Figure 1

Compilation of current lattice calculations of the spectrum of the even-parity spin-$1/2$ excited states of the nucleon. In each study the ground state and excited state masses are shown. Burch et al. (solid triangles) report two excited states, one as the $N^{\prime }$ the other as a Roper candidate. Basak et al. (diamonds) report the masses of three excited states. Note that the two data points with degenerate masses from Basak et al. [13] have been displaced horizontally for clarity. To aid in understanding the results, lines of best fit to the $N^{\prime }$ and ground state masses are included. The solid line is a line of best fit to the $N^{\prime }$ excited state masses extracted in this study, and the studies of Basak et al., Burch et al. and Brömmel et al. The dashed line is a line of best fit to the ground state mass for all of the data shown.Reuse & Permissions

Figure 2

Masses extracted with a $2\times 2$ correlation matrix with ${\chi }_1$ and ${\chi }_3^{\mu }$ (left), and ${\chi }_2$ and ${\chi }_3^{\mu }$ (right). For comparison the masses extracted with the ${\chi }_1$ and ${\chi }_2$ interpolators are also shown. The data correspond to $m_{\pi }\simeq 830$ (rightmost points), 770, 700, 616, 530 and 460 MeV (leftmost points).Reuse & Permissions

Figure 3

As in Fig. 2, but for the $3\times 3$ correlation matrix with the ${\chi }_1$, ${\chi }_2$ and ${\chi }_3^{\mu }$ interpolators.Reuse & Permissions

Figure 4

A summary of existing lattice calculations of the nucleon spectrum based on correlation matrix techniques. The data points with degenerate masses from Basak et al. [13] have been displaced horizontally for clarity. $P$-wave two particle energies are illustrated by the two lines. The difference in the energies reflects the difference in the lattice volumes.Reuse & Permissions