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We investigate the axial $U(1)$ symmetry restoration at finite temperature in two flavor QCD. We employ the M\"obius domain-wall formalism that is designed to achieve good chiral symmetry. We show the measurements of a difference of meson susceptibilities, sensitive to the $U(1)_A$ symmetry breaking. The signal is dominated by zero and near-zero modes. By reweighting the measure to that of overlap fermions we find a suppression of the $U(1)_A$ breaking effects above the chiral transition temperature.

Axial U(1) symmetry at finite temperature with Mobius domain-wall fermions