Amplitude analysis of reaction pi +n

Abstract

We present a model independent amplitude analysis of reaction ${\mathrm{\ensuremath{\pi}}}^{+}$${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$p at 5.98 and 11.85 GeV/c using Saclay data obtained with a transversely polarized deuteron target at the CERN Proton Synchrotron. The analysis makes use of the data in two sets of binnings to examine the dependence of amplitudes on momentum transfer t [-t\ensuremath{\le}1.0 (GeV/c${)}^{2}$] in the ${\mathrm{\ensuremath{\rho}}}^{0}$ 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 (\ensuremath{\pi} 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{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${\mathit{p}}_{\mathrm{\ensuremath{\uparrow}}}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${\mathrm{\ensuremath{\pi}}}^{+}$n at 17.2 GeV/c.We suggest this difference may signal the influence of composite structure of hadrons and nonperturbative QCD effects in pion production. Although the mass dependence of partial-wave cross sections averaged over nucleon spins is smooth, we observe large and systematic structures in moduli squared of nucleon transversity amplitudes which reveal the essential role of nucleon spin in the pion production process. This behavior of moduli does not support the hypothesis of factorization of mass and t dependence of production amplitudes previously used in studies of meson-meson scattering. The mass dependence of S-wave amplitudes suggests the existence of a scalar state I=0 ${0}^{++}$(750) with a width of 100--150 MeV. Our results emphasize the need for a systematic study of pion production on the level of amplitudes in a new generation of dedicated experiments with spin at the recently proposed high-intensity hadron facilities.