33.4 Particles, patterns, and conservation laws  (Page 4/21)

The forces experienced by particles also govern how particles interact with themselves if they are unstable and decay. For example, the stronger the force, the faster they decay and the shorter is their lifetime. An example of a nuclear decay via the strong force is ${}^8\text{Be}\to \alpha +\alpha$ with a lifetime of about ${\text{10}}^{-\text{16}}\text{s}$ . The neutron is a good example of decay via the weak force. The process $n\to p+e^{-}+{\stackrel{-}{v}}_e$ has a longer lifetime of 882 s. The weak force causes this decay, as it does all $\beta$ decay. An important clue that the weak force is responsible for $\beta$ decay is the creation of leptons, such as $e^{-}$ and ${\stackrel{-}{v}}_e$ . None would be created if the strong force was responsible, just as no leptons are created in the decay of ${}^8\text{Be}$ . The systematics of particle lifetimes is a little simpler than nuclear lifetimes when hundreds of particles are examined (not just the ones in the table given above). Particles that decay via the weak force have lifetimes mostly in the range of ${\text{10}}^{-\text{16}}$ to ${\text{10}}^{-\text{12}}$ s, whereas those that decay via the strong force have lifetimes mostly in the range of ${\text{10}}^{-\text{16}}$ to ${\text{10}}^{-\text{23}}$ s. Turning this around, if we measure the lifetime of a particle, we can tell if it decays via the weak or strong force.

Yet another quantum number emerges from decay lifetimes and patterns. Note that the particles $\text{Λ}\text{,}\text{Σ}\text{,}\text{Ξ}$ , and $\Omega$ decay with lifetimes on the order of ${\text{10}}^{-\text{10}}$ s (the exception is ${\text{Σ}}^0$ , whose short lifetime is explained by its particular quark substructure.), implying that their decay is caused by the weak force alone, although they are hadrons and feel the strong force. The decay modes of these particles also show patterns—in particular, certain decays that should be possible within all the known conservation laws do not occur. Whenever something is possible in physics, it will happen. If something does not happen, it is forbidden by a rule. All this seemed strange to those studying these particles when they were first discovered, so they named a new quantum number strangeness    , given the symbol $S$ in the table given above. The values of strangeness assigned to various particles are based on the decay systematics. It is found that strangeness is conserved by the strong force , which governs the production of most of these particles in accelerator experiments. However, strangeness is not conserved by the weak force . This conclusion is reached from the fact that particles that have long lifetimes decay via the weak force and do not conserve strangeness. All of this also has implications for the carrier particles, since they transmit forces and are thus involved in these decays.

Calculating quantum numbers in two decays

(a) The most common decay mode of the ${\text{Ξ}}^{-}$ particle is ${\text{Ξ}}^{-}\to {\text{Λ}}^0+{\pi }^{-}$ . Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family numbers are unaffected.

(b) Is the decay $K^{+}\to {\mu }^{+}+{\nu }_{\mu }$ allowed, given the quantum numbers in the table given above?

Strategy

In part (a), the conservation laws can be examined by adding the quantum numbers of the decay products and comparing them with the parent particle. In part (b), the same procedure can reveal if a conservation law is broken or not.