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FAQ8: I was looking for a SU3 chart of the quark model.First a warning -- this answer will make no sense unless you know a little about group theory. There are two SU(3) structures in the quark model. There is the color-charge SU(3) structure, which is the same for any flavor of quark. There is also a flavor SU(3) involving only the lightest three quark flavors, up, down and strange. This symmetry is only approximate, as it is broken by the differences in the masses of these three quarks. These differences are reasonably small on the scale of the typical hadron masses for hadrons made from these quarks, a scale set by the physics of the color forces that bind the quarks to make hadrons, not by the light quark masses. This means there is a sense in which there is an approximate symmetry, with symmetry breaking effects scaled by quarkmasses divided by hadron masses. (That also explains why we don't talk about flavor SU(6) of the six quark flavors, the larger masses of the 4th through 6th quark flavor types cannot be ignored, there is not any sense in which it is reasonable to talk about an approximate flavor symmetry involving these quarks as if their masses were all the same.) The (unbroken) SU(3) of color charge, under which each flavor of quark comes with a fundamental triplet of color charge possibilities, while gluons populate the adjoint representation (8). Observable particles such as mesons or baryons are all singlets (1) under this SU(3), as you see in the counting below, there is a singlet in the product of a triplet and an antitriplet (meson), and one in the product of three triplets (baryon), or three anti-triplets (antibaryon). The SU(3) flavor structure of the quark model is as follows. The u d and s quarks form a fundamental triplet, the antiquarks are a 3-bar or antitriplet. Then you combine these to get the representations populated by mesons (3 x 3-bar = 8+1, octet and singlet) and by baryons (3 x 3 x 3 = 8 + 8' + 10 + 1, two octets, a decuplet and a singlet). You can find charts of how to display the quarks made up the baryons and mesons in old text books such as Gell-Mann and Neimann "the Eightfold Way" and Kokkedee "The Quark Model" both published by Benjamin and probably out of print by now. A more modern source would most likely be Georgi or Cahn's text books on group theory in particle physics (but I haven't actually looked to see what is there). I hope this helps. |
