  The factorisation of QCD matrix elements in the limit of two external partons
becoming collinear is described by process-independent splitting amplitudes,
which can be expanded systematically in perturbation theory. Working in
conventional dimensional regularisation, we compute the two-loop splitting
amplitudes for all simple collinear splitting processes, including subleading
terms in the regularisation parameter. Our results are then applied to derive
an analytical expression for the two-loop single-real contribution to inclusive
Higgs boson production in gluon fusion to fourth order (N3LO) in perturbative
QCD.
