Scattering amplitude from Bethe-Salpeter wave function inside the interaction range

Abstract

We propose a method to calculate scattering amplitudes using the Bethe-Salpeter wave function inside the interaction range on the lattice. For an exploratory study of this method, we evaluate a scattering length of $I=2$ S-wave two pions by the use of the on-shell scattering amplitude. Our result is confirmed to be consistent with the value obtained from the conventional finite volume method. The half-off-shell scattering amplitude is also evaluated.

5 pages, 4 figures; published version

References in corpus (2)

• Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory
• $I=2$ $\pi \pi$ scattering phase shift from the HAL QCD method with the LapH smearing

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• Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory
• Comment on "Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory"
• Reply to "Comment on `Relation between scattering amplitude and Bethe-Salpeter wave function in quantum field theory"'
• Quark mass dependence of on-shell and half off-shell scattering amplitudes from Bethe-Salpeter wave function inside the interaction range
• Two-pion scattering amplitude from Bethe-Salpeter wave function at the interaction boundary