The paper by Robert V. Harlander and William B. Kilgore calculates the next-to-next-to-leading order (NNLO) corrections to Higgs boson production cross sections at hadron colliders, specifically at the LHC and Tevatron. The authors focus on the gluon fusion channel, which is crucial for Higgs discovery at the LHC. They evaluate the partonic cross section using a perturbative expansion and find that the series converges well, indicating reliable predictions. The study also resolves ambiguities in previous works by computing sub-leading terms and providing a consistent approach. Additionally, the authors report an error in the NNLO correction to Drell-Yan production, which they correct. The numerical results show good perturbative convergence and reduced scale dependence, enhancing the reliability of the predictions.The paper by Robert V. Harlander and William B. Kilgore calculates the next-to-next-to-leading order (NNLO) corrections to Higgs boson production cross sections at hadron colliders, specifically at the LHC and Tevatron. The authors focus on the gluon fusion channel, which is crucial for Higgs discovery at the LHC. They evaluate the partonic cross section using a perturbative expansion and find that the series converges well, indicating reliable predictions. The study also resolves ambiguities in previous works by computing sub-leading terms and providing a consistent approach. Additionally, the authors report an error in the NNLO correction to Drell-Yan production, which they correct. The numerical results show good perturbative convergence and reduced scale dependence, enhancing the reliability of the predictions.