Measuring the a0-a2 pion scattering lengths through K to 3 pi decays

Abstract

We discuss the recent Cabibbo's proposal to measure the pion-pion scattering lengths combination a0-a2 from the cusp effect in the pi0-pi0 energy spectrum at threshold for K+ to (pi0 pi0 pi+) and KL to (pi0 pi0 pi0). We estimate the theoretical uncertainty of the a0-a2 determination at NLO in our approach and obtain that it is not smaller than 5% for K+ to (pi0 pi0 pi+). One gets similar theoretical uncertainties if the neutral KL to (pi0 pi0 pi0) decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lengths.

arXiv commentInvited talk at ``QCD 06'', 3-7 July 2006, Montpellier, France

References in corpus (12)

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• Cusps in K --> 3 pi decays
• Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to $\pi \pi$ scattering
• Determination of the a0-a2 pion scattering length from K->pi+ pi0 pi0 decay
• Pion-pion scattering and the K->3pi decay amplitudes
• K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2
• Isospin Breaking in $K\to 3\pi$ Decays III: Bremsstrahlung and Fit to Experiment
• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
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• Isospin Breaking in $K\to 3\pi$ Decays I: Strong Isospin Breaking
• Virtual Photon Correction to the $K^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$ Decay
• Three-body dispersion-relation N/D equations for the coupled decay channels ppbar (J^{PC}=0^{-+}) --> pi^0 pi^0 pi^0, eta pi^0 pi^0, eta eta pi^0, K Kbar pi^0