A theorem on the real part of the high-energy scattering amplitude near the forward direction

TL;DR

This paper proves that under certain high-energy scattering conditions, the real part of the amplitude near the forward direction cannot maintain a constant sign, revealing fundamental constraints on scattering behavior.

Contribution

It establishes a new theorem linking the asymptotic behavior of differential and total cross-sections to the sign of the real part of the scattering amplitude.

Findings

Real part of the amplitude cannot have a constant sign under specified conditions.

Differential cross-section tending to zero implies constraints on amplitude sign.

Total cross-section divergence influences the amplitude's real part near t=0.

Abstract

We show that if for fixed negative (physical) square of the momentum transfer t, the differential cross-section ${d\sigma\over dt}$ tends to zero and if the total cross-section tends to infinity, when the energy goes to infinity, the real part of the even signature amplitude cannot have a constant sign near t = 0.