The Eightfold Way — Question 3

Question 3

Counting the baryon octet by horizontal rows

A baryon multiplet contains an N doublet at Y=1, a Sigma triplet and Lambda singlet at Y=0, and a Xi doublet at Y=-1. All have B=1. Use $Q/e=I_3+Y/2$.

1. Count states and determine the strangeness of each row.

2. Count states of charge +e, zero and -e.

Question 3 - Solution

Counting the baryon octet by horizontal rows

(a) Method and calculation

$$\boxed{N_{\mathrm{states}}=2+3+1+2=8}.$$$$\boxed{S=Y-B:\quad 0,-1,-2\ \text{for the three rows}}.$$

(b) Interpretation and further calculation

$$Q_N/e=(0,1),\quad Q_{\Sigma,\Lambda}/e=(-1,0,1,0),\quad Q_\Xi/e=(-1,0).$$$$\boxed{N_{+}=2,\quad N_0=4,\quad N_-=2}.$$

Physical check

The octet count includes both neutral states at the central weight; counting dots alone would miss one state.