New dispersion relations in the description of $\pi\pi$ scattering amplitudes

TL;DR

This paper introduces new once-subtracted dispersion relations for $$ scattering amplitudes, offering a more precise and stringent test of crossing symmetry and analyticity below 1 GeV compared to traditional Roy's equations.

Contribution

The paper develops and compares new once-subtracted dispersion relations with Roy's equations, demonstrating improved precision in testing crossing symmetry for $$ partial waves.

Findings

Once-subtracted dispersion relations provide more precise crossing tests.

Uncertainties are significantly reduced in the 400 to 1.1 GeV region.

Results outperform standard Roy's equations with the same input.

Abstract

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the $\pi\pi$ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three $\pi\pi$ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for $\pi\pi$ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.