  We present the results of the experimental study of the reaction of dipion
production by the beam of the negative pions with momentum 1.78 GeV/c on the
polarized proton and liquid hydrogen targets. The experiment covers the region
of dipion masses near the mass of rho-meson and small momenta transferred
|t|<0.2(GeV/c)^2. The whole set of spin density matrix elements was
reconstructed and model-independent and model-dependent amplitude analyses of
the reaction were performed. The experiment allows to exclude the ambiguity of
the amplitude analysis existing at high energies. The results contain evidences
in favour of existing of narrow sigma(750). The data also allows to estimate
intercept of a_1-meson Regge trajectory.
  The experiment was performed at the ITEP proton synchrotron, Moscow.
