On the momentum transfer dependence of the phase in elastic scattering

Vladimir A. Petrov

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arXiv · 2001.04844

On the momentum transfer dependence of the phase in elastic scattering

Vladimir A. Petrov

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Abstract

The question is discussed: to what extent the often assumed independence of the phase of the elastic scattering amplitude from the momentum transfer \textit{in the region of only small values} of $ t $ limits $ t $-dependence of the phase generally. Analyticity allows to give a proof that if the phase of a strong interaction scattering amplitude is independent on the transferred momentum $ t $ at small values of $ t $ then it does so in all physical region. Moreover, if such an independence holds in any physical energy $ \sqrt{s} $ region including the values infinitesimally close to the first inelastic threshold from below the whole scattering amplitude vanishes. Relationship of the $ t $-dependence of the phase with the size of the interaction range is also discussed.

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Vladimir A. Petrov. 2020-01-14. On the momentum transfer dependence of the phase in elastic scattering. https://arxiv.org/abs/2001.04844

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