$\rho$-polarization in the reaction $\pi^{-}p \rightarrow \pi^{+} \pi^{-}n$ at 17 GeV

The data from a spark chamber experiment are analysed for dipion masses below 1 GeV in terms of the s- and p-wave density matrix. The measured elements are given as functions of the dipion mass and of the momentum transfer. Bounds for the unmeasured matrix elements rho /sub 11/, Im rho /sub 10/, Im rho /sub 0s/, Im rho /sub 1s/ are calculated using the positivity constraint. The intervals are very small and suggest that the production process has the property of equal phases of the amplitudes referring to the same pi pi angular momentum. Next, the eigenvalues of the density matrix are determined within the positivity domain, and presented as functions of the dipion mass and the momentum transfer, showing that the rank is never greater than 3, and equal to 2 at the peak of the rho meson, but could also be generally 2. (5 refs).