  We have recently established a new method for measuring the mass of unstable
particles produced at hadron colliders based on the analysis of the energy
distribution of a massless product from their two-body decays. The central
ingredient of our proposal is the remarkable result that, for an unpolarized
decaying particle, the location of the peak in the energy distribution of the
observed decay product is identical to the (fixed) value of the energy that
this particle would have in the rest-frame of the decaying particle, which, in
turn, is a simple function of the involved masses. In addition, we utilized the
property that this energy distribution is symmetric around the location of peak
when energy is plotted on a logarithmic scale. The general strategy was
demonstrated in several specific cases, including both beyond the SM particles,
as well as for the top quark. In the present work, we generalize this method to
the case of a massive decay product from a two-body decay; this procedure is
far from trivial because (in general) both the above- mentioned properties are
no longer valid. Nonetheless, we propose a suitably modified parametrization of
the energy distribution that was used successfully for the massless case, which
can deal with the massive case as well. We establish the accuracy of this
parametrization using concrete examples of energy spectra of Z bosons from the
decay of a heavier stop into a Z boson and a lighter stop. We then study a
realistic application for the same process, but now including dominant
backgrounds and using foreseeable statistics at LHC14, in order to determine
the performance of this method for an actual mass measurement. The upshot of
our present and previous work is that, in spite of energy being a
Lorentz-variant quantity, its distribution emerges as a powerful tool for mass
measurement at hadron colliders.
