Roper State from Overlap Fermions

The Roper state is extracted with valence overlap fermions on a 2 + 1-flavor domain-wall fermion lattice (spacing a = 0.114 fm and m(pi) = 330 MeV) using both the sequential empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. The SEB and variational calculation with large smearing size are also carried out for an anisotropic clover lattice with similar parameters (spatial lattice spacing a(s) = 0.12 fm and pion mass m(R) = 396 MeV) and obtain consistent results. However, these calculations with clover fermions give a Roper mass of m(R) = 1.92(6) GeV, while the same approach with overlap fermions finds the Roper approximate to 280 MeV lower, at m(R) = 1.64(9) GeV, for identical valence pion mass. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin Z-diagram in the isovector scalar meson (a(0)) correlator in the quenched approximation. The lack of quark loops in the quenched approximation turns the a(0) correlator negative; giving rise to a ghost "would-be" eta pi state. Comparing the a(0), correlators for valence clover and overlap fermions, at a valence pion mass of 290 MeV, on three quenched Wilson-gauge lattices, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at a = 0.12 fm and 0.09 fm-the ratios of the Wilson ghost-state magnitudes (correlator minima) arc about half of those of overlap-whereas, the whole a(0) correlators of clover and overlap at a = 0.06 fm coincide within errors. This suggests that chiral symmetry is restored for clover at a <= 0.06 fm and that the Roper mass should agree between clover and overlap fermions toward the continuum limit. We conclude that the present work supports a resolution of the "Roper puzzle" due to Z-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g., N pi, N pi pi states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of N, Delta and A.