-29-13014 ofim, 17-02-00305 A) (Rus-sia), and NCN (Grant No. UMO 2013/10/E/ST2/00180)(Poland). We acknowledge the generous hospitality andsupport of the Laboratory Nazionali del Gran Sasso

8

pep rate (cpd/100 t)0 1 2 3 4 5 6

2 χ∆

0

10

20

30

40

50

60

70

CNO fixed to LZ solar model

CNO fixed to HZ solar model

CNO rate (cpd/100 t)0 2 4 6 8 10 12 14 16

2 χ ∆

0

5

10

15

20

25

30

HZ solar modelpp/pep ratio fixed toHZ solar modelpp/pep ratio fixed to

FIG. 6. ∆χ2 profile for the pep (left) and CNO ν rates (right).

Energy (keV)210 310 410

) eν → eν

P(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

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1

pp

pepBe7

B8

FIG. 7. Pee for ν’s from the pp chain in the Sun as measuredby Borexino (obtained under the HZ assumption). The val-ues for the pp, 7Be, and pep neutrinos are from this work, 8Bneutrinos are derived from [22]. The violet band correspondsto the ±1σ prediction of the MSW-LMA solution [20]. Thevertical error bars of each data point represent the ±1σ in-terval (experimental + theoretical); the horizontal bar showsthe neutrino energy range spanned by the ν component underconsideration. For 7Be neutrinos the error is dominated bythe theoretical uncertainty, while for pp, pep, and 8B the erroris dominated by the experimental one.

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