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K -> 3π final state interactions at NLO in CHPT and Cabibbo's proposal to measure a(0)-a(2)

AuthorsGámiz, Elvira; Prades, Joaquim ; Scimemi, Ignazio
KeywordsChiral perturbation theory
π-π scattering
Isospin breaking
Virtual photons
[PACS] Decays of K mesons
[PACS] Chiral Lagrangians
[PACS] Meson-meson interactions
Issue Date26-Jan-2007
Società Italiana di Fisica
CitationEuropean Physical Journal C 50(2): 405-422 (2007)
AbstractWe present the analytical results for the K -> 3π final state interaction phases at next-to-leading order (NLO) in CHPT. We also study the recent proposal of Cabibbo to measure the ππ scattering lengths combination a(0)-a(2) from the cusp effect in the π(0)π(0) energy spectrum at threshold for K+ -> π(0)π(0)π(+) and K-L -> π(0)π(0)π(0), and we give the relevant formulas to describe it at NLO. We estimate the theoretical uncertainty of the a(0)-a(2) determination at NLO in our approach and obtain the result that it is not smaller than 5% if added quadratically and 7% if added linearly, for K+ -> π(0)π(0)π(+). One gets similar theoretical uncertainties if the neutral K-L -> π(0)π(0)π(0) 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. We do not include isospin corrections apart from two-pion phase space factors which are physical. We compare our results for the cusp effect with those due to Cabibbo and Isidori.
Description18 pages, 7 figures.-- PACS nrs.: 13.25.Es; 12.39.Fe; 13.75.Lb.-- ISI Article Identifier: 000245431700012.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-ph/0602023
Printed version published in Apr 2007.
Publisher version (URL)http://dx.doi.org/10.1140/epjc/s10052-006-0201-7
Appears in Collections:(IFIC) Artículos
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