The Quark Model — Question 4

Question 4

A sea pair changes abundance without changing valence quantum numbers

Begin with proton valence content uud. Add two $u\bar u$ pairs and one $s\bar s$ pair. Ignore gluons for this counting exercise.

1. Find total numbers of quarks and antiquarks, net up flavor and net strangeness.

2. Calculate B and Q of the entire component and compare with the original proton.

Question 4 - Solution

A sea pair changes abundance without changing valence quantum numbers

(a) Method and calculation

$$\boxed{N_q=3+3=6,\quad N_{\bar q}=3,\quad N_u-N_{\bar u}=4-2=2}.$$$$\boxed{S=-(N_s-N_{\bar s})=-(1-1)=0}.$$

(b) Interpretation and further calculation

$$\boxed{B=(6-3)/3=1}.$$$$\boxed{Q/e=(2/3)(4-2)-(1/3)(1)-(1/3)(1-1)=1}.$$

Physical check

Only flavor differences enter the additive charges. The number of constituents in a quantum field component need not remain three.