On the momentum transfer dependence of the phase in elastic scattering

TL;DR

This paper investigates how the phase of elastic scattering amplitudes depends on momentum transfer, demonstrating that small- extit{t} independence implies broader constraints and relates to the interaction range.

Contribution

It provides a proof that phase independence at small extit{t} extends to all physical regions and links phase behavior to the interaction range.

Findings

Phase independence at small extit{t} implies independence across the physical region.

If phase is independent at small extit{t}, the scattering amplitude vanishes near the inelastic threshold.

Relationship established between phase extit{t}-dependence and interaction size.

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.