Narrow structures in the range of a few MeV have been searched for in p p pi+ and p p pi- invariant mass spectra obtained from exclusive measurements of the p p -> p p pi+ pi- reaction at Tp = 725, 750 and 775 MeV using the PROMICE/WASA detector at CELSIUS. The selected reaction is particularily well suited for the search for NN and / or N Delta decoupled dibaryon resonances. Except for a possible fluctuation at 2087 MeV/c^2 in Mpppi- no narrow structures could be identified neither in Mpppi+ nor in Mpppi- on the 3 sigma level of statistical significance, giving an upper limit (95% C.L.) for dibaryon production in this reaction of sigma < 20 nb for 2020 MeV/c^2 < m(dibaryon) < 2085 MeV/c^2
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