The Quark Model — Question 9

Question 9

Exotic valence bookkeeping permits a five-quark baryon

Consider hypothetical valence content $uudd\bar s$. Use charges $Q_u=2e/3$, $Q_d=Q_s=-e/3$, B=1/3 per quark, S=-1 for s, and reversed signs for antiquarks.

1. Calculate Q, B and S.

2. For any component with B=1 and one antiquark, derive the number of quarks required. State whether these arithmetic tests prove a bound state exists.

Question 9 - Solution

Exotic valence bookkeeping permits a five-quark baryon

(a) Method and calculation

$$\boxed{Q/e=2(2/3)+2(-1/3)+1/3=1}.$$$$\boxed{B=(4-1)/3=1,\quad S=+1}.$$

(b) Interpretation and further calculation

$$B=(N_q-N_{\bar q})/3=1,\quad N_{\bar q}=1\Rightarrow\boxed{N_q=4}.$$$$\boxed{N_{\mathrm{constituents}}=5}\quad\text{but binding and resonance formation require dynamics}.$$

Physical check

An allowed valence assignment is not a claim that this particular particle has been experimentally established.