Abstract
The off-mass shell scattering amplitude, satisfying the Bethe–Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.
Highlights
Obtaining the solutions of Bethe-Salpeter (BS) equation in its original Minkowski space formulation [1] has raised an increasing interest in the recent years [2, 3, 4, 5, 6]
A method based on the Nakanishi representation [16] of the BS amplitude was developed in [3, 4] allowing to compute for the first time the bound state Minkowski amplitude and latter on [7, 8] the corresponding form factors
The aim of this paper is to presents a direct solution of the original BS equation in Minkowski space providing the scattering length, elastic and inelastic phase shifts and the first results for the half-off-shell BS amplitude
Summary
Obtaining the solutions of Bethe-Salpeter (BS) equation in its original Minkowski space formulation [1] has raised an increasing interest in the recent years [2, 3, 4, 5, 6]. A method based on the Nakanishi representation [16] of the BS amplitude was developed in [3, 4] allowing to compute for the first time the bound state Minkowski amplitude and latter on [7, 8] the corresponding form factors. This approach could be naturally extended to the scattering states, we have found that the problem could be solved in a simplest and more straightforward way. The aim of this paper is to presents a direct solution of the original BS equation in Minkowski space providing the scattering length, elastic and inelastic phase shifts and the first results for the half-off-shell BS amplitude
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