Amplitude analysis of reactions pi(-)p->eta pi(-)p and pi(-)p->eta pi(0)n measured on a polarized target and the exotic 1(-+) meson

Recently several experimental groups analyzed data on pi(-)p-->eta pi(-)p and pi(-)p-->eta pi(0)n reactions with an exotic 1(-+) P wave and found conflicting evidence for an exotic meson I=11(-+)(1405). High statistics data on these reactions are presently being analyzed by the BNL E852 Collaboration. All these analyses are based on the crucial assumption that the production amplitudes do not depend on nucleon spin. This assumption is in sharp conflict with the results of measurements of pi(-)p-->pi(-)pi(+)n, pi(+)n-->pi(+) pi(-)p, and K(+)n-->K(+)pi(-)p on polarized targets at CERN, which find a strong dependence of production amplitudes on the nucleon spin. To ascertain the existence of an exotic meson 1(-+)(1405), it is necessary to perform a model-independent amplitude analysis of reactions pi(-)p-->eta pi(-)p and pi(-)p-->eta pi(0)n. We demonstrate that measurements of these reactions on transversely polarized targets enable the required model-independent amplitude analysis without the assumption that production amplitudes are independent of nucleon spin. Two variants of the Monte Carlo method are proposed for finding the amplitudes and their errors. We suggest that high statistics measurements of the reactions pi(-)p-->eta pi(-)p and pi(-)p-->eta pi(0)n be made on polarized targets at BNL and at Protvino IHEP and that model-independent amplitude analyses of these polarized data be performed to advance hadron spectroscopy on the level of spin-dependent production amplitudes.