Nucleon-nucleon interactions via Lattice QCD: Methodology --HAL QCD approach to extract hadronic interactions in lattice QCD--

Abstract

We review the potential method in lattice QCD, which has recently been proposed to extract nucleon-nucleon interactions via numerical simulations. We focus on the methodology of this approach by emphasizing the strategy of the potential method, the theoretical foundation behind it, and special numerical techniques. We compare the potential method with the standard finite volume method in lattice QCD, in order to make pros and cons of the approach clear. We also present several numerical results for the nucleon-nucleon potentials.

12 pages, 10 figures

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• Hadron-Hadron Interactions from Imaginary-time Nambu-Bethe-Salpeter Wave Function on the Lattice
• Light Hadron Masses from Lattice QCD
• Hyperon-nucleon force from lattice QCD
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• Microscopically constrained mean field models from chiral nuclear thermodynamics
• Three pion nucleon coupling constants
• Possible existence of a dibaryon candidate $N\Delta$ ($D_{21}$)
• Coarse graining of NN inelastic interactions up to 3 GeV:Repulsive vs Structural core
• Low energy peripheral scaling in Nucleon-Nucleon Scattering and uncertainty quantification
• Theoretical study of a $d^{\ast }$ resonance in ${}^3{G}_3$ partial wave of nucleon-nucleon scattering
• From QCD Symmetries to Nuclei and Neutron Stars
• Dense Baryonic Matter and Strangeness in Neutron Stars
• New many-body method using cluster expansion diagrams with tensor-optimized antisymmetrized molecular dynamics
• Successive variational approach with the tensor-optimized antisymmetrized molecular dynamics for the ${}^5$He nucleus
• Lattice QCD and Baryon-Baryon Interactions
• Matching effective few-nucleon theories to QCD