Analytical dispersive parameterization for elastic scattering of spinless particles

TL;DR

This paper introduces an improved dispersive parameterization for elastic scattering of spinless particles, incorporating dispersion relations and crossing symmetry to enhance analysis of scattering data beyond traditional methods.

Contribution

It develops a dispersive inverse amplitude parameterization that properly accounts for left- and right-hand cuts, crossing symmetry, and threshold effects, improving elastic scattering analysis.

Findings

Provides a compact analytic form for scattering amplitudes.

Enhances analysis of lattice data in the elastic region.

Improves upon Breit-Wigner and K-matrix approaches.

Abstract

In this paper, we present an improved parameterization of the elastic scattering of spin-0 particles, which is based on a dispersive representation for the inverse scattering amplitude. Besides being based on well known general principles, the requirement that the inverse amplitude should satisfy the dispersion relation significantly constrains its possible forms and have not been incorporated in the existing parameterizations so far. While the right-hand cut of the inverse scattering amplitude is controlled by unitarity, the contribution from the left-hand cut, which comes from the crossing symmetry, is commonly ignored or incorporated improperly. The latter is parameterized using the expansion in a suitably constructed conformal variable, which accounts for its analytic structure. The correct implementations of the Adler zero and threshold factors for angular momentum $J>0$ are discussed in detail as well. The amplitudes are written in a compact analytic form and provide a useful tool to analyze current and future lattice data in the elastic region improving upon the commonly used Breit-Wigner or K-matrix approaches.