Nucleon-Nucleon Potential and its Non-locality in Lattice QCD

Abstract

By the quenched lattice QCD simulation for two nucleons with finite scattering energy, validity of the delivative expansion of the general nucleon-nucleon potential U(r,r') = V(r, {\nabla}_r) δ^3(r-r') is studied. The relative kinetic energy between two nucleons is introduced through the anti-periodic boundary condition in the spatial directions. On a hypercubic lattice with the lattice spacing a ~ 0.137 fm and the spatial extent L_s ~ 4.4 fm with the pion mass m_π ~ 530 MeV, the local potentials for two different energies (E ~ 0 MeV and 45 MeV) are compared and found to be identical within statistical errors, which validates the local approximation of U(r,r') up to E=45 MeV for the central and tensor potentials. Central potentials in the spin-singlet channel for different orbital angular momentums (l=0 and l=2) at E ~ 45 MeV are also found to be the same within the errors, which also supports the local approximation.

15 pages, 16 figures

References in corpus (8)

• Nuclear Force from Lattice QCD
• Bound H-dibaryon in Flavor SU(3) Limit of Lattice QCD
• Hyperon-nucleon force from lattice QCD
• Baryon-Baryon Interactions in the Flavor SU(3) Limit from Full QCD Simulations on the Lattice
• Nuclear Force from Monte Carlo Simulations of Lattice Quantum Chromodynamics
• Charmonium-nucleon potential from lattice QCD
• Bethe--Salpeter wave functions in integrable models
• The study of the Three Nucleon Force in full QCD Lattice calculations

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