The Roper state is extracted with valence overlap fermions on a 2+1-flavor domain-wall fermion lattice (spacing a=0.114 fm and mπ=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 as=0.12 fm and pion mass mπ=396 MeV) and obtain consistent results. However, these calculations with clover fermions give a Roper mass of mR=1.92(6) GeV, while the same approach with overlap fermions finds the Roper ≈280 MeV lower, at mR=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 (a0) correlator in the quenched approximation. The lack of quark loops in the quenched approximation turns the a0 correlator negative; giving rise to a ghost "would-be" ηπ state. Comparing the a0 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) are about half of those of overlap - whereas, the whole a0 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., Nπ, Nππ 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, Δ and Λ.
|Journal||Physical Review D|
|State||Published - Mar 1 2020|
Bibliographical noteFunding Information:
We thank the RBC and UKQCD Collaborations for providing their DWF gauge configurations. This work is supported in part by the U.S. DOE Grant No. DE-SC0013065 and DOE Grant No. DE-AC05-06OR23177 which is within the framework of the TMD Topical Collaboration. A. A. is supported by National Science Foundation CAREER Grant No. PHY-1151648. A. A. and F. L. are supported by U.S. DOE Grant No. DE-FG02-95ER40907. A. L. thanks the Institute for Nuclear Theory at the University of Washington for its kind hospitality and stimulating research environment. His research was supported in part by the INT’s U.S. DOE Grant No. DE-FG02-00ER41132. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This work used Stampede time under the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. We also thank the National Energy Research Scientific Computing Center (NERSC) for providing HPC resources that have contributed to the research results reported within this paper. We acknowledge the facilities of the USQCD Collaboration used for this research in part, which are funded by the Office of Science of the U.S. Department of Energy.
© 2020 authors. Published by the American Physical Society.
ASJC Scopus subject areas
- Nuclear and High Energy Physics