The Low Energy Expansion for Pion-Pion Scattering and Crossing Symmetry in Dispersion Relations

Abstract

We show that a suitable setting for comparison of the low-energy representation for pion-pion scattering amplitudes, with dispersive representation for these amplitudes, is provided by certain manifestly crossing symmetric dispersion relations. We begin with a discussion of fixed-t dispersion relations and discuss the origin of crossing constraints that arise in this context when we consider resonance saturation with certain $l\ge 2$ states. We demonstrate that the approach advocated here does not require us to enforce such constraints. Our results are contrasted with those from fixed-t dispersion relations. We finally discuss the numerical import of our results.

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References in corpus (3)

• Chiral two-loop pion-pion scattering parameters from crossing-symmetric constraints
• Higher Threshold Parameters in pi pi Scattering
• Probing the quark condensate by means of pi-pi scattering

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