  The measurement of the underlying event (UE) and its separation from hard
interactions in hadron-collider events is a conceptually and practically
challenging task. We develop a simple, mostly analytical toy model for the UE
in order to understand how different UE measurement approaches fare on the
practical aspects of this problem, comparing the traditional approach used so
far at Tevatron with a recently proposed "jet-area/median" approach. Both are
found to perform comparably well in measuring average properties of the UE,
such as the mean transverse momentum flow, but the jet-area/median approach has
distinct advantages in determining its fluctuations. We then use the
jet-area/median method to investigate a range of UE properties in existing
Monte Carlo event-generator tunes, validating the main results of the toy-model
and highlighting so-far unmeasured characteristics of the UE such as its
rapidity dependence, as well as its intra- and inter-event fluctuations and
correlations.
