Data accumulated recently for the exclusive measurement of the $pp\to pp\pi^+\pi^-$ reaction at a beam energy of 0.793 GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the $pp \to nn\pi^+\pi^+$ reaction channel. The latter is expected to be the only $\pi\pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $\pi\pi$ production process. No single event has been found, which meets all conditions for being a candidate for the $pp \to nn \pi^+\pi^+$ reaction. This gives an upper limit for the cross section of 0.16 $\mu$b (90% C.L.), which is more than an order of magnitude smaller than the cross sections of the other two-pion production channels at the same incident energy.
The two-pion production in pp-collisions has been investigated at CELSIUS in exclusive measurements from threshold up to $T_p$ = 1.36 GeV. Total and differential cross sections have been obtained for the channels $pn\pi^+\pi^0$, $pp\pi^+\pi^-$, $pp\pi^0\pi^0$ and also $nn\pi^+\pi^+$. For intermediate incident energies $T_p >$ 1 GeV, i.e. in the region which is beyond the Roper excitation but at the onset of $\Delta\Delta$ excitation, the total $pp\pi^0\pi^0$ cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the $nn\pi^+\pi^+$ cross section is a factor of five larger than predicted. An isospin decompostion of the total cross sections exhibits a s-channel-like energy dependence in the region of the Roper excitation as well as a significant contribution of an isospin 3/2 resonance other than the $\Delta(1232)$. As possible candidates the $\Delta(1600)$ and the $\Delta(1700)$ are discussed.
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