Once and twice subtracted dispersion relations in the analysis of pi pi amplitudes

TL;DR

This paper compares once and twice subtracted dispersion relations for analyzing pi pi scattering data, demonstrating that the former provides stronger constraints in the 400-1100 MeV range.

Contribution

It introduces a detailed comparison of once and twice subtracted dispersion relations, highlighting the advantages of the former in constraining pi pi amplitudes.

Findings

Once subtracted dispersion relations offer stronger constraints than twice subtracted ones.

Both methods effectively test pi pi amplitudes up to about 1 GeV.

The analysis improves understanding of low-energy pi pi scattering amplitudes.

Abstract

Once and twice subtracted crossing symmetric dispersion relations applied to $\pi\pi \to \pi\pi$ scattering data are analyzed and compared. Both sets of dispersion relations can be used to test the $\pi\pi$ amplitudes in low partial waves up to about 1 GeV. We show how once subtracted dispersion relations can provide stronger constraints for $\pi\pi$ amplitudes than twice subtracted ones in the 400 to 1100 MeV range, given the same experimental input.