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We derive the three loop soft function for inclusive Higgs production ingluon fusion, and use it to perform the resummation of the Higgs cross sectionat N$^3$LL$^\prime$ in SCET. We improve the accuracy of the resummation byincluding contributions of collinear origin. We include finite top, bottom andcharm mass effect where available. These results are available through thepublic code ResHiggs.

The three loop soft function for N$^3$LL$^\prime$ gluon fusion Higgs production in SCET