Reanalysis of three-pion production data with fully analytic, unitary functions

The angular momentum analysis of the reaction ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}{\pi }^{-}p$ has been improved by using three-pion-state amplitudes which both satisfy unitarity and have proper analytic structure. The integral equations for these amplitudes and the method of solution used are discussed. The results of fitting the CERN-IHEP data at 25 and 40 GeV/c for ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}{\pi }^{-}p$ are almost identical to the earlier fits; in particular, the amplitude for the $J^P=1^{+}$ state still has no large phase change over the mass region where its magnitude has a maximum (the $A_1$ bump). We do, however, point out that there are ambiguities in the fit which make the phase determination less clear than earlier indicated.