Mesons upon low-lying Dirac mode exclusion

We study the isoscalar and isovector $J=0,1$ mesons with the overlap operator within two flavour lattice QCD. After subtraction of the lowest-lying Dirac eigenmodes from the valence quark propagator all disconnected contributions vanish and all possible point-to-point $J=0$ correlators become identical, signaling a simultaneous restoration of both $SU(2)_L \times SU(2)_R$ and $U(1)_A$ symmetries. The ground states of the $\pi,\sigma,a_0,\eta$ mesons do not survive this truncation. All possible $J=1$ states have a very clean exponential decay and become degenerate, demonstrating a $SU(4)$ symmetry of a dynamical QCD-like string.