Natural Science Forum / Physics / Particle Physics / May 2006

Excellent question.
If it is short-lived, that means that it decays into products. The
products are things that we can measure, including their energy and
momentum. (How we do that is whole other question.)
What we know is that the invariant mass of the decaying particle is the
same as the invariant mass of the system of final products. The
invariant mass of the system of final products is m = sqrt (E^2 - p^2),
where E is the (scalar) sum of the energies of all the final products,
and p is the (magnitude of the vector) sum of the momenta of all the
final products. In principle, if we do this just once -- for even one
decay -- then we've found the mass of the particle.
In practice, however, sometimes these final products do not come from
the decay of the short-lived particle. Sometimes they come from other
processes which happen to mimic the same products from the decay of the
particle. This is called background. If you do the same calculation for
a background event, you will get a completely different mass than what
you'd see from a short-lived particle decay.
But if you look at a bunch of these kinds of events, all with the
distinguishing final products, and you do the same calculation for each
of these events, and plot the distribution of those calculated masses,
you'll see a sharp hump on top of a flat background distribution. An
example is shown here: http://history.fnal.gov/jyoh_docs/jpg/604.jpg
This sharp hump is the signal of the decay of the short-lived particle,
and the central mass of that hump is the mass of the particle. In fact,
you learn something from the *width* of that distribution, because the
Heisenberg Uncertainty Principle tells you that the shorter the life of
that particle, the wider that mass distribution will be -- so that
measuring the width actually gives you a measurement of the lifetime of
the particle.

PD