Isoscalar mesons upon unbreaking of chiral symmetry

Understand

In a dynamical lattice simulation with the overlap Dirac operator and $N_f=2$ mass degenerate quarks we study all possible $J=0$ and $J=1$ correlators upon exclusion of the low lying "quasi-zero" modes from the valence quark propagators.

• After subtraction of a small amount of such Dirac eigenmodes all disconnected contributions vanish and all possible point-to-point $J=0$ correlators with different quantum numbers become identical, signaling a restoration of the $SU(2)_L \times SU(2)_R \times U(1)_A$.
• The original ground state of the $\pi$ meson does not survive this truncation, however.
• In contrast, in the $I=0$ and $I=1$ channels for the $J=1$ correlators the ground states have a very clean exponential decay.