Breakdown of Chiral Perturbation Theory for the Axion Hot Dark Matter Bound

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