Three loop soft function for N3LL′ gluon fusion Higgs boson production in soft-collinear effective theory

We derive the three loop soft function for inclusive Higgs production in gluon fusion, and use it to perform the resummation of the Higgs cross section at N3LL′ in soft-collinear effective theory. We improve the accuracy of the resummation by including contributions of collinear origin. We include finite top, bottom and charm mass effect where available. These results are available through the public code ResHiggs.