Derivative Expansion of Wave Function Equivalent Potentials

Abstract

Properties of the wave function equivalent potentials introduced by HAL QCD collaboration are studied in a non-relativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and non-local potentials. The expansion coefficients are determined from analytic solutions to the Nambu-Bethe-Salpeter wave functions. The scattering phase shifts computed from these potentials are compared with the exact values to examine the convergence of the expansion. It is confirmed that the generalized derivative expansion converges in terms of the scattering phase shift rather than the functional structure of the non-local potentials. It is also found that the convergence can be improved by tuning either the choice of interpolating fields or expansion scale in the generalized derivative expansion.

16 pages, 17 figures

References in corpus (5)

• Nuclear Force from Lattice QCD
• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Two Nucleon Systems at $m_{\pi }\sim 450\mathrm{MeV}$ from Lattice QCD
• Two-Nucleon Higher Partial-Wave Scattering from Lattice QCD
• Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD

Cited by in corpus (4)

• Lattice QCD and baryon-baryon interactions: HAL QCD method
• Charmonium-nucleon interactions from the time-dependent HAL QCD method
• Renormalization of a Contact Interaction on a Lattice
• Current matrix element in HAL QCD's wave function equivalent potential method