# Particle interaction selection rules

I'm currently studying for a physics exam, and I'm coming up with some trouble on a particle physics question. I'd probably be able to get it, but I'm not actually sure if the content was taught and as far as I can tell there's no practice material (with worked answers that might help me understand more) for this particular type of question. I could just not study it, but I'd rather not be left in the dark if it comes up.

The question is as below:

Each of the decays or reactions is missing a particle. Use the various selections rules, including that of quark flavour, to identify the particle.

1. $K^- + p \rightarrow \Sigma^+ + \pi^- + \ ?$

2. $\pi^- + p \rightarrow p + \overline{\Sigma^+} + \ ?$

3. $\Sigma^+ + n \rightarrow \Xi^0 + n + \ ?$

4. $\Lambda^0 + p \rightarrow \Sigma^+ + \ ?$

5. ${ \left( \Delta^* \right) }^+ \rightarrow \pi^+ + \ ?$

We are also given a 'useful information' sheet, which give the charge, spin, strangeness, baryon number, rest energy and mean lifetime of various baryons, mesons, leptons, and the up, down, spin quarks. We aren't given the quark components of the baryons or mesons.

I guess my main confusion is what these 'selection rules' are that are alluded to by the question, and how I would apply these to solve this type or problem?

Many thanks if you can help. I know homework questions aren't really appreciated but I'm really stuck and would be very thankful.

Strong interactions conserve

• baryon number
• electric charge
• strangeness, charm, and other heavy-quark quantum numbers
• total energy, including rest energy --- which constrains decays, but not so much beam interactions
• total angular momentum (more important when computing relative cross sections than for identifying particles)
• total isospin (using angular momentum rules; you may not have covered this one)
• total parity (but orbital angular momentum contributes here)
• probably some other things

For one example, your #2 has baryon number $B_\pi+B_p = 0+1 = +1$ on the left, but currently baryon number $B_p + B_{\overline\Sigma} = 1-1=0$ on the right, so whatever is missing must be another baryon --- a neutral baryon with strangeness $S_? = -1$.

• So for your example for #2, there won't necessarily be just one particle which would be a solution? It could be a $\Lambda^0$ or a $\Sigma^0$. Also, I was particularly struggling with identifying an issue with #1? Everything seemed fine there that I could see using the conservation laws you mentioned... I might have missed something though – LiggyRide Jun 13 '17 at 5:10
• The quantum number that distinguishes a $\Lambda^0$ from a $\Sigma^0$ is isospin. It may be that both are permitted but occur at different rates; see physics.stackexchange.com/q/292963/44126 – rob Jun 13 '17 at 14:41