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Dependence of the phase of the elastic scattering amplitude on momentum transfer

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Abstract

We discuss the extent to which the often assumed independence of the phase of the elastic scattering amplitude from momentum transfer in the domain of only small \(t\) constrains the dependence of the phase on \(t\) in general. Based on analyticity, we prove that if the scattering amplitude phase is independent of the transferred momentum in the domain of its small values in strong couplings, then this remains the case in the whole physical domain. Moreover, if such independence holds in any domain of physical energies including values infinitely close to the first inelastic threshold from below, then the whole scattering amplitude vanishes. We also discuss the relation between the dependence of the phase on \(t\) and the size of the interaction domain.

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Notes

  1. \(T_ \mathrm{N} (s;t)=T_ \mathrm{N} (s+i0,t),s\ge s_ \mathrm{el} \).

  2. We are grateful to A. Samokhin for this observation.

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Acknowledgments

The author is grateful to A. Samokhin for the effective discussion of some special details in the paper. His remarks allowed improving the paper.

Funding

This research was supported by the Russian Foundation for Basic Research (Grant No. 17-02-00120).

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Authors and Affiliations

  1. Logunov Institute for High Energy Physics, National Research Center “Kurchatov Institute”, Protvino, Russia

    V. A. Petrov

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  1. V. A. Petrov
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Petrov, V.A. Dependence of the phase of the elastic scattering amplitude on momentum transfer. Theor Math Phys 204, 896–900 (2020). https://doi.org/10.1134/S0040577920070041

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