Dispersion relations with crossing symmetry for pipi D and F wave amplitudes

TL;DR

This paper derives and analyzes new dispersion relations with crossing symmetry for pipi D- and F-wave amplitudes, providing analytical tools to test and constrain pipi interactions in the 1.1 GeV range.

Contribution

It introduces a complete set of dispersion relations for D- and F-wave pipi amplitudes with analytical expressions, enhancing analysis capabilities.

Findings

New dispersion relations impose strong constraints on pipi interactions.

Analytical expressions facilitate easier application of the relations.

Relations are effective in testing D- and F-wave pipi amplitudes.

Abstract

A set of once subtracted dispersion relations with imposed crossing symmetry condition for the pipi D- and F-wave amplitudes is derived and analyzed. An example of numerical calculations in the effective two pion mass range from the threshold to 1.1 GeV is presented. It is shown that these new dispersion relations impose quite strong constraints on the analyzed pipi interactions and are very useful tools to test the pipi amplitudes. One of the goals of this work is to provide a complete set of equations required for easy use. Full analytical expressions are presented. Along with the well known dispersion relations successful in testing the pipi S- and P-wave amplitudes, those presented here for the D and F waves give a complete set of tools for analyzes of the pipi interactions.