Next-to-leading order QCD calculations with parton showers. I. Collinear singularities

Programs that calculate observables in quantum chromodynamics at next-to-leading order typically suffer from the problem that, when considered as event generators, the events generated consist of partons rather than hadrons and just a few partons at that. Thus the events generated are completely unrealistic. These programs would be much more useful if the few partons were turned into parton showers, in the style of standard Monte Carlo event generators. Then the parton showers could be given to one of the Monte Carlo event generators to produce hadron showers. We show how to generate parton showers related to the final state collinear singularities of the next-to-leading order perturbative calculation for the example of $e^{+}{+e}^{-}\to 3\mathrm{jets}.$ The soft singularities are left for a separate publication.