Still Another Conservation Law — Question 4

Question 4

Neutral kaons remain distinct through their opposite strangeness

Assign $S(K^0)=+1$ and $S(\bar K^0)=-1$, with Q=B=0 for both. A neutral initial state has S=0 and sufficient energy. Consider strong production of either $K^0\bar K^0$ or $K^0K^0$.

1. Test both final states against strangeness conservation.

2. For a beam with 70 percent $K^0$ and 30 percent $\bar K^0$, find mean S and its variance per particle.

Question 4 - Solution

Neutral kaons remain distinct through their opposite strangeness

(a) Method and calculation

$$\boxed{S(K^0\bar K^0)=1-1=0}\quad\text{passes the additive-number test}.$$$$\boxed{S(K^0K^0)=2\ne0}\quad\text{strong production excluded from }S_i=0.$$

(b) Interpretation and further calculation

$$\boxed{\langle S\rangle=.70-.30=.40}.$$$$\boxed{\operatorname{Var}(S)=\langle S^2\rangle-\langle S\rangle^2=1-.40^2=.84}.$$

Physical check

Zero electric charge does not remove the distinction between a neutral particle and its antiparticle. This beam is an incoherent mixture.