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We present a next-to-leading order QCD calculation for single-inclusive high-${p}_{T}$ jet production in longitudinally polarized pp collisions within the ``small-cone'' approximation. The fully analytical expressions obtained for the underlying partonic hard-scattering cross sections greatly facilitate the analysis of upcoming BNL-RHIC data on the double-spin asymmetry ${A}_{\mathrm{LL}}^{\mathrm{jet}}$ for this process in terms of the unknown polarization of gluons in the nucleon. We simultaneously rederive the corresponding QCD corrections to unpolarized scattering and confirm the results existing in the literature. We also numerically compare to results obtained with Monte Carlo methods and assess the range of validity of the ``small-cone'' approximation for the kinematics relevant at BNL-RHIC.

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