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Pion-pion scattering and the K->3pi decay amplitudes

Nicola Cabibbo·Gino Isidori
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Abstract

We revisit the recently proposed method for the determination of the pi-pi scattering length combination a_{0}-a_{2}, based on the study of the pi0 pi0 spectrum in K+ -> pi+ pi0 pi0. In view of a precision measurement, we discuss here the effects due to smaller absorptive contributions to the K+ -> pi+ pi0 pi0 and K+ -> pi+ pi+ pi- amplitudes. We outline a method of analysis that can lead to a precision determination of a_{0}-a_{2} and is based on very general properties of the S matrix. The discussion of final-state rescattering and cusp effects is also extended to the two K_L -> 3pi coupled channels. Thanks to the present work, the theoretical error on the a_{0}-a_{2} combination extracted from the K+ -> pi+ pi0 pi0 spectrum is reduced to about 5%. A further reduction requires the evaluation of the effects arising from radiative corrections.

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Nicola Cabibbo, Gino Isidori. 2005-02-14. Pion-pion scattering and the K->3pi decay amplitudes. https://doi.org/10.1088/1126-6708%2F2005%2F03%2F021

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