Soffer positivity bound and a suggestion for measuring valence quark transverse spin distributions at BNL RHIC

A positivity bound obtained by Soffer severely restricts the magnitude of quark transverse spin distributions for those quark flavors with negative longitudinal polarization. Since the interpretation of lepton scattering data on longitudinally polarized protons suggests a strong negative longitudinal polarization for antiquarks in the sea, a hard-scattering process which depends only on the transverse spin distribution of valence u quarks should be investigated. The large transverse-momentum production processes ${\mathit{A}}_{\mathit{N}\mathit{N}}$dσ(p↑p↑→${\mathrm{\pi }}^{+}$X) and ${\mathit{A}}_{\mathit{N}\mathit{N}}$dσ(p↑p↑→${\mathrm{\pi }}^{+}$ ${\mathit{p}}^{+}$X) could be considered a backup to the measurement of ${\mathit{A}}_{\mathit{N}\mathit{N}}$dσ(p↑p↑→γ(${\mathit{Q}}^2$)X) and other production processes involving antiquarks.