Quantum Numbers From Quark Composition

The composition of the ${\text{Ξ}}^0$ is given as $\text{uss}$ in Table 33.4. The quantum numbers for the constituent quarks are given in Table 33.3. We will not consider spin, because that is not given for the ${\text{Ξ}}^0$. But we can check on charge and the other quantum numbers given for the quarks.

The total charge of uss is $+\left(\frac{2}{3}\right)q_e-\left(\frac{1}{3}\right)q_e-\left(\frac{1}{3}\right)q_e=0$, which is correct for the ${\text{Ξ}}^0$. The baryon number is $+\left(\frac{1}{3}\right)+\left(\frac{1}{3}\right)+\left(\frac{1}{3}\right)=1$, also correct since the ${\text{Ξ}}^0$ is a matter baryon and has $B=1$, as listed in Table 33.2. Its strangeness is $S=0-1-1=-2$, also as expected from Table 33.2. Its charm, bottomness, and topness are 0, as are its lepton family numbers (it is not a lepton).

This procedure is similar to what the inventors of the quark hypothesis did when checking to see if their solution to the puzzle of particle patterns was correct. They also checked to see if all combinations were known, thereby predicting the previously unobserved ${\Omega }^{-}$ as the completion of a pattern.