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We show that the commonly adopted hot dark matter (HDM) bound on the axionmass $m_a \lesssim$ 1 eV is not reliable, since it is obtained by extrapolatingthe chiral expansion in a region where the effective field theory breaks down.This is explicitly shown via the calculation of the axion-pion thermalizationrate at the next-to-leading order in chiral perturbation theory. We finallyadvocate a strategy for a sound extraction of the axion HDM bound via latticeQCD techniques.

Breakdown of chiral perturbation theory for the axion hot dark matter bound