Roper Resonance and S₁₁(1535) from Lattice QCD

Using the constrained curve fitting method and overlap fermions with the lowest pion mass at $180 {\rm MeV}$, we observe that the masses of the first positive and negative parity excited states of the nucleon tend to cross over as the quark masses are taken to the chiral limit. Both results at the physical pion mass agree with the experimental values of the Roper resonance ($N^{1/2+}(1440)$) and $S_{11}$ ($N^{1/2-}(1535)$). This is seen for the first time in a lattice QCD calculation. These results are obtained on a quenched Iwasaki $16^3 \times 28$ lattice with $a = 0.2 {\rm fm}$. We also extract the ghost $\eta' N$ states (a quenched artifact) which are shown to decouple from the nucleon interpolation field above $m_{\pi} \sim 300 {\rm MeV}$. From the quark mass dependence of these states in the chiral region, we conclude that spontaneously broken chiral symmetry dictates the dynamics of light quarks in the nucleon.