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The strongest upper bounds on the axion mass come from astrophysical observations like the neutrino burst duration of SN1987A, which depends on the axion couplings to nucleons, or the white-dwarf cooling rates and red-giant evolution, which involve the axion-electron coupling.
P. Carenza, T. Fischer, M. Giannotti, and A. Mirizzi, (2019), arXiv:1906.11844 [hep-ph]
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