Spin dependence of matter creation in hadron collisions

First measurements of pion production on polarized targets in reactions ${\pi }^{+}{n}_{\uparrow }\to {\pi }^{+}{\pi }^{-}p$ and $K^{+}{n}_{\uparrow }\to K^{+}{\pi }^{-}p$ at 6 and 12 GeV/c and in ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ at 17.2 GeV/c provide direct information on the momentum-transfer evolution of dimeson-mass dependence of moduli squared of production amplitudes for dimeson masses below 1000 MeV and $-t\lesssim 0.6$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$. We observe significant and complex dependence of pion production processes on nucleon spin and dimeson helicity, with unexpected structures near resonant masses.