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

## TL;DR

This paper employs the Maximum Entropy Principle to constrain the axion mass in models with axion-neutrino interactions, providing specific mass ranges and implications for dark matter and experimental tests.

## Contribution

It introduces a novel application of MEP to infer axion mass considering neutrino interactions and current experimental bounds, offering new mass interval predictions.

## Key findings

- Inferred axion mass range: 0.1 eV to 0.2 eV with full parameter fixing.
- Broader axion mass range: 0.1 eV to 6.3 eV when fixing only the axion mass.
- Light axion as a viable dark matter candidate.

## Abstract

In this work we use the Maximum Entropy Principle (MEP) to infer the mass of an axion which interacts to photons and neutrinos in an effective low energy theory. The Shannon entropy function to be maximized is suitably defined in terms of the axion branching ratios. We show that MEP strongly constrains the axion mass taking into account the current experimental bounds on the neutrinos masses. Assuming that the axion is massive enough to decay into all the three neutrinos and that MEP fixes all the free parameters of the model, the inferred axion mass is in the interval $0.1\ $eV$\ <m_{A}<0.2$ eV, which can be tested by forthcoming experiments such as IAXO. However, even in the case where MEP fixes 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 light axion, allowed to decay to photons and the lightest neutrino only, is determined by MEP as a viable dark matter candidate.