Splitting Functions at High Transverse Momentum

Among the production channels of the Higgs boson one contribution could become significant at high transverse momentum which is the radiation of a Higgs boson from another particle. This note focuses on the calculation of splitting functions and cross sections of such processes. The calculation is first carried out on the example $e\rightarrow e\gamma$ to illustrate the way splitting functions are calculated. Then the splitting function of $e\rightarrow eh$ is calculated in similar fashion. This procedure can easily be generalized to processes such as $q\rightarrow qh$ or $g\rightarrow gh$.