Once the eightfold way (as the SU(3) symmetry was poetically referred to) was discovered, the race was on to explain it. As I have shown before the decaplet and two octets occur in the product
(9.14) |
A very natural assumption is to introduce a new particle that comes in three “flavours” called up, down and strange ( , and , respectively), and assume that the baryons are made from three of such particles, and the mesons from a quark and anti-quark (remember, .) Each of these quarks carries one third a unit of baryon number. The properties can now be tabulated, see table 9.2 .
In the multiplet language I used before, we find that the quarks form a triangle, as given in Fig. 9.7 .
Once we have made this assignment, we can try to derive what combination corresponds to the assignments of the meson octet, figure 9.8 . We just make all possible combinations of a quark and antiquark, apart from the scalar one (why?).
A similar assignment can be made for the nucleon octet, and the nucleon decaplet, see e.g., see Fig. 9.9 .