(a) Is the decay $\Lambda^0 \rightarrow n + \pi^0$ possible considering the appropriate conservation laws? State why or why not. (b) Write the decay in terms of the quark constituents of the particles.
This is College Physics Answers with Shaun Dychko. Considering our conservation laws, is it possible for the lambda zero particle to decay into a neutron and a neutral pion? Well if you look at the baryon number in table [33.2], the lambda particle has a baryon number of plus 1 and the neutron also has a baryon number of plus 1 and the pion has a baryon number of 0 and that means it's conserved— it's 1 on the left and 1 on the right. The charge is 0 for all these particles so it's conserved, the strangeness of the lambda zero particle is negative 1 whereas the neutron has zero and the pion has zero strangeness so it's not conserved and for the lepton numbers, we can see that the lepton numbers are 0 across the board for the lambda particle, the neutron and for the neutral pion. and so it's conserved because it's 0 on the left and total of 0 on the right. Now strangeness is not conserved but that does not preclude the decay because strangeness is a bit of a looser conservation law—and it doesn't even deserve the word 'law'— it doesn't have to be conserved all the time and if this decay is mediated by the weak nuclear force then it's possible for strangeness to not be conserved and that's okay so it could occur and it will probably have a rather long lifetime as a result of being mediated by the weak nuclear force. We will write this decay in terms of the constituent quarks so the lambda zero particle has an up, down and strange quark and I found that in table [33.4] and it turns into a neutron with an up, down, down quark and a neutral pion, which is a mixture of some of them having an up and an up anti-quark and other neutral pions having a down and down anti-quark.