An Interlude — Question 3

Question 3

Antiparticle quantum numbers reverse while mass and spin remain equal

A hypothetical particle X has charge +2e, baryon number B=1, and spin 1/2. Its antiparticle has the opposite additive charges and the same mass and spin. Consider a system of three X particles and two antiparticles.

1. Find the total electric charge and baryon number.

2. If all available particle-antiparticle pairs annihilate into states with zero net additive charges, identify the unmatched inventory and verify conservation.

Question 3 - Solution

Antiparticle quantum numbers reverse while mass and spin remain equal

(a) Method and calculation

$$\boxed{Q_{\bar X}=-2e,\quad B_{\bar X}=-1,\quad s_{\bar X}=1/2}.$$$$\boxed{Q_{\mathrm{initial}}=3(2e)+2(-2e)=2e,\quad B_{\mathrm{initial}}=3-2=1}.$$

(b) Interpretation and further calculation

$$3X+2\bar X=X+2(X\bar X)\Rightarrow\boxed{\text{one unmatched }X}.$$$$\boxed{Q_{\mathrm{final}}=2e,\quad B_{\mathrm{final}}=1}\quad\text{including all annihilation products}.$$

Physical check

The bookkeeping does not specify which annihilation channels are dynamically possible. A neutral particle need not be its own antiparticle if other charges distinguish the pair.