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We study the resummation of large logarithmic perturbative corrections to thepartonic cross sections relevant for the process pp-> h X at high transversemomentum of the hadron h, when the initial protons are longitudinallypolarized. We perform the resummation to next-to-leading logarithmic accuracy.We present numerical results for center-of-mass energies of 19.4 GeV, relevantfor comparisons to data from the Fermilab E704 experiment, and 62.4 GeV, wherepreliminary data from RHIC have recently become available. We find significantenhancements of the spin-dependent cross sections, but a decrease of thedouble-spin asymmetry for the process. This effect is less pronounced at thehigher energy.

Single-Inclusive Hadron Production in Polarized pp Scattering at Next-to-Leading Logarithmic Accuracy