We thank J. Menéndez for sharing his expertise in the theory of double β decay. We gratefully acknowledge support from the National Science Foundation, Swiss National Science Foundation, German Ministry for Education and Research, Max Planck Gesellschaft, Deutsche Forschungsgemeinschaft, Netherlands Organisation for Scientific Research (NWO), NLeSC, Weizmann Institute of Science, I-CORE, Pazy-Vatat, Initial Training Network Invisibles (Marie Curie Actions, PITNGA-2011-289442), Fundacao para a Ciencia e a Tecnologia, Region des Pays de la Loire, Knut and Alice Wallenberg Foundation, Kavli Foundation, Abeloe Graduate Fellowship, and Istituto Nazionale di Fisica Nucleare. Data processing was performed using infrastructures of the Open Science Grid and European Grid Initiative. We are grateful to Laboratori Nazionali del Gran Sasso for hosting and supporting the XENON project. B.K. was also at Albert Einstein Center for Fundamental Physics, University of Bern, Bern, Switzerland. S.K. is also at Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan. J.A.M.L. is also at Coimbra Polytechnic – ISEC, Coimbra, Portugal.

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Nature thanks Jouni Suhonen and the other anonymous reviewer(s) for their contribution to the peer review of this work.