Still Another Conservation Law — Question 8

Question 8

Counting strange particles is different from measuring net strangeness

A final state contains 12 positive kaons with S=+1, 4 negative kaons with S=-1, 6 Lambdas with S=-1, and one Xi with S=-2. All other particles have S=0.

1. Find net S and the sum of absolute strangeness magnitudes.

2. If the initial state has S=0, decide whether net conservation is satisfied. Explain why the total number of strange particles need not be conserved.

Question 8 - Solution

Counting strange particles is different from measuring net strangeness

(a) Method and calculation

$$\boxed{S_{\mathrm{net}}=12-4-6-2=0}.$$$$\boxed{\sum_i|S_i|=12+4+6+2=24}.$$

(b) Interpretation and further calculation

$$\boxed{N_{\mathrm{strange\ particles}}=12+4+6+1=23}.$$$$\boxed{\Delta S_{\mathrm{net}}=0}\quad\text{while opposite-strangeness production changes abundance}.$$

Physical check

Conservation constrains the signed sum, not absolute content or particle count. A doubly strange baryon contributes two units to the absolute sum.