Abstract
A special treatment based on the highest division algebra, that of octonions and their split algebraic formulation is developed for the description of diquark states made up of two quark pairs. We describe symmetry properties of mesons and baryons through such formulation and derive mass formulae relating π, ρ, N and Δ trajectories showing an incredible agreement with experiments. We also comment on formation of diquark-antidiquark as well as pentaquark states and point the way toward applications into multiquark formulations expected to be seen at upcoming CERN experiments. A discussion on relationship of our work to flux bag models, string pictures and to string-like configurations in hadrons based on spectrum generating algebras will be given.
Highlights
In mid sixties Miyazawa, in a series of papers[1], extended the SU (6) group to the supergroupSU (6/21) that could be generated by constituent quarks and diquarks that could be transformed to each other
The parameters B and αs have been determined[25].[26] using the experimental information from the low lying hadron states: B 4 = 0.146 GeV and αs = 0.55 GeV. If we use these values in Eq(68) we find α (0) = 0.88 (GeV )−2 (69)
We look at various ways of partitioning of the total angular momentum into two subsystems
Summary
In mid sixties Miyazawa, in a series of papers[1], extended the SU (6) group to the supergroup. SU (6/21) that could be generated by constituent quarks and diquarks that could be transformed to each other. He found the following: (a) A general definition of SU (m/n) superalgebras, expressing the symmetry between m bosons and n fermions, with Grassman-valued parameters. This work contained the first classification of superalgebras (later rediscovered by mathematicians in the seventies). Because of the field-theoretic prejudice against SU (6), Miyazawa’s work was generally ignored. Examples of supersymmetric field theories were given and the general method based on the super-Poincaregroup was discovered by Wess and Zumino[6].
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