# Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun

## Abstract

For most of their existence, stars are fuelled by the fusion of hydrogen into helium. Fusion proceeds via two processes that are well understood theoretically: the proton–proton (pp) chain and the carbon–nitrogen–oxygen (CNO) cycle1,2. Neutrinos that are emitted along such fusion processes in the solar core are the only direct probe of the deep interior of the Sun. A complete spectroscopic study of neutrinos from the pp chain, which produces about 99 per cent of the solar energy, has been performed previously3; however, there has been no reported experimental evidence of the CNO cycle. Here we report the direct observation, with a high statistical significance, of neutrinos produced in the CNO cycle in the Sun. This experimental evidence was obtained using the highly radiopure, large-volume, liquid-scintillator detector of Borexino, an experiment located at the underground Laboratori Nazionali del Gran Sasso in Italy. The main experimental challenge was to identify the excess signal—only a few counts per day above the background per 100 tonnes of target—that is attributed to interactions of the CNO neutrinos. Advances in the thermal stabilization of the detector over the last five years enabled us to develop a method to constrain the rate of bismuth-210 contaminating the scintillator. In the CNO cycle, the fusion of hydrogen is catalysed by carbon, nitrogen and oxygen, and so its rate—as well as the flux of emitted CNO neutrinos—depends directly on the abundance of these elements in the solar core. This result therefore paves the way towards a direct measurement of the solar metallicity using CNO neutrinos. Our findings quantify the relative contribution of CNO fusion in the Sun to be of the order of 1 per cent; however, in massive stars, this is the dominant process of energy production. This work provides experimental evidence of the primary mechanism for the stellar conversion of hydrogen into helium in the Universe.

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## Data availability

The datasets generated during the current study are freely available from the repository https://bxopen.lngs.infn.it/. Additional information is available from the Borexino Collaboration spokesperson (spokesperson-borex@lngs.infn.it) upon reasonable request.

## References

1. 1.

Bahcall, J. N. Neutrino Astrophysics (Cambridge Univ. Press, 1989).

2. 2.

Vinyoles, N. et al. A new generation of standard solar models. Astrophys. J. 835, 202 (2017).

3. 3.

The Borexino Collaboration. Comprehensive measurement of pp-chain solar neutrinos. Nature 562, 505–510 (2018).

4. 4.

Salaris, M. & Cassisi, S. Evolution of Stars and Stellar Populations (John Wiley & Sons, 2005).

5. 5.

Angulo, C. et al. A compilation of charged-particle induced thermonuclear reaction rates. Nucl. Phys. A 656, 3–183 (1999).

6. 6.

Davis, R. Jr A Half-Century with Solar Neutrinos. Nobel Prize Lecture https://www.nobelprize.org/prizes/physics/2002/davis/lecture/ (2002).

7. 7.

GALLEX collaboration. Solar neutrinos observed by GALLEX at Gran Sasso. Phys. Lett. B 285, 376 (1992).

8. 8.

SAGE collaboration. Results from SAGE (The Russian–American Gallium solar neutrino experiment). Phys. Lett. B 328, 234 (1994).

9. 9.

McDonald, A. B. The Sudbury Neutrino Observatory: Observation of Flavor Change for Solar Neutrinos. Nobel Prize Lecture https://www.nobelprize.org/prizes/physics/2015/mcdonald/lecture/ (2015).

10. 10.

Hirata, K. et al. Observation of 8B solar neutrinos in the Kamiokande-II detector. Phys. Rev. Lett. 63, 16 (1989).

11. 11.

Ahmad, Q. et al. Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory. Phys. Rev. Lett. 89, 011301 (2002).

12. 12.

Araki, T. et al. Measurement of neutrino oscillation with KamLAND: evidence of spectral distortion. Phys. Rev. Lett. 94, 081801 (2005).

13. 13.

Borexino Collaboration. Neutrinos from the primary proton–proton fusion process in the Sun. Nature 512, 383–386 (2014).

14. 14.

Bellini, G. et al. Precision measurement of the 7Be solar neutrino interaction rate in Borexino. Phys. Rev. Lett. 107, 141302 (2011).

15. 15.

Bethe, H. A. Energy production in stars. Phys. Rev. 55, 434–456 (1939).

16. 16.

von Weizsäcker, C. F. Über Elementumwandlungen im Innern der Sterne I. Phys. Z. 38, 176 (1937).

17. 17.

Serenelli, A. M., Haxton, W. C. & Peña-Garay, C. Solar models with accretion. I. application to the solar abundance problem. Astrophys. J. 743, 24 (2011).

18. 18.

Alimonti, G. et al. The Borexino detector at the Laboratori Nazionali del Gran Sasso. Nucl. Instrum. Methods Phys. Res. A 600, 568–593 (2009).

19. 19.

Bellini, G. et al. Final results of Borexino Phase-I on low-energy solar neutrino spectroscopy. Phys. Rev. D 89, 112007 (2014).

20. 20.

Agostini, M. et al. Simultaneous precision spectroscopy of pp, 7Be and pep solar neutrinos with Borexino Phase-II. Phys. Rev. D 100, 082004 (2019).

21. 21.

Alimonti, G. et al. Science and technology of BOREXINO: a real-time detector for low energy solar neutrinos. Astropart. Phys. 16, 205–234 (2002).

22. 22.

Agostini, M. et al. Comprehensive geoneutrino analysis with Borexino. Phys. Rev. D 101, 012009 (2020).

23. 23.

Ding, X. F. GooStats: A GPU-based framework for multi-variate analysis in particle physics. J. Instrum. 13, P12018 (2018).

24. 24.

Agostini, M. et al. Sensitivity to neutrinos from the solar CNO cycle in Borexino. Eur. Phys. J. C https://doi.org/10.1140/epjc/s10052-020-08534-2 (2020).

25. 25.

Vissani, F. Luminosity constraint and entangled solar neutrino signals. In Solar Neutrinos, Proc. 5th International Solar Neutrino Conference (eds Meyer, M. & Zuber, K.) 121–141 (World Scientific, 2019).

26. 26.

Bergström, J., Gonzalez-Garcia, M. C., Maltoni, M., Peña-Garay, C., Serenelli, A. M. & Song, N. Updated determination of the solar neutrino fluxes from solar neutrino data. J. High Energy Phys. 2016, 132 (2016).

27. 27.

Capozzi, F., Lisi, E., Marrone, A. & Palazzo, A. Global analysis of oscillation parameters. J. Phys. Conf. Ser. 1312, 012005 (2019).

28. 28.

Villante, F. L., Ianni, A., Lombardi, F., Pagliaroli, G. & Vissani, F. A step toward CNO solar neutrino detection in liquid scintillators. Phys. Lett. B 701, 336–341 (2011).

29. 29.

Bravo-Berguño, D. et al. The Borexino Thermal Monitoring & Management System and simulations of the fluid-dynamics of the Borexino detector under asymmetrical, changing boundary conditions. Nucl. Instrum. Methods Phys. Res. A 885, 38–53 (2018).

30. 30.

Di Marcello, V. et al. Fluid-dynamics and transport of 210Po in the scintillator Borexino detector: a numerical analysis. Nucl. Instrum. Methods Phys. Res. A 964, 163801 (2020).

31. 31.

Agostini, M. et al. The Monte Carlo simulation of the Borexino detector. Astropart. Phys. 97, 136–159 (2018).

32. 32.

Daniel, H. Das β-spektrum des RaE. Nucl. Phys. 31, 293–307 (1962).

33. 33.

Grau Carles, A. & Grau Malonda, A. Precision measurement of the RaE shape factor. Nucl. Phys. A 596, 83–90 (1996).

34. 34.

Alekseev, I. E. et al. Precision measurement of 210Bi β-spectrum. Preprint at https://arxiv.org/abs/2005.08481 (2020).

35. 35.

Back, H. et al. Borexino calibrations: hardware, methods, and results. J. Instrum. 7, P10018 (2012).

36. 36.

de Holanda, P. C., Liao, W. & Smirnov, A. Yu. Toward precision measurements in solar neutrinos. Nucl. Phys. B 702, 307–332 (2004).

37. 37.

Capozzi, F., Lisi, E., Marrone, A. & Palazzo, A. Current unknowns in the three neutrino framework. Prog. Part. Nucl. Phys. 102, 48–72 (2018).

38. 38.

Cowan, G., Cranmer, K., Gross, E. & Vitells, O. Asymptotic formulae for likelihood-based tests of new physics. Eur. Phys. J. C 71, 1554 (2011).

39. 39.

Bahcall, J. N. Line versus continuum solar neutrinos. Phys. Rev. D 41, 2964–2966 (1990).

40. 40.

Stonehill, L. C., Formaggio, J. A. & Robertson, R. G. H. Solar neutrinos from CNO electron capture. Phys. Rev. C 69, 015801 (2004).

41. 41.

Villante, F. L. ecCNO solar neutrinos: a challenge for gigantic ultra-pure liquid scintillator detectors. Phys. Lett. B 742, 279–284 (2015).

42. 42.

Birks, J. B. The Theory and Practice of Scintillation Counting (Pergamon, 1964).

43. 43.

Benziger, J. et al. The scintillator purification system for the Borexino solar neutrino detector. Nucl. Instrum. Methods Phys. Res. A 587, 277–291 (2008).

44. 44.

Alimonti, G. et al. The liquid handling systems for the Borexino solar neutrino detector. Nucl. Instrum. Methods Phys. Res. A 609, 58–78 (2009).

45. 45.

Bellini, G. et al. Cosmic-muon flux and annual modulation in Borexino at 3800 m water-equivalent depth. J. Cosmol. Astropart. Phys. 2012, 015 (2012).

46. 46.

Bellini, G. et al. Cosmogenic backgrounds in Borexino at 3800 m water-equivalent depth. J. Cosmol. Astropart. Phys. 2013, 049 (2013).

47. 47.

Bellini, G. et al. Muon and cosmogenic neutron detection in Borexino. J. Instrum. 6, P05005 (2011).

48. 48.

Cruickshank Miller, C. The Stokes–Einstein law for diffusion in solution. Proc. R. Soc. Lond. A 106, 724–729 (1924).

49. 49.

Wójcik, M., Wlazlo, W., Zuzel, G. & Heusser, G. Radon diffusion through polymer membranes used in the solar neutrino experiment Borexino. Nucl. Instrum. Methods Phys. Res. A 449, 158–171 (2000).

50. 50.

Hoecker, A., Speckmayer, P., Stelzer, J., Therhaag, J., von Toerne, H. & Voss, E. TMVA - toolkit for multivariate data analysis. Preprint at https://arxiv.org/abs/physics/0703039 (2007).

51. 51.

Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N. Importance nested sampling and the MultiNest algorithm. Open J. Astrophys. 2, 10 (2019).

52. 52.

Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).

53. 53.

Feroz, F. & Hobson, M. P. Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses. Mon. Not. R. Astron. Soc. 384, 449–463 (2008).

54. 54.

Fick, A. Ueber Diffusion. Ann. Phys. 170, 59–86 (1855).

55. 55.

Gorski, K. M., Wandelt, B. D., Hansen, F. K., Hivon, E. & Banday, A. J. The HEALPix Primer. Preprint at https://arxiv.org/abs/astro-ph/9905275 (1999).

56. 56.

Agostini, M. et al. Seasonal modulation of the 7Be solar neutrino rate in Borexino. Astropart. Phys. 92, 21–29 (2017).

57. 57.

Bellini, G. et al. First evidence of pep solar neutrinos by direct detection in Borexino. Phys. Rev. Lett. 108, 051302 (2012).

58. 58.

Cousins, R. D. & Highland, V. L. Incorporating systematic uncertainties into an upper limit. Nucl. Instrum. Methods Phys. Res. A 320, 331–335 (1992).

59. 59.

Brown, L. D., Cai, T. T. & Das Gupta, A. Interval estimation for a binomial proportion. Stat. Sci. 16, 101–133 (2001).

## Acknowledgements

We acknowledge the hospitality and support of the Laboratori Nazionali del Gran Sasso (Italy). The Borexino program is made possible by funding from Istituto Nazionale di Fisica Nucleare (INFN) (Italy), National Science Foundation (NSF) (USA), Deutsche Forschungsgemeinschaft (DFG) and Helmholtz-Gemeinschaft (HGF) (Germany), Russian Foundation for Basic Research (RFBR) (grant numbers 16-29-13014ofi-m, 17-02-00305A and 19-02-00097A), Russian Science Foundation (RSF) (grant number 17-12-01009) and Ministry of Science and Higher Education of the Russian Federation (contract number 075-15-2020-778) (Russia), and Narodowe Centrum Nauki (NCN) (grant number UMO 2017/26/M/ST2/00915) (Poland). We acknowledge the computing services of Bologna INFN-CNAF data centre and U-Lite Computing Center and Network Service at LNGS (Italy), and the computing time granted through JARA on the supercomputer JURECA at Forschungszentrum Jülich (Germany). This research was supported in part by PLGrid Infrastructure (Poland).

## Author information

### Contributions

The Borexino detector was designed, constructed and commissioned by the Borexino Collaboration over the span of more than 30 years. The Borexino Collaboration sets the science goals. Scintillator purification and handling, material radiopurity assay, source calibration campaigns, photomultiplier tube and electronics operations, signal processing and data acquisition, Monte Carlo simulations of the detector, and data analyses were performed by Borexino members, who also discussed and approved the scientific results. This Article was prepared by a subgroup of authors that was appointed by the Collaboration and was subjected to an internal collaboration-wide review process. All authors reviewed and approved the final version of the manuscript.

### Corresponding author

Correspondence to G. Ranucci.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Marc Pinsonneault, Gabriel Orebi Gann and David Wark for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 The Borexino detector.

Schematic view of the structure of the Borexino apparatus. From inside to outside: the liquid scintillator, the buffer liquid, the stainless steel sphere with the photomultipliers, and the water tank.

### Extended Data Fig. 2 The Borexino detector after the thermal stabilization.

The Borexino water tank after completion of the thermal insulation and deployment of the active temperature control system.

### Extended Data Fig. 3 Temperature probes of the Borexino detector.

Distribution of temperature probes around and inside the Borexino detector. For simplicity, the probes on the water tank (WT) dome and in the pit below the detector are not shown.

### Extended Data Fig. 4 Temperature evolution over time in the Borexino detector.

Graph depicting the temperature as a function of time in different volumes of the Borexino detector. The vertical dashed lines show the beginning of the thermal insulation installation (1), the turning off of the water loop inside the water tank (2), the completing of the thermal insulation installation (3), the activation of the temperature control system on the dome of the water tank (4), the set-point change (5) and the activation of the air control system in experimental hall C (6).

### Extended Data Fig. 5 The low polonium field in the Borexino scintillator.

Three-dimensional view of the 210Po activity inside the entire nylon vessel (see colour code). The innermost blue region contains the LPoF (black grid). The white grid is the software-defined fiducial volume. a.u., arbitrary units.

### Extended Data Fig. 6 Analysis of the low polonium field.

Top, the rate of 210Po in cylinders of 3-m radius and 10-cm height located along the z axis from −2 m to 2 m, as a function of time with 1-month binning. The dashed lines indicate the z coordinate of the fiducial volume. The markers show the positions of the centre of the LPoF obtained with two fit methods: paraboloid (red) and spline (white). Both fit methods follow the dark-blue minimum of the 210Po activity well. The structure visible in mid-2019 is due to a local instability produced by a tuning of the active temperature control system. This transient has no effect on the final result. Bottom, distribution of 210Po events after the blind alignment of data using the z0 from the paraboloidal fit (red markers in the top graph). The red solid lines indicate the paraboloidal fit within 20 t with equation (4).

### Extended Data Fig. 7 Angular and radial uniformity of the β events in the optimized energy window.

Top, angular power spectrum as a function of the multipole moment l of observed β events (black points) compared with 104 uniformly distributed events from Monte Carlo simulations at 1σ (dark pink) and 2σ (pink) confidence levels (C.L.). Data are compatible with a uniform distribution within the uncertainty of 0.59 cpd per 100 t. Inset, angular distribution of the β events. Bottom, normalized radial distribution of β events r/r0 (black points), where r0 = 2.5 m is the radius of the sphere surrounding the analysis fiducial volume. The linear fit of the data (red solid line) is shown along with the 1σ (yellow) and 2σ (green) confidence level bands. The data are compatible with a uniform distribution within 0.52 cpd per 100 t.

### Extended Data Fig. 8 Energy distributions from a multivariate fit of the Borexino data.

Full multivariate fit results for the TFC-subtracted (left) and the TFC-tagged (right) energy spectra with corresponding residuals. In both graphs the magenta lines represent the resulting fit function, the red line is the CNO neutrino electron recoil spectrum, the green dotted line is the pep neutrino electron recoil spectrum, the dashed blue line is the 210Bi β spectrum, and in grey we report the remaining background (bkgs) contributions.

### Extended Data Fig. 9 Radial distribution from a multivariate fit of the Borexino data.

Radial distribution of events in the multivariate fit. The red line is the resulting fit, the green line represents the internal uniform contribution and the blue line shows the non-uniform contribution from the external background. NDF, the number of degrees of freedom in the fit.

### Extended Data Fig. 10 Frequentist hypothesis test for the CNO observation.

Distribution of the test statistics q (equation (5) from Monte Carlo pseudo-datasets). The grey distribution q0 is obtained with no CNO simulated data and includes the systematic uncertainty. The black vertical line represents qdata = 30.05. The corresponding P value of q0 with respect to qdata gives the significance of the CNO discovery (>5.0σ at 99% confidence level). For comparison, in blue is the q0 without the systematics. The red histogram represents the expected test statistics distribution for an injected CNO rate equal to 7.2 cpd per 100 t—that is, our best fit value.

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The Borexino Collaboration., Agostini, M., Altenmüller, K. et al. Experimental evidence of neutrinos produced in the CNO fusion cycle in the Sun. Nature 587, 577–582 (2020). https://doi.org/10.1038/s41586-020-2934-0

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