Is there any evidence in the data from Fermi Lab or CERN for 3 particle quark Baryon states or 2 particle Meson quark in the 21 dimensional 2,2 highest weight representation of SU(3) with any of the 6 known quarks charm, truth, beauty, up, down, or strange?
No, baryons don't transform under the (2,2)=27 of SU(3), nor do the mesons. This is just group theory.
Other hadrons do, cf. https://www.ggi.infn.it/talkfiles/slides/GGI_aps.pdf
Thank you for your response. The paper you cited does not appear to say whether pentaquark or tetraquark states cannot be organized with 21 dimensional (2,2) highest weight representation. 6^4 = 1296
Is there any evidence for pentaquarks or tetraquarks in the particle data.
Ok tetraquarks are 4 particle quark states with 3^4 = 81 and pentaquarks are 5 particle quark states with 3^5 = 243. Is it just that tetraquarks have not been organized on 3 distinct (2,2) highest weight diagrams on the weight lattice of SU(3). There would be 3 distinct tetraquarks on the center of this diagram. There would then be a surrounding equalateral hexagon with 2 distinct tetraquarks at each its 6 vertices. Surrounding that hexagon would be an equalateral hexagon with 1 distinct tetraquark at each of its 6 vertices and 1 distinct tetraquark at each of the midpoints of this hexagon.
Does this fit the description of the X(3872) exotic Hadron could be organized on SU(3) weight lattice?
See B. Hall, Lie Groups, Lie Algebras and Representations, p 151 for the (2,2) highest weight diagram.
(2,2) + (2,2) + (2,2) = 27 + 27 + 27 = 81
As I work more on the mathematical physics side, does anyone have any suggestions on how I could have this idea of looking at the 2-dimensional weight diagram for the (2,2) + (2,2)+ (2,2) = 81, the direct sum of 3 irreducible representations of the SU(3) Lie algebra describing tetraquark, that is 4 quark particle states published in a physics journal. See B. Hall, Lie Groups, Lie Algebras and Representations for descriptions of several of the irreducible representations of SU(3) on the weight lattice of the SU(3) Lie Algebra.
In trying to find a physics journal for the (2,2) + (2,2) + (2,2) = 81 for SU(3) tetraquark states, that is 4 quark particle states idea, I was thinking of this as a theoretical model from mathematical physics about how tetraquark particle states are arranged on the 2-dimensional weight lattice of the SU(3) Lie Algebra from which one could make predictions about undiscovered tetraquarks based on the existence of the X(3872) tetraquark. Any suggestions on finding a physics journal for a paper about this?
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