Zero energy scattering calculation in Euclidean space

Abstract

We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.

11 pages, 3 figures, to be published in Phys. Lett. B

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• Nuclear Physics from Lattice QCD
• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Solving Bethe-Salpeter scattering state equation in Minkowski space
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Cited by in corpus (6)

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• Asymptotic behavior of Nambu-Bethe-Salpeter wave functions for scalar systems with a bound state
• Quark mass dependence of on-shell and half off-shell scattering amplitudes from Bethe-Salpeter wave function inside the interaction range
• Hermitizing the HAL QCD potential in the derivative expansion
• Scattering solutions of Bethe-Salpeter equation in Minkowski and Euclidean spaces
• Two-pion scattering amplitude from Bethe-Salpeter wave function at the interaction boundary