Amplitude analysis of reactionπ+n↑→π+π−pat 5.98 and 11.85 GeV/c

We present a model independent amplitude analysis of reaction ${\mathrm{\pi }}^{+}$ ${\mathit{n}}_{\mathrm{\uparrow }}$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$p at 5.98 and 11.85 GeV/c using Saclay data obtained with a transversely polarized deuteron target at the CERN Proton Synchrotron. The analysis makes use of the data in two sets of binnings to examine the dependence of amplitudes on momentum transfer t [-t≤1.0 (GeV/c${)}^2$] in the ${\mathrm{\rho }}^0$ mass region and their dependence on dipion mass below 1000 MeV for momentum transfers -t=0.2–0.4 (GeV/c${)}^2$. The analysis is performed in both t-channel and s-channel helicity frames of the dimeson state and it is verified by comparison with linear bounds on the moduli. The data yield two solutions for 8 moduli and 6 cosines of relative phases of nucleon transversity amplitudes with dimeson spin J=0 (S wave) and J=1 (P wave). The two solutions differ mainly in the S-wave contributions. Both solutions require nonzero nucleon helicity-nonflip amplitudes (${\mathit{A}}_1$ exchange) with phases different from phases of nucleon helicity-flip amplitudes (π exchange). Natural exchange amplitudes (${\mathit{A}}_2$ exchange) with opposite nucleon transversities show a crossover in their t dependence at -${\mathit{t}}_{\mathit{c}}$=0.4–0.5 (GeV/c${)}^2$ which has not been observed in the earlier amplitude analysis of ${\mathrm{\pi }}^{\mathrm{-}}$ ${\mathit{p}}_{\mathrm{\uparrow }}$→${\mathrm{\pi }}^{\mathrm{-}}$ ${\mathrm{\pi }}^{+}$n at 17.2 GeV/c.