Structure and flow of the nucleon eigenstates in lattice QCD

Abstract

A determination of the excited energy eigenstates of the nucleon, s = 1 2 , I = 1 2 , N ± , is presented in full QCD using 2 + 1 flavor PACS-CS gauge configurations. The correlation-matrix method is used and is built using standard nucleon interpolators employing smearings at the fermion sources and sinks. We develop and demonstrate a new technique that allows the eigenvectors obtained to be utilized to track the propagation of the intrinsic nature of energy-states from one quark mass to the next. This approach is particularly useful for larger dimension correlation matrices where more near-degenerate energy-states can appear in the spectrum.

Baryons as relativistic three-quark bound states

“…The lattice data are a typical example of such calculations [399]; many other groups have performed similar simulations with results that agree very well with each other [400,405,[414][415][416][417][418], see e.g. Fig.…”

“…Consequently, also here the errors are substantial and the results by far do not have the quality of the positive-parity ground state calculations. Nevertheless, within error bars there is agreement between different groups that the N (1535) is seen although the extracted mass is still larger than the experimental one, see [264,279,416,417,425,427] and references therein. The structure of this state has been investigated in Ref.…”

“…This includes the use of a sufficiently large sets of operators, the systematic identification of scattering states and the need to extend the simulations to the physical point. Results so far are therefore still on the preliminary level, although very promising [264,265,281,399,[415][416][417][418][419][420]. In the functional framework results for excited baryons are still scarce.…”

Searching for low-lying multi-particle thresholds in lattice spectroscopy

“…We enforce this symmetry by working with the improved unbiased symmetric construction (G i j + G ji )/2. To ensure that the matrix elements are all ∼ O(1), each element of G i j (t) is normalized [9] by the diagonal elements of G(0) as…”

“…Correlation matrices composed of traditional three-quark operators have been very successful in revealing a dense spectrum of baryon excited states in lattice QCD [1][2][3][4][5][6][7][8][9][10][11][12]. However the lowest lying multi-particle scattering state thresholds are often absent in the observed spectra.…”