Past exam of the particle and nuclear physics course of the University of Cambridge / 2012 / Paper 1 / 3 / b

The initial strangeness is $-2$. The $\Lambda {\pi }^0$ final state has strangeness $-1$, so its allowed nonleptonic amplitude is weak. One representative topology is $s\to u{W}^{-\ast }$ followed by $W^{-\ast }\to d\bar{u}$; spectator $u,s$ combine with the produced $d$ into the $\Lambda$, while $u\bar{u}$ contributes to the neutral pion. The available rest energy is $1314.8-1115.7-135.0=64.1\mathrm{MeV}$.

The $\Lambda {\bar{K}}^0$ state would conserve strangeness and could have a strong vertex, but its threshold exceeds the parent mass by $1115.7+497.6-1314.8=298.5\mathrm{MeV}$. It is kinematically forbidden. Coupling strength cannot rescue a closed decay channel.

The radiative channel also changes strangeness. It is a weak radiative hyperon decay, not an ordinary electromagnetic decay between states of the same flavour. A representative two-quark contribution is W exchange $su\to ud$ with a photon attached to a charged line; the other allowed attachments, hadronic intermediate states and short-distance loop contributions must be included for a complete amplitude. Its extra electromagnetic coupling and hadronic dynamics suppress it relative to the nonleptonic channel. ConsequentlyNA48 Collaboration measured a radiative branching fraction of about $1.16\times 10^{-3}$, corroborating the suppression rather than a purely electromagnetic interpretation.^[ref]