33.5 Quarks: is that all there is?  (Page 3/20)

Quantum numbers from quark composition

Verify the quantum numbers given for the ${\text{Ξ}}^0$ particle in [link] by adding the quantum numbers for its quark composition as given in [link] .

Strategy

The composition of the ${\text{Ξ}}^0$ is given as $\text{uss}$ in [link] . The quantum numbers for the constituent quarks are given in [link] . 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.

Solution

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 [link] . Its strangeness is $S=0-1-1=-2$ , also as expected from [link] . Its charm, bottomness, and topness are 0, as are its lepton family numbers (it is not a lepton).

Discussion

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.