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The contribution of Delta(1232) to the piN -> pipiN reaction is examined bymaking use of the chiral reduction formula developed by Yamagishi and Zahed.The influence of the pi-Delta-Delta and rho-N-Delta interactions on thisreaction, which has not been regarded as important so far, is considered forall channels with the initial pi^{+ -}p states. The total cross sections arecalculated to tree level for the energy up to T_{pi}=400 MeV. Although thepi-Delta-Delta and rho-N-Delta interactions give a small effect on the pi^{+}p-> pi^{+}pi^{+}n, pi^{-}p -> pi^{+}pi^{-}n and pi^{-}p -> pi^{0}pi^{0}pchannels, the pi^{+ -}p -> pi^{+ -}pi^{0}p channels are found to be sensitiveto these interactions.Comment: 19 pages, 6 figures, Version to appear in Phys. Rev. C. Part of  introduction and summary are renewed. Some references are added and a few  typos are correcte

physical review. c. nuclear physics/physical review. c, nuclear physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Δ</mml:mi><mml:mo>(</mml:mo><mml:mn>1232</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>π</mml:mi><mml:mi>N</mml:mi><mml:mo>→</mml:mo><mml:mi>π</mml:mi><mml:mi>π</mml:mi><mml:mi>N</mml:mi></mml:mrow></mml:math>reaction

Δ(1232)inπN→ππNreaction