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In this work we use the Maximum Entropy Principle (MEP) to infer the mass ofan axion which interacts to photons and neutrinos in an effective low energytheory. The Shannon entropy function to be maximized is suitably defined interms of the axion branching ratios. We show that MEP strongly constrains theaxion mass taking into account the current experimental bounds on the neutrinosmasses. Assuming that the axion is massive enough to decay into all the threeneutrinos and that MEP fixes all the free parameters of the model, the inferredaxion mass is in the interval $0.1\ $eV$\ <m_{A}<0.2$ eV, which can be testedby forthcoming experiments such as IAXO. However, even in the case where MEPfixes just the axion mass and no other parameter, we found that $0.1$ eV $< m_A< 6.3$ eV in the DFSZ model with right-handed neutrinos. Moreover, a lightaxion, allowed to decay to photons and the lightest neutrino only, isdetermined by MEP as a viable dark matter candidate.

Maximum Entropy Inferences on the Axion Mass in Models with Axion-Neutrino Interaction