We have already seen that the width of each dimuon mass distribution, and thus the range of allowable parent particle masses, increases with mass. It turns out that this effect is not due to measurement alone. To see this, we need to notice another property that changes with mass: mean particle lifetime. It turns out that the more massive a particle is, the shorter its lifetime, that is, the less time it hangs around before it decays. (Lifetime changes with many other factors as well, of which its mass is just one that we'll consider here.)

Why do more massive particles decay more quickly, other things being equal? The answer lies in part with conservation of energy, which is inter-convertible with mass. (We'll see more of this in the next milestone.) In order to decay into another type of particle, the parent must have as much or more energy as the children, the decay products. The more mass the parent particle has, the more possible ways there are for that parent to decay. We sometimes speak of unstable states of affairs as "an accident waiting to happen." Think of a very massive particle as "an interaction waiting to happen": insofar as it is more massive, it is more likely to find more ways to decay, since it has sufficient mass/energy to decay into more massive sets of offspring. Thus, heavier particles are shorter-lived. (Why are some particles heavier than others? The current best answer to that question involves the Higgs mechanism, and finding the Higgs boson is a primary discovery goal of the LHC!)

So—other things being equal—more massive particles are shorter-lived. But shorter-lived particles have a wider mass distribution. Why should this be?