Excited state nucleon spectrum with two flavors of dynamical fermions

Highly excited states for isospin $\frac{1}{2}$ baryons are calculated for the first time using lattice QCD with two flavors of dynamical quarks. Anisotropic lattices are used with two pion masses, $m_{\pi }=416(36)\mathrm{MeV}$ and 578(29) MeV. The lowest four energies are reported in each of the six irreducible representations of the octahedral group at each pion mass. The lattices used have dimensions ${24}^3\times 64$, spatial lattice spacing $a_s\approx 0.11\mathrm{fm}$, and temporal lattice spacing $a_t=\frac{1}{3}{a}_s$. Clear evidence is found for a $\frac{5^{-}}{2}$ state in the pattern of negative-parity excited states. This agrees with the pattern of physical states and spin $\frac{5}{2}$ has been realized for the first time on the lattice.

Figure 1

Pion effective mass results for different smearings (S denotes smeared, P denotes point) and operators (op1 denotes operators of Table  and op2 denotes operators including an extra factor of ${\gamma }^4$). Results are based on 862 gauge configurations, quark mass parameter $m_0=-0.4125$, and a ${24}^3\times 64$ lattice.

Figure 2

Dispersion relation for $\pi$ (left panel) and $\rho$ (right panel) mesons for quark mass parameter $m_0=-0.4125$ and ${24}^3\times 64$ lattice.

Figure 3

The spatial arrangements of the extended three-quark baryon operators. Smeared quark fields are shown by solid circles, line segments indicate gauge-covariant displacements, and each hollow circle indicates the location of a Levi-Cività color coupling. For simplicity, all displacements have the same length in an operator. Results presented here used displacement lengths of $3a_s$ ($\sim 0.3\mathrm{fm}$).

Figure 4

The spatial arrangements of the quark-antiquark meson operators. In the illustrations, the smeared quarks fields are depicted by solid circles, each hollow circle indicates a smeared “barred” antiquark field, and the solid line segments indicate covariant displacements.

Figure 5

Effective masses $M(t)$ for unsmeared (black circles) and smeared (red triangles) operators $O_{\mathrm{SS}}$, $O_{\mathrm{SD}}$, and $O_{\mathrm{TDT}}$, which are representative single-site, singly displaced, and triply displaced-T nucleon operators, respectively. Top row: only quark-field smearing $n_{\sigma }=32$, ${\sigma }_s=4.0$ is used. Middle row: only link-variable smearing $n_{\rho }=16$, $n_{\rho }\rho =2.5$ is applied. Bottom row: both quark and link smearing $n_{\sigma }=32$, ${\sigma }_s=4.0$, $n_{\rho }=16$, $n_{\rho }\rho =2.5$ are used, dramatically improving the signal for all three operators. Results are based on 50 quenched configurations on a ${12}^3\times 48$ anisotropic lattice using the Wilson action with $a_s\sim 0.1\mathrm{fm}$, $a_s/a_t\sim 3.0$.

Figure 6

The energies obtained for each symmetry channel of isospin $\frac{1}{2}$ baryons are shown based on the ${24}^3\times 64$ $N_f=2$ lattice QCD data for $m_{\pi }=416\mathrm{MeV}$ (left panel) and $m_{\pi }=578\mathrm{MeV}$ (right panel). The scale shows energies in MeV and errors are indicated by the vertical size of the boxes. The overall error in the scale setting is not included. Empty boxes show thresholds for multihadron states.

Figure 7

Plots of Eq. (49) versus time for $G_{1g}$ states (left panels) and $G_{1u}$ states (right panels) for $m_{\pi }=416\mathrm{MeV}$. For the two lowest energy states in the $G_{1u}$ channel we first subtract off the backward exponential.

Figure 8

Plots of Eq. (49) versus time for $H_g$ states (left panels) and $H_u$ states (right panels) for $m_{\pi }=416\mathrm{MeV}$.

Figure 9

Plots of Eq. (49) versus time for $G_{2g}$ states (left panels) and $G_{2u}$ states (right panels) for $m_{\pi }=416\mathrm{MeV}$.

Figure 10

Plots of Eq. (49) versus time for $G_{1g}$ states (left panels) and $G_{1u}$ states (right panels) for $m_{\pi }=578\mathrm{MeV}$.

Figure 11

Plots of Eq. (49) versus time for $H_g$ states (left panels) and $H_u$ states (right panels) for $m_{\pi }=578\mathrm{MeV}$.

Figure 12

Plots of Eq. (49) versus time for $G_{2g}$ states (left panels) and $G_{2u}$ states (right panels) for $m_{\pi }=578\mathrm{MeV}$.