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Zero energy scattering calculation in Euclidean space

Carbonell, J. ; Karmanov, V.A.

Physics letters. B, 2016-03, Vol.754 (C), p.270-274 [Peer Reviewed Journal]

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Title:
Zero energy scattering calculation in Euclidean space
Author: Carbonell, J. ; Karmanov, V.A.
Subjects: Bethe–Salpeter equation ; Euclidean scattering ; High Energy Physics - Lattice ; High Energy Physics - Phenomenology ; High Energy Physics - Theory ; Lattice simulations ; Nuclear Theory ; Physics
Is Part Of: Physics letters. B, 2016-03, Vol.754 (C), p.270-274
Description: 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.
Publisher: Elsevier B.V
Language: English;Italian

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