Pion-pion scattering and the K→3π decay amplitudes

We revisit the recently proposed method for the determination of the pi-piscattering length combination a_{0}-a_{2}, based on the study of the pi0 pi0spectrum in K+ -> pi+ pi0 pi0. In view of a precision measurement, we discusshere the effects due to smaller absorptive contributions to the K+ -> pi+ pi0pi0 and K+ -> pi+ pi+ pi- amplitudes. We outline a method of analysis that canlead to a precision determination of a_{0}-a_{2} and is based on very generalproperties of the S matrix. The discussion of final-state rescattering and cuspeffects is also extended to the two K_L -> 3pi coupled channels. Thanks to thepresent work, the theoretical error on the a_{0}-a_{2} combination extractedfrom the K+ -> pi+ pi0 pi0 spectrum is reduced to about 5%. A further reductionrequires the evaluation of the effects arising from radiative corrections.Comment: 32 pages, 6 figure