The Eightfold Way — Question 4

Question 4

Antiparticle reflection organizes the pseudoscalar meson octet

An ideal light meson octet contains a kaon doublet at Y=+1, an antikaon doublet at Y=-1, a pion triplet at Y=0 and an eta singlet at Y=0. B=0 throughout.

1. Find charges for the doublets and count all states.

2. Under charge conjugation, show how a weight changes and identify the partner of $K^+$ at $(I_3,Y)=(1/2,1)$.

Question 4 - Solution

Antiparticle reflection organizes the pseudoscalar meson octet

(a) Method and calculation

$$Y=+1:\ Q/e=(0,1);\quad Y=-1:\ Q/e=(-1,0).$$$$\boxed{N=2+2+3+1=8}.$$

(b) Interpretation and further calculation

$$\boxed{(I_3,Y,Q)\mapsto(-I_3,-Y,-Q)}.$$$$\boxed{K^+:(1/2,1)\mapsto K^-:(-1/2,-1)}.$$

Physical check

The eta here is an ideal octet state; physical neutral mesons can mix. Charge conjugation preserves baryon number zero.