Nucleon, $\ensuremath{\Delta}$, and $\ensuremath{\Omega}$ excited state spectra in ${N}_{f}=2+1$ lattice QCD

Nucleon, $Δ$ , and $Ω$ excited state spectra in $N_{f} = 2 + 1$ lattice QCD

J. Bulava, R. G. Edwards, E. Engelson, B. Joó, H-W. Lin, C. Morningstar, D. G. Richards, and S. J. Wallace (Hadron Spectrum Collaboration)

Phys. Rev. D 82, 014507 – Published 22 July 2010

Abstract

The energies of the excited states of the nucleon, $Δ$ , and $Ω$ are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculation is performed at three values of the light quark mass, corresponding to pion masses $m_{π} = 392 (4)$ , 438(3), and 521(3) MeV. We employ the variational method with a large basis of interpolating operators enabling six energies in each irreducible representation of the lattice to be distinguished clearly. We compare our calculation with the low-lying experimental spectrum, with which we find reasonable agreement in the pattern of states. The need to include operators that couple to the expected multihadron states in the spectrum is clearly identified.

Received 28 April 2010

DOI:https://doi.org/10.1103/PhysRevD.82.014507

Authors & Affiliations

J. Bulava¹, R. G. Edwards², E. Engelson³, B. Joó², H-W. Lin⁴, C. Morningstar⁵, D. G. Richards², and S. J. Wallace³ (Hadron Spectrum Collaboration)

¹NIC, DESY, Platanenallee 6, D-15738, Zeuthen, Germany
²Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA
³Department of Physics, University of Maryland, College Park, Maryland 20742, USA
⁴Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA
⁵Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

Excited state nucleon spectrum with two flavors of dynamical fermions

John M. Bulava, Robert G. Edwards, Eric Engelson, Justin Foley, Bálint Joó, Adam Lichtl, Huey-Wen Lin, Nilmani Mathur, Colin Morningstar, David G. Richards, and Stephen J. Wallace

Phys. Rev. D 79, 034505 (2009)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 82, Iss. 1 — 1 July 2010

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Nucleon $G_{1 g}$ effective energies are shown for the lowest states in the upper six graphs. The effective energy increases from left to right along the first row and continues to increase from left to right along the second row. The lower six graphs show nucleon $G_{1 u}$ effective energies increasing in the same pattern. Calculations are for $m_{π} = 392 (4) MeV$ . Vertical bars show the effective energy and the curved dashed line shows the effective energy calculated from the fit function. Horizontal dashed lines show the fit results for $E \pm σ$ and their extent shows the fitting interval $(t_{i}, t_{f})$ .
Reuse & Permissions
Figure 2
Nucleon $H_{g}$ effective energies are shown for the lowest states in the upper six graphs and nucleon $H_{u}$ effective energies are shown in the lower six graphs with effective energies increasing in the same pattern as in Fig. 1. Calculations are for $m_{π} = 392 (4) MeV$ . Vertical bars show the effective energy and the curved dashed line shows the effective energy calculated from the fit function. Horizontal dashed lines show the fit results for $E \pm σ$ and their extent shows the fitting interval $(t_{i}, t_{f})$ .
Reuse & Permissions
Figure 3
Nucleon $G_{2 g}$ effective energies are shown for the lowest states in the upper six graphs and nucleon $G_{2 u}$ effective energies are shown in the lower six graphs with effective energies increasing in the same pattern as in Fig. 1. Calculations are for $m_{π} = 392 (4) MeV$ . Vertical bars show the effective energy and the curved dashed line shows the effective energy calculated from the fit function. Horizontal dashed lines show the fit results for $E \pm σ$ and their extent shows the fitting interval $(t_{i}, t_{f})$ .
Reuse & Permissions
Figure 4
Spectra for isospin $\frac{1}{2}$ (nucleon family) at three values of $m_{π}$ are compared with experimental spectra. Plots in the first row show $G_{1 g}$ and $G_{1 u}$ lattice irreps, plots in the second row show $H_{g}$ and $H_{u}$ irreps and plots in the third row show $G_{2 g}$ and $G_{2 u}$ irreps. Columns labeled by $m_{π} = 392$ , 438, and 521 show lattice spectra at those values of $m_{π}$ . Two, three and four-star experimental resonances are shown in columns labeled by their $J^{P}$ values. Each $J^{P}$ value listed has a subduction to the lattice irrep shown. Each box for an experimental resonance has height equal to the full decay width and an inner box (color aqua) showing the uncertainty in the Breit-Wigner energy. Triangles to the right of lattice spectra point to the threshold for scattering states at that value of $m_{π}$ .
Reuse & Permissions
Figure 5
Spectra for isospin $\frac{3}{2}$ ( $Δ$ family) at three values of $m_{π}$ are compared with experimental spectra. Plots in the first row show $G_{1 g}$ and $G_{1 u}$ lattice irreps, plots in the second row show $H_{g}$ and $H_{u}$ irreps and plots in the third row show $G_{2 g}$ and $G_{2 u}$ irreps. Columns labeled by $m_{π} = 392$ , 438, and 521 show lattice spectra at those values of $m_{π}$ . Two, three and four-star experimental resonances are shown in columns labeled by their $J^{P}$ values. Each $J^{P}$ value listed has a subduction to the lattice irrep shown. Each box for an experimental resonance has height equal to the full decay width and an inner box (color aqua) showing the uncertainty in the Breit-Wigner energy. Triangles to the right of lattice spectra point to the threshold for scattering states at that value of $m_{π}$ .
Reuse & Permissions
Figure 6
Spectra for isospin 0, strangeness $- 3$ ( $Ω$ family) at three values of $m_{π}$ are compared with experimental spectra. Plots in the first row show $G_{1 g}$ and $G_{1 u}$ irreps, plots in the second row show $H_{g}$ and $H_{u}$ irreps and plots in the third row show $G_{2 g}$ and $G_{2 u}$ lattice irreps. Columns labeled by $m_{π} = 392$ , 438, and 521 show lattice spectra at those values of $m_{π}$ . Two, three and four-star experimental resonances are shown in columns labeled by their $J^{P}$ values. Each $J^{P}$ value listed has a subduction to the lattice irrep shown. For the $Ω$ , the spins and parities of the experimentally observed states other than the lightest are not clearly determined; for comparison, we assign the states to ${\frac{3}{2}}^{+}$ , with the heights of the boxes indicating the widths. Triangles to the right of lattice spectra point to the threshold for scattering states at that value of $m_{π}$ .
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology

Nucleon, $Δ$ , and $Ω$ excited state spectra in $N_{f} = 2 + 1$ lattice QCD

J. Bulava, R. G. Edwards, E. Engelson, B. Joó, H-W. Lin, C. Morningstar, D. G. Richards, and S. J. Wallace (Hadron Spectrum Collaboration)

Phys. Rev. D 82, 014507 – Published 22 July 2010

Abstract

Authors & Affiliations

See Also

Excited state nucleon spectrum with two flavors of dynamical fermions

John M. Bulava, Robert G. Edwards, Eric Engelson, Justin Foley, Bálint Joó, Adam Lichtl, Huey-Wen Lin, Nilmani Mathur, Colin Morningstar, David G. Richards, and Stephen J. Wallace

Phys. Rev. D 79, 034505 (2009)

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review D

covering particles, fields, gravitation, and cosmology

Nucleon, Δ, and Ω excited state spectra in Nf=2+1 lattice QCD

J. Bulava, R. G. Edwards, E. Engelson, B. Joó, H-W. Lin, C. Morningstar, D. G. Richards, and S. J. Wallace (Hadron Spectrum Collaboration)

Phys. Rev. D 82, 014507 – Published 22 July 2010

Abstract

Authors & Affiliations

See Also

Excited state nucleon spectrum with two flavors of dynamical fermions

John M. Bulava, Robert G. Edwards, Eric Engelson, Justin Foley, Bálint Joó, Adam Lichtl, Huey-Wen Lin, Nilmani Mathur, Colin Morningstar, David G. Richards, and Stephen J. Wallace

Phys. Rev. D 79, 034505 (2009)

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Nucleon, $Δ$ , and $Ω$ excited state spectra in $N_{f} = 2 + 1$ lattice QCD