Still Another Conservation Law — Question 3

Question 3

Missing-hadron quantum numbers can be inferred before its identity is known

An observed strong reaction is $\pi^-+p\to K^++X$. The kaon has Q=+e, B=0 and S=+1. Initial total values are Q=0, B=1 and S=0.

1. Infer Q, B and S of X.

2. Compare X with candidate A having (-e,1,-1) and candidate B having (-e,0,-1). State what further information is needed after these tests.

Question 3 - Solution

Missing-hadron quantum numbers can be inferred before its identity is known

(a) Method and calculation

$$\boxed{Q_X=0-(+e)=-e}.$$$$\boxed{B_X=1-0=1,\quad S_X=0-(+1)=-1}.$$

(b) Interpretation and further calculation

$$\boxed{A:\text{ matches};\quad B:\text{ fails baryon number}}.$$$$(Q,B,S)_X=(-e,1,-1)\quad\text{does not uniquely fix mass or spin}.$$

Physical check

Conservation narrows possible identities. Mass reconstruction, spin information and decay channels can distinguish states with identical additive numbers.