Bucknell Physics 212 Supplement

Section 11.3 Particle Lifetimes

Let's see how the quark model can help us predict particle lifetimes. The two most important factors are the type of interaction involved and the amount of energy available. We'll first illustrate with an example and then develop some general rules.

In doing Problem  Exercise 11.6.4, you'll discover that energy considerations severely limit the possible decay modes for \(\Sigma^-(1197)\text{.}\) In fact, only \(\Sigma^- \to n + \pi^-\) is allowed. See [cross-reference to target(s) "fig_weak_sigma-minus_decay" missing or not unique]. There is a flavor change, because a strange quark has to turn into an up quark, so a \(W^-\) boson must be involved, indicating the weak interaction. And because the weak interaction is much weaker than the strong, it acts much more slowly and \(\Sigma^-(1197)\) lives a relatively long time. Compare the mean lifetimes: \(1.5 \times 10^{-10}\Xunits{s}\) for \(\Sigma^-(1197)\) and \(2 \times 10^{-23}\Xunits{s}\) for \(\Sigma^{*-}(1387)\text{.}\) The fact that only a weak decay can occur allows \(\Sigma^-(1197)\) to live 10 trillion times longer!

Here are some general rules about decay schemes and lifetimes.

• A decay proceeds by the strongest interaction allowed: strong, then electromagnetic, then weak. The typical times for these interactions are given in Tables 11.4 and Table 11.5.

• Particles can only decay to lighter particles. The more excess energy available, the faster the decay proceeds.

• A baryon's decay products must include a baryon.

• If quark flavor is not conserved, the decay must proceed by the weak interaction (because a \(W\) or \(Z\) boson must be involved).

• If photons are involved, the decay process proceeds by the electromagnetic interaction.

• Hadrons tend to decay to more hadrons. Only when a decay into hadrons is energetically impossible do hadrons decay to photons or leptons.