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

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

1998-02-17

arxiv.org/abs/hep-ph/9802338v1

Phys.Rev.D58:036002,1998

Physics

High Energy Physics

High Energy Physics - Phenomenology

24 pages plain LaTeX, to be run twice

Scientific paper

10.1103/PhysRevD.58.036002

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 $l\geq 2$ 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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