  We investigate QCD threshold resummation effects beyond the next-to-leading
logarithmic (NLL) order for the process H1 H2->h1 h2 X at high invariant mass
of the produced hadron pair. We take into account the color structure of the
underlying partonic hard-scattering cross sections and determine the relevant
hard and soft matrices in color space that contribute to the resummed cross
section at next-to-next-to-leading logarithmic (NNLL) accuracy. We present
numerical results for fixed-target and collider regimes. We find a significant
improvement compared to previous results at NLL accuracy. In particular, the
scale dependence of the resummed cross section is greatly reduced. Use of the
most recent set of fragmentation functions also helps in improving the
comparison with the experimental data. Our calculation provides a step towards
a systematic NNLL extension of threshold resummation also for other hadronic
processes, in particular for jet production.
