Abstract
The origin of the low-lying nature of the $N$*(1440), or Roper resonance, has been the subject of significant interest for many years, including several investigations using lattice QCD. The majority of lattice studies have not observed a low-lying excited state energy level in the region of the Roper resonance. However, it has been claimed that chiral symmetry could play an important role in our understanding of this resonance. The purpose of this study is to systematically examine the role of chiral symmetry in the low-lying nucleon spectrum by directly comparing the clover and overlap fermion actions. To ensure any differences in results are attributable to the choice of fermion action, simulations are performed on the same set of gauge field configurations at matched pion masses. Correlation matrix techniques are employed to determine the excitation energy of the first positive-parity excited state for each action. The clover and overlap actions show a remarkable level of agreement. We do not find any evidence that fermion action chiral symmetry plays a significant role in understanding the Roper resonance on the lattice.
Highlights
The true nature of the Roper resonance (Nð1440Þ12þP11), the first positive-parity excited state of the nucleon discovered in 1964 via a partial-wave analysis of pion-nucleon scattering data [1], is a long-standing source of debate
With an energy of 1440 MeV the Roper resonance is the lowest-lying resonance in the nucleon spectrum, sitting even below the first negative-parity excitation, the (Nð1535Þ12−S11) state. This is a reversal of the ordering predicted by simple quark models, which place the energy of the positive-parity P11 state well above that of the negative-parity S11 state. This apparent discrepancy persists in lattice QCD calculations, with the majority of lattice calculations obtaining an energy level for the first positive-parity nucleon excitation that sits high relative to that expected for the Roper resonance, even near the physical quark mass regime [2,3,4,5,6,7,8,9,10,11]
Any differences which exist between the actions will be apparent in the results presented, preserving our ability to search for a nontrivial role for chiral symmetry in the nucleon spectrum
Summary
The true nature of the Roper resonance (Nð1440Þ12þP11), the first positive-parity excited state of the nucleon discovered in 1964 via a partial-wave analysis of pion-nucleon scattering data [1], is a long-standing source of debate. With an energy of 1440 MeV the Roper resonance is the lowest-lying resonance in the nucleon spectrum, sitting even below the first negative-parity excitation, the (Nð1535Þ12−S11) state This is a reversal of the ordering predicted by simple quark models, which place the energy of the positive-parity P11 state well above that of the negative-parity S11 state. This apparent discrepancy persists in lattice QCD calculations, with the majority of lattice calculations obtaining an energy level for the first positive-parity nucleon excitation that sits high relative to that expected for the Roper resonance, even near the physical quark mass regime [2,3,4,5,6,7,8,9,10,11]. The exception to this is the χQCD Collaboration, which using overlap fermions in combination with the sequential empirical Bayes (SEB) analysis method [12] were able to find a low-lying positive-parity excited state on the lattice
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