The Quark Model — Question 1

Question 1

Reconstructing valence counts from a baryon charge

A nonstrange three-quark baryon contains only u and d quarks. Their charges are $+2e/3$ and $-e/3$, and each has B=1/3. Its total charge is +e.

1. Solve simultaneously for the numbers of u and d valence quarks.

2. Repeat for a neutral baryon and determine the antiquark content of its antiparticle.

Question 1 - Solution

Reconstructing valence counts from a baryon charge

(a) Method and calculation

$$N_u+N_d=3,\quad(2N_u-N_d)/3=1.$$$$\boxed{N_u=2,\ N_d=1:\ uud,\quad B=1}.$$

(b) Interpretation and further calculation

$$Q=0\Rightarrow 2N_u=N_d\Rightarrow\boxed{udd}.$$$$\boxed{\bar u\bar d\bar d:\quad Q=0,\ B=-1}.$$

Physical check

Valence counts specify net flavor. Real hadrons also contain gluons and quark-antiquark sea components.