  The traditional method to measure the W-Boson mass at a hadron collider (more
precisely, its ratio to the Z-mass) utilizes the distributions of three
variables in events where the W decays into an electron or a muon: the
charged-lepton transverse momentum, the missing transverse energy and the
transverse mass of the lepton pair. We study the putative advantages of the
additional measurement of a fourth variable: an improved phase-space
singularity mass. This variable is statistically optimal, and simultaneously
exploits the longitudinal- and transverse-momentum distributions of the charged
lepton. Though the process we discuss is one of the simplest realistic ones
involving just one unobservable particle, it is fairly non-trivial and
constitutes a good "training" example for the scrutiny of phenomena involving
invisible objects. Our graphical analysis of the phase space is akin to that of
a Dalitz plot, extended to such processes.
