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tokens: Acknowledgments This research is mainly supported by the University of Padova and by the ERC Consolidator Grant funding scheme (project STARKEY, G.A. n. 615604). The LUNA experiment was supported by INFN, DFG (BE 4100-2/1), NAVI (HGF VH-VI-417) and OTKA (K101328). We thank Maria Lugaro for helpful comments and discussion.