Figure 1.
With the considerable advantage of hindsight afforded by nearly 40 years of development in the theory of quantum chromodynamics, and the experimental discovery of the quarks, we can now assign appropriate quark flavors to each of the baryons in the Gell-Mann diagram. This operation immediately reveals the ordering principle underlying the triangular arrangement: the diagram is completely ordered in terms of quark flavor.
The Gell-Mann diagram is the set of all possible combinations, in triplets, of the u, d, and s quark flavors. These flavors are arranged such that one axis of the triangle is ordered in terms of increasing concentrations of the u quark; a second axis is similarly ordered in terms of d quark abundance; and likewise the third axis is ordered in terms of increasing saturation by the s quark. It is not possible to increase the order of this arrangement in terms of its flavor components.
Today we know there are 6 quark species in 3 "families" of paired "flavors": u, d (up, down); c, s (charm, strange); and t, b (top, bottom). It is therefore evident that the same type of ordered triangular diagram presented in the cited article can be constructed for quark flavor combinations of the heavier baryons.
In Fig. 1 I show the triangularly ordered combinations for interactions between the ud and cs quark families. Note that the ud family is only shown once on the diagonal but serves as the "backbone" or baseline-axis for both the uds interaction (below the diagonal) and the udc interaction (above the diagonal). There are in addition 4 cs combinations which lie outside the square, but are shown for completeness; if I had used the cs instead of the ud family as the diagonal baseline, these four combinations would be inside the diagram and their ud counterparts would be the "outliers". The lower, uds triangle is similar to the one Gell-Mann used to predict the existence of the omega-minus (SSS-). Nowadays it looks so simple!
In Fig. 2 I show the possible flavor combinations for interactions between the cs and tb quark families, using the cs family as the diagonal baseline. Four flavor combinations lie outside the square in Fig. 2, and for the same reasons given regarding the outliers of Fig.1: if I had used the tb rather than the cs quarks for the baseline diagonal, these tb combinations would be "insiders" and their cs analogs would be "outsiders". I show them to complete the interaction set for these two quark families.
In the final diagram, Fig. 3, I show the flavor combinations for ud-tb interactions. In addition to the usual 4 outlier combinations, there are 8 others produced by "hidden" combinations between the 3 quark family levels: that is, each baryon contains one quark from each of the three levels. Such "triplet" combinations are unique to this set and complete the roster of the 56 possible quark flavor combinations. Triplet combinations occur only here because the ud-tb interaction bridges the intermediate cs energy level.
While we can also simply list all 56 flavor combinations in a single tabulation of the possible baryons (Table 1), doing so is neither as interesting nor as orderly as the triangular diagrams, which historically were so important to the development of QCD and the theory of quarks.
(It should not be supposed that this is an exhaustive list of possible baryons; although it does exhaust the flavor combinations, because baryons are composite entities, most flavor combinations can exist in many different excited states having different spins and masses (resonances). The naming of baryons can depend on their spin as well as their flavors and electric charge; hence the names of baryons ("delta plus", "delta minus", etc.) may only tangentially reflect differences in their flavor composition).
Literature Cited:
Alex R. Dzierba, C. A. Meyer, and E. S. Swanson. American Scientist: Sept.-Oct. 2000. 88:406-15.
Links:
Homepage
Table of baryon flavors
Fig 1. Diagram of the UD-CS baryon Flavors
Fig. 2. Diagram of the CS-TB baryon Flavors
Fig. 3. Diagram of the UD-TB baryon flavors
The Mechanism of the Weak Force
| . | Electric Charge | |||
| Number | +2 | -1 | 0 | +1 |
| 1 | UUU | DDD | UDD | DUU |
| 2 | CCC | SSS | CDD | SUU |
| 3 | TTT | BBB | TDD | BUU |
| 4 | UUC | DDS | USS | DCC |
| 5 | UUT | DDB | CSS | SCC |
| 6 | CCU | SSD | TSS | BCC |
| 7 | CCT | SSB | UBB | DTT |
| 8 | TTU | BBD | CBB | STT |
| 9 | TTC | BBS | TBB | BTT |
| 10 | UCT | DSB | UDS | DUC |
| 11 | . | . | CDS | SUC |
| 12 | . | . | TDS | BUC |
| 13 | . | . | UDB | DUT |
| 14 | . | . | CDB | SUT |
| 15 | . | . | TDB | BUT |
| 16 | . | . | USB | DCT |
| 17 | . | . | CSB | SCT |
| 18 | . | . | TSB | BCT |
U, C, T quarks carry partial electric charges of +2/3; D, S, B quarks carry partial charges of -1/3. For antiquarks (not shown), the sign of the electric charge is reversed. The U, D ("up", "down") quark "family" is the lightest, exclusively comprising ordinary matter, including the hottest stars (the quark flavor composition of the neutron is DDU, the proton DUU). The C, S ("charm", "strange") family is intermediate in mass, and the T, B ("top", "bottom") quark family is the heaviest. Heavy quark combinations (more commonly found as mesons, or quark-antiquark pairs) exist only momentarily in our particle accelerators, in collisions between matter and "cosmic rays", during the "Big Bang", in supernovas, the environs of black holes, or as products of other extreme astrophysical phenomena.
