The phase space slicing method of two cutoffs for next-to-leading-order Monte-Carlo style QCD corrections has been applied to many physics processes. The method is intuitive, simple to implement, and relies on a minimum of process dependent information. Although results for specific applications exist in the literature, there is not a full and detailed description of the method. Herein such a description is provided, along with illustrative examples; details, which have not previously been published, are included so that the method may be applied to additional hard scattering processes.

We present a new next-to-leading order calculation for fully differential single-topquark final states. The calculation is performed using phase space slicing and dipole subtraction methods. The results of the methods are found to be in agreement. The dipole subtraction method calculation retains the full spin dependence of the final state particles. We show a few numerical results to illustrate the utility and consistency of the resulting computer implementations.

A calculation of the next-to-leading order exclusive extrinsic charm quark differential distributions in deeply inelastic electroproduction has recently been completed. Using these results we compare the NLO extrinsic contributions to the charm structure function F 2 (x, Q 2 , m 2 c ) with the corresponding