Transverse spin asymmetries for three-jet production in hadronic collisions

Using helicity-amplitude techniques, we derive the partonic level transverse spin-spin asymmetries ${\hat{a}}_{\mathrm{NN}}$ for the processes relevant to the hadronic production of three-jet events: namely, $q{q}^{\prime }\to q{q}^{\prime }g$ and $\mathrm{qq}\to \mathrm{qqg}$. Just as in the case of two-jet production, we find that the partonic level asymmetries (${\hat{a}}_{\mathrm{NN}}$) are roughly 10 times smaller than the corresponding longitudinal asymmetries (${\hat{a}}_{\mathrm{LL}}$).