  Parton showers are widely used to generate fully exclusive final states
needed to compare theoretical models to experimental observations. While, in
general, parton showers give a good description of the experimental data, the
precise functional form of the probability distribution underlying the event
generation is generally not known. The reason is that realistic parton showers
are required to conserve four-momentum at each vertex. In this paper we
investigate in detail how four-momentum conservation is enforced in a standard
parton shower and why this destroys the analytic control of the probability
distribution. We show how to modify a parton shower algorithm such that it
conserves four-momentum at each vertex, but for which the full analytic form of
the probability distribution is known. We then comment how this analytic
control can be used to match matrix element calculations with parton showers,
and to estimate effects of power corrections and other uncertainties in parton
showers.
