Asymptotics and zeros of the imaginary part of the elastic scattering amplitude

TL;DR

This paper investigates the asymptotic behavior and zeros of the imaginary part of the elastic scattering amplitude in high-energy hadronic interactions, analyzing unitarity conditions and their implications for the black disk limit.

Contribution

It derives an integral equation for the imaginary part incorporating asymptotic real part behavior, providing new insights into amplitude zeros and the black disk limit.

Findings

Asymptotic approach to the black disk limit is analyzed.

Conditions for zeros of the imaginary part are discussed.

Implications for current experimental observations are considered.

Abstract

The s-channel unitarity condition for the imaginary part of the hadronic elastic scattering amplitude outside the diffraction peak is studied within different assumptions about the behavior of its real part. The integral equation for the imaginary part is derived with the asymptotical expression for the real part inserted in the unitarity condition. The conclusions about the asymptotical approach to the black disk limit and possible zeros of the imaginary part of the amplitude are obtained. Their relation to the present day experiments is discussed.