Nature of the $a_1$ meson in lattice quantum chromodynamics studied with chiral fermions

We study the $a_1$ meson using a quenched lattice quantum chromodynamics simulation with the truncated overlap fermions formalism based on the domain wall fermions. The obtained lightest mass of the $a_1$ meson, 1272(45) MeV, is consistent with the experimental value for $a_1$(1260). Thus, $a_1$(1260) can be identified to have a simple two-body constituent-quark structure. Our quenched simulation result of $a_1$(1420) can not explain the experimental mass value, which suggests $a_1$(1420) is not a simple $q\bar{q}$ two quark state.