If the QCD axion and neutrino masses share a single symmetry-breaking scale, the axion necessarily couples to neutrinos and can decay into a monochromatic neutrino signal.
Notice that the quark mass matrices are related to the observed CP-violation in the quark sector given by the Cabibbo-Kobayaski-Maskawa matrix,V CKM
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The QCD Axion and Neutrino Masses
If the QCD axion and neutrino masses share a single symmetry-breaking scale, the axion necessarily couples to neutrinos and can decay into a monochromatic neutrino signal.