---
abstract: 'We observed, for the first time, solar neutrinos in the 1.0–1.5MeV energy range. We measured the rate of  solar neutrino interactions in Borexino to be (3.1$\pm$0.6$_{\rm stat}$$\pm$0.3$_{\rm syst}$) and provided a constraint on the  solar neutrino interaction rate of $<$7.9 (95% C.L.). The absence of the solar neutrino signal is disfavored at 99.97% C.L., while the absence of the  signal is disfavored at 98% C.L. This unprecedented sensitivity was achieved by adopting novel data analysis techniques for the rejection of cosmogenic , the dominant background in the 1–2MeV region. Assuming the MSW-LMA solution to solar neutrino oscillations, these values correspond to solar neutrino fluxes of  and $<$ (95% C.L.), respectively, in agreement with the Standard Solar Model. These results represent the first measurement of the  neutrino flux and the strongest constraint of the  solar neutrino flux to date.'
author:
- 'G. Bellini'
- 'J. Benziger'
- 'D. Bick'
- 'S. Bonetti'
- 'G. Bonfini'
- 'D. Bravo'
- 'M. Buizza Avanzini'
- 'B. Caccianiga'
- 'L. Cadonati'
- 'F. Calaprice'
- 'C. Carraro'
- 'P. Cavalcante'
- 'A. Chavarria'
- 'D. D’Angelo'
- 'S. Davini'
- 'A. Derbin'
- 'A. Etenko'
- 'K. Fomenko'
- 'D. Franco'
- 'C. Galbiati'
- 'S. Gazzana'
- 'C. Ghiano'
- 'M. Giammarchi'
- 'M. Goeger-Neff'
- 'A. Goretti'
- 'L. Grandi'
- 'E. Guardincerri'
- 'S. Hardy'
- Aldo Ianni
- Andrea Ianni
- 'D. Korablev'
- 'G. Korga'
- 'Y. Koshio'
- 'D. Kryn'
- 'M. Laubenstein'
- 'T. Lewke'
- 'E. Litvinovich'
- 'B. Loer'
- 'F. Lombardi'
- 'P. Lombardi'
- 'L. Ludhova'
- 'I. Machulin'
- 'S. Manecki'
- 'W. Maneschg'
- 'G. Manuzio'
- 'Q. Meindl'
- 'E. Meroni'
- 'L. Miramonti'
- 'M. Misiaszek'
- 'D. Montanari'
- 'P. Mosteiro'
- 'V. Muratova'
- 'L. Oberauer'
- 'M. Obolensky'
- 'F. Ortica'
- 'K. Otis'
- 'M. Pallavicini'
- 'L. Papp'
- 'L. Perasso'
- 'S. Perasso'
- 'A. Pocar'
- 'J. Quirk'
- 'R.S. Raghavan'
- 'G. Ranucci'
- 'A. Razeto'
- 'A. Re'
- 'A. Romani'
- 'A. Sabelnikov'
- 'R. Saldanha'
- 'C. Salvo'
- 'S. Schönert'
- 'H. Simgen'
- 'M. Skorokhvatov'
- 'O. Smirnov'
- 'A. Sotnikov'
- 'S. Sukhotin'
- 'Y. Suvorov'
- 'R. Tartaglia'
- 'G. Testera'
- 'D. Vignaud'
- 'R.B. Vogelaar'
- 'F. von Feilitzsch'
- 'J. Winter'
- 'M. Wojcik'
- 'A. Wright'
- 'M. Wurm'
- 'J. Xu'
- 'O. Zaimidoroga'
- 'S. Zavatarelli'
- 'G. Zuzel'
title: First evidence of  solar neutrinos by direct detection in Borexino
---

Over the past 40 years solar neutrino experiments [@bib:rchem-cl; @bib:rchem-ga; @bib:kamiokande; @bib:sno; @bib:bxbe7] have proven to be sensitive tools to test both astrophysical and elementary particle physics models. Solar neutrino detectors have demonstrated that stars are powered by nuclear fusion reactions. Two distinct processes, the main  fusion chain and the sub-dominant  cycle, are expected to produce solar neutrinos with different energy spectra and fluxes. Until now only fluxes from the  chain have been measured: , , and, indirectly, . Experiments involving solar neutrinos and reactor anti-neutrinos [@bib:kamland] have shown that solar neutrinos undergo flavor oscillations.

Results from solar neutrino experiments are consistent with the Mikheyev-Smirnov-Wolfenstein Large Mixing Angle (MSW-LMA) model [@bib:msw], which predicts a transition from vacuum-dominated to matter-enhanced oscillations, resulting in an energy dependent $\nu_e$ survival probability, $P_{ee}$. Non-standard neutrino interaction models formulate $P_{ee}$ curves that deviate significantly from MSW-LMA, particularly in the 1–4MeV transition region, see e.g. [@bib:nonstandard]. The mono-energetic 1.44MeV  neutrinos, which belong to the  chain and whose Standard Solar Model (SSM) predicted flux has one of the smallest uncertainties (1.2%) due to the solar luminosity constraint [@bib:ssm2011], are an ideal probe to test these competing hypotheses.

The detection of neutrinos resulting from the  cycle has important implications in astrophysics, as it would be the first direct evidence of the nuclear process that is believed to fuel massive stars ($>$1.5$M_{\odot}$). Furthermore, its measurement may help to resolve the solar metallicity problem [@bib:metallicity; @bib:ssm2011]. The energy spectrum of neutrinos from the  cycle is the sum of three continuous spectra with end point energies of 1.19 (), 1.73 () and 1.74MeV (), close to the  neutrino energy. The total  flux is similar to that of the  neutrinos but its predicted value is strongly dependent on the inputs to the solar modeling, being 40% higher in the High Metallicity (GS98) than in the Low Metallicity (AGSS09) solar model [@bib:ssm2011].

Neutrinos interact through elastic scattering with electrons in the $\sim$278 ton organic liquid scintillator target of Borexino [@bib:bxdetectorpaper]. The electron recoil energy spectrum from  neutrino interactions in Borexino is a Compton-like shoulder with end point of 1.22MeV. High light yield and unprecedentedly low background levels [@bib:bxbe7; @bib:bxliquid] make Borexino the only detector presently capable of performing solar neutrino spectroscopy below 2MeV. Its potential has already been demonstrated in the precision measurement of the 0.862MeV  solar neutrino flux [@bib:bxbe7; @bib:daynight]. The detection of  and  neutrinos is even more challenging, as their expected interaction rates are $\sim$10 times lower, a few counts per day in a 100ton target.

![ Top: energy spectra of the events in the FV before and after the TFC veto is applied. The solid and dashed blue lines show the data and estimated  rate before any veto is applied. The solid black line shows the data after the procedure, in which the  contribution (dashed) has been greatly suppressed. The next largest background, , and the electron recoil spectra of the best estimate of the  neutrino rate and of the upper limit of the  neutrino rate are shown for reference. Rate values in the legend are quoted in units of counts/(day$\cdot$100metricton). Bottom: residual energy spectrum after best-fit rates of all considered backgrounds are subtracted. The electron recoil spectrum from  neutrinos at the best-fit rate is shown for comparison. []{data-label="fig:tfc"}](tfc.pdf "fig:"){width="\linewidth"} ![ Top: energy spectra of the events in the FV before and after the TFC veto is applied. The solid and dashed blue lines show the data and estimated  rate before any veto is applied. The solid black line shows the data after the procedure, in which the  contribution (dashed) has been greatly suppressed. The next largest background, , and the electron recoil spectra of the best estimate of the  neutrino rate and of the upper limit of the  neutrino rate are shown for reference. Rate values in the legend are quoted in units of counts/(day$\cdot$100metricton). Bottom: residual energy spectrum after best-fit rates of all considered backgrounds are subtracted. The electron recoil spectrum from  neutrinos at the best-fit rate is shown for comparison. []{data-label="fig:tfc"}](residuals.pdf "fig:"){width="\linewidth"}

![Experimental distribution of the pulse shape parameter (black). The best-fit distribution (black dashed) and the corresponding $e^-$ (red) and $e^+$ (blue) contributions are also shown.[]{data-label="fig:bdt"}](bdt.pdf){width="\linewidth"}

We adopted novel analysis procedures to suppress the dominant background in the 1–2MeV energy range, the cosmogenic $\beta^+$-emitter  (lifetime: 29.4 min).  is produced in the scintillator by cosmic muon interactions with  nuclei. The muon flux through Borexino is $\sim$4300$\mu$/day, yielding a  production rate of $\sim$27. In 95% of the cases at least one free neutron is spalled in the  production process [@bib:c11cris], and then captured in the scintillator with a mean time of 255$\mu$s [@bib:bxmuon]. The  background can be reduced by performing a space and time veto after coincidences between signals from the muons and the cosmogenic neutrons [@bib:deutsch; @bib:pep-ctf], discarding exposure that is more likely to contain  due to the correlation between the parent muon, the neutron and the subsequent  decay (the Three-Fold Coincidence, TFC). The technique relies on the reconstructed track of the muon and the reconstructed position of the neutron-capture $\gamma$-ray [@bib:bxmuon]. The rejection criteria were chosen to obtain the optimal compromise between  rejection and preservation of fiducial exposure, resulting in a  rate of (2.5$\pm$0.3), (9$\pm$1)$\%$ of the original rate, while preserving 48.5% of the initial exposure. The resulting spectrum (Fig. \[fig:tfc\], top) corresponds to a fiducial exposure of 20409 ton$\cdot$day, consisting of data collected between January 13, 2008 and May 9, 2010.

The  surviving the TFC veto is still a significant background. We exploited the pulse shape differences between $e^-$ and $e^+$ interactions in organic liquid scintillators [@bib:annihilation; @bib:positronium] to discriminate  $\beta^+$ decays from neutrino-induced $e^-$ recoils and $\beta^-$decays. A slight difference in the time distribution of the scintillation signal arises from the finite lifetime of ortho-positronium as well as from the presence of annihilation $\gamma$-rays, which present a distributed, multi-site event topology and a larger average ionization density than electron interactions. An optimized pulse shape parameter was constructed using a boosted-decision-tree algorithm [@bib:tmva], trained with a TFC-selected set of  events ($e^+$) and  events ($e^-$) selected by the fast  $\alpha$-$\beta$ decay sequence.

We present results of an analysis based on a binned likelihood multivariate fit performed on the energy, pulse shape, and spatial distributions of selected scintillation events whose reconstructed position is within the fiducial volume (FV), i.e. less than 2.8m from the detector center and with a vertical position relative to the detector center between -1.8m and 2.2m. We confirmed the accuracy of the modeling of the detector response function used in the fit by means of an extensive calibration campaign with $\alpha$, $\beta$, $\gamma$ and neutron sources deployed within the active target [@bib:bxbe7].

The distribution of the pulse shape parameter (Fig. \[fig:bdt\]) was a key element in the multivariate fit, where decays from cosmogenic  (and ) were considered $e^+$ and all other species $e^-$.

The energy spectra and spatial distribution of the external $\gamma$-ray backgrounds have been obtained from a full, Geant4-based Monte Carlo simulation, starting with the radioactive decays of contaminants in the detector peripheral structure and propagating the particles into the active volume. We validated the simulation with calibration data from a high-activity $^{228}$Th source [@maneschg] deployed in the outermost buffer region, outside the active volume. The non-uniform radial distribution of the external background was included in the multivariate fit and strongly constrained its contribution. Neutrino-induced $e^-$ recoils and internal radioactive backgrounds were assumed to be uniformly distributed. Fig. \[fig:rdist\] shows the radial component of the fit.

![ Experimental distribution of the radial coordinate of the reconstructed position within the FV (black). The best-fit distribution (black dashed) and the corresponding contributions from bulk events (red) and external $\gamma$-rays (blue) are also shown. []{data-label="fig:rdist"}](rdist.pdf){width="\linewidth"}

We removed $\alpha$ events from the energy spectrum by the method of statistical subtraction [@bib:bxbe7]. We excluded from the fit all background species whose rates were estimated to be less than 5% of the predicted rate from  neutrinos in the energy region of interest. Furthermore, we constrained all rates to positive values. The thirteen species left free in the fit were the internal radioactive backgrounds , , , , , , and  (from  decay chain), electron recoils from , , and  solar neutrinos, and external $\gamma$-rays from , , and . We fixed the contribution from  solar neutrinos to the SSM predicted rate (assuming MSW-LMA with $\tan^2\theta_{12}$=0.47$^{+0.05}_{-0.04}$, $\Delta m^2_{12}$=eV$^2$ [@bib:pdg2010]) and the contribution from  neutrinos to the rate from the measured flux [@bib:sno]. We fixed the rate of the radon daughter  using the measured rate of  delayed coincidence events.

Simultaneously to the fit of events surviving the TFC veto, we also fit the energy spectrum of events rejected by the veto, corresponding to the remaining 51.5% of the exposure. We constrained the rate for every non-cosmogenic species to be the same in both data sets, since only cosmogenic isotopes are expected to be correlated with neutron production.

Fits to simulated event distributions, including all species and variables considered for the data fit, returned results for the  and  neutrino interaction rates that were unbiased and uncertainties that were consistent with frequentist statistics. These tests also yielded the distribution of best-fit likelihood values, from which we determined the p-value of our best-fit to the real data to be 0.3. Table \[tab:results-summary\] summarizes the results for the  and  neutrino interaction rates. The absence of the solar neutrino signal was rejected at 99.97% C.L. using a likelihood ratio test between the result when the  and  neutrino interaction rates were fixed to zero and the best-fit result. Likewise, the absence of a  neutrino signal was rejected at 98% C.L. Due to the similarity between the electron-recoil spectrum from CNO neutrinos and the spectral shape of , whose rate is $\sim$10 times greater, we can only provide an upper limit on the  neutrino interaction rate. The 95% C.L. limit reported in Table \[tab:results-summary\] has been obtained from a likelihood ratio test with the  neutrino rate fixed to the SSM prediction [@bib:ssm2011] under the assumption of MSW-LMA, (2.80$\pm$0.04), which leads to the strongest test of the solar metallicity. For reference, Fig. \[fig:dchi2\] shows the full $\Delta \chi^2$ profile for  and  neutrino interaction rates.

  ------- ----------------------------------------------- ------------------ -------------
  $\nu$                  Interaction rate                  Solar-$\nu$ flux    Data/SSM
                               \[\]                              \[\]            ratio
           $3.1 \pm 0.6_{\rm stat} \pm$ 0.3$_{\rm syst}$     $1.6\pm0.3$      $1.1\pm0.2$
                 $<7.9$ ($<7.1_{\rm stat\,only}$)               $<7.7$          $<1.5$
  ------- ----------------------------------------------- ------------------ -------------

  :  The best estimates for the  and  solar neutrino interaction rates. For the results in the last two columns both statistical and systematic uncertainties are considered. Total fluxes have been obtained assuming MSW-LMA and using the scattering cross-sections from [@bib:BahcallRadiativeCorrection; @bib:pdg2010; @bib:erlerRadCorr] and a scintillator $e^-$ density of ton$^{-1}$. The last column gives the ratio between our measurement and the High Metallicity (GS98) SSM [@bib:ssm2011]. []{data-label="tab:results-summary"}

  --------------- ------------------ -----------------------
  Background       Interaction rate       Expected rate
                         \[\]                 \[\]
                    $19^{+5}_{-3}$    $30\pm6$ [@bib:bxbe7]
                    $55^{+3}_{-5}$              –
                     $27.4\pm0.3$           $28\pm5$
                     $0.6\pm0.2$          $0.54\pm0.04$
                         $<2$             $0.31\pm0.04$
                        $<0.4$                  –
                        $<0.5$            $0.57\pm0.05$
  Ext. $\gamma$      $2.5\pm0.2$                –
  --------------- ------------------ -----------------------

  :  The best estimates for the total rates of the background species included in the fit. The statistical and systematic uncertainties were added in quadrature. The expected rates for the cosmogenic isotopes ,  and  have been obtained following the methodology outlined in [@bib:bxb8]. The expected  rate was determined from the  measured coincidence rate, under the assumption of secular equilibrium. Ext. $\gamma$ includes the estimated contributions from ,  and  external $\gamma$-rays. []{data-label="tab:bkg"}

The estimated  neutrino interaction rate is consistent with our measurement [@bib:bxbe7]. Table \[tab:bkg\] summarizes the estimates for the rates of the other background species. The higher rate of  compared to [@bib:bxbe7] is due to the exclusion of data from 2007, when the observed decay rate of  in the FV was smallest.

Table \[tab:syst\] shows the relevant sources of systematic uncertainty. To evaluate the uncertainty associated with the fit methods we have performed fits changing the binning of the energy spectra, the fit range and the energy bins for which the radial and pulse-shape parameter distributions were fit. This has been done for energy spectra constructed from both the number of PMTs hit and the total collected charge in the event. Further systematic checks have been carried out regarding the stability of the fit over different exposure periods, the spectral shape of the external $\gamma$-ray background and electron recoils from  neutrinos, the fixing of  and  and  neutrinos to their expected values, and the exclusion of minor radioactive backgrounds (short-lived cosmogenics and decays from the  chain) from the fit.

![ $\Delta\chi^2$ profile obtained from likelihood ratio tests between fit results where the  and  neutrino interaction rates are fixed to particular values (all other species are left free) and the best-fit result. []{data-label="fig:dchi2"}](dchi2.pdf){width="\linewidth"}

  Source                                                         \[%\]
  -------------------------------------------------------- ------------------
  Fiducial exposure                                         $^{+0.6}_{-1.1}$
  Energy response                                               $\pm4.1$
   spectral shape                                           $^{+1.0}_{-5.0}$
  Fit methods                                                   $\pm5.7$
  Inclusion of independent  estimate                        $^{+3.9}_{-0.0}$
  $\gamma$-rays in pulse shape distributions                    $\pm2.7$
  Statistical uncertainties in pulse shape distributions         $\pm5$
  Total systematic uncertainty                                  $\pm10$

  :  Relevant sources of systematic uncertainty and their contribution in the measured  neutrino interaction rate. These systematics increase the upper limit in the  neutrino interaction rate by 0.8. []{data-label="tab:syst"}

Table \[tab:results-summary\] also shows the solar neutrino fluxes inferred from our best estimates of the  and  neutrino interaction rates, assuming the MSW-LMA solution, and the ratio of these values to the High Metallicity (GS98) SSM predictions [@bib:ssm2011]. Both results are consistent with the predicted High and Low Metallicity SSM fluxes assuming MSW-LMA. Under the assumption of no neutrino flavor oscillations, we would expect a  neutrino interaction rate in Borexino of (4.47$\pm$0.05); the observed interaction rate disfavors this hypothesis at 97% C.L. If this discrepancy is due to $\nu_e$ oscillation to $\nu_\mu$ or $\nu_\tau$, we find =0.62$\pm$0.17 at 1.44MeV. This result is shown alongside other solar neutrino  measurements in Fig. \[fig:pee\]. The MSW-LMA prediction is shown for comparison.

![ Electron neutrino survival probability as a function of energy. The red line corresponds to the measurement presented in this letter. The  and  measurements of  given in [@bib:bxbe7] are also shown. The  measurements of  were obtained from [@bib:kamiokande; @bib:sno; @bib:bxb8], as indicated in the legend. The MSW-LMA prediction band is the $1\sigma$ range of the mixing parameters given in [@bib:pdg2010]. []{data-label="fig:pee"}](pee.pdf){width="\linewidth"}

We have achieved the necessary sensitivity to provide, for the first time, evidence of the rare signal from  neutrinos and to place the strongest constraint on the  neutrino flux to date. This has been made possible by the combination of the extremely low levels of intrinsic background in Borexino, and the implementation of novel background discrimination techniques. This result raises the prospect for higher precision measurements of  and  neutrino interaction rates, if the next dominant background, , is further reduced by scintillator re-purification.

The Borexino program is made possible by funding from INFN (Italy), NSF (USA), BMBF, DFG and MPG (Germany), NRC Kurchatov Institute (Russia), and MNiSW (Poland). We acknowledge the generous support of the Gran Sasso National Laboratories (LNGS).

[00]{}

B.T. Cleveland et al., Ap. J. [**496**]{}, 505 (1998); K. Lande and P. Wildenhain, Nucl. Phys. B (Proc. Suppl.) [**118**]{}, 49 (2003); R. Davis, Nobel Prize Lecture (2002). F. Kaether et al., Phys. Lett. B [**685**]{}, 47 (2010); W. Hampel et al. (GALLEX Collaboration), Phys. Lett. B [**447**]{}, 127 (1999); J.N. Abdurashitov et al. (SAGE collaboration), Phys. Rev. C [**80**]{}, 015807 (2009). K.S. Hirata et al. (KamiokaNDE Collaboration), Phys. Rev. Lett. [**63**]{}, 16 (1989); Y. Fukuda et al. (Super-Kamiokande Collaboration), Phys. Rev. Lett. [**81**]{}, 1562 (1998); J.P. Cravens et al. (SuperKamiokaNDE Collaboration), Phys. Rev. D [**78**]{}, 032002 (2008). Q.R. Ahmad et al. (SNO Collaboration), Phys. Rev. Lett. [**87**]{}, 071301 (2001); B. Aharmim et al. (SNO Collaboration), Phys. Rev. C [**75**]{}, 045502 (2007); B. Aharmim et al. (SNO Collaboration), Phys. Rev. C [**81**]{}, 055504 (2010); B. Aharmin et al. (SNO Collaboration), . C. Arpesella et al. (Borexino Collaboration), Phys. Lett. B [**658**]{}, 101 (2008); C. Arpesella et al. (Borexino Collaboration), Phys. Rev. Lett. [**101**]{}, 091302 (2008); G. Bellini et al. (Borexino Collaboration), Phys. Rev. Lett. [**107**]{}, 141302 (2011). S. Abe et al. (KamLAND Collaboration), Phys. Rev. Lett. [**100**]{}, 221803 (2008). S.P. Mikheyev and A.Yu. Smirnov, Sov. J. Nucl. Phys. [**42**]{}, 913 (1985); L. Wolfenstein, Phys. Rev. D [**17**]{}, 2369 (1978); P.C. de Holanda and A.Yu. Smirnov, JCAP [**0302**]{}, 001 (2003). A. Friedland et al., Phys. Lett. B [**594**]{}, 347 (2004); S. Davidson et al., JHEP [**0303**]{}, 011 (2003); P.C. de Holanda and A. Yu. Smirnov, Phys. Rev. D [**69**]{}, 113002 (2004); A. Palazzo and J.W.F. Valle, Phys. Rev. D [**80**]{}, 091301 (2009). A.M. Serenelli, W.C. Haxton and C. Peña-Garay, . S. Basu, ASP Conference Series [**416**]{}, 193 (2009). G. Alimonti et al. (Borexino Collaboration), Nucl. Instr. and Meth. A [**600**]{}, 568 (2009). G. Alimonti et al. (Borexino Collaboration), Nucl. Instr. and Meth. A [**609**]{}, 58 (2009). G. Bellini et al. (Borexino Collaboration), . C. Galbiati, A. Pocar, D. Franco, A. Ianni, L. Cadonati, and S. Schönert, Phys. Rev. C [**71**]{}, 055805 (2005). G. Bellini et al. (Borexino Collaboration), JINST [**6**]{}, P05005 (2011). M. Deutsch, [*“Proposal for a Cosmic Ray Detection System for the Borexino Solar Neutrino Experiment”*]{}, Massachusetts Institute of Technology, Cambridge, MA (1996). H. Back et al. (Borexino Collaboration), Phys. Rev. C [**74**]{}, 045805 (2006). Y. Kino et al., Jour. Nucl. Radiochem. Sci [**1**]{}, 63 (2000). D. Franco, G. Consolati, and D. Trezzi, Phys. Rev. C [**83**]{}, 015504 (2011). TMVA Users Guide, [http://tmva.sourceforge.net/docu/ TMVAUsersGuide.pdf](http://tmva.sourceforge.net/docu/ TMVAUsersGuide.pdf). W. Maneschg et al., . Review of Particle Physics, K. Nakamura et al. (Particle Data Group), J. Phys. G [**37**]{}, 075021 (2010). J.N. Bahcall, M. Kamionkowski and A. Sirlin, Phys. Rev. D [**51**]{}, 6146 (1995). J. Erler and M.J. Ramsey-Musolf, Phys. Rev. D [**72**]{}, 073003 (2005). G. Bellini et al. (Borexino Collaboration), Phys. Rev. D [**82**]{}, 033006 (2010).
