We study the two-body decay of a mother particle into a massless daughter. We
further assume that the mother particle is unpolarized and has a generic boost
distribution in the laboratory frame. In this case, we show analytically that
the laboratory frame energy distribution of the massless decay product has a
peak, whose location is identical to the (fixed) energy of that particle in the
rest frame of the corresponding mother particle. Given its simplicity and
"invariance" under variations of the boost distribution of the mother particle,
our finding should be useful for the determination of masses of mother
particles. In particular, we anticipate that such a procedure will then not
require a full reconstruction of this two-body decay chain (or for that matter,
information about the rest of the event). With this eventual goal in mind, we
make a proposal for extracting the peak position by fitting the data to a
well-motivated analytic function describing the shape of such energy
distribution. This fitting function is then tested on the theoretical
prediction for top quark pair production and its decay and it is found to be
quite successful in this regard. As a proof of principle of the usefulness of
our observation, we apply it for measuring the mass of the top quark at the
LHC, using simulated data and including experimental effects.Comment: 5 pages, 2 figures, discussions and references adde
