Symmetries and Mass Predictions of the Supersymmetric Quark Model (original) (raw)
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Il Nuovo Cimento A, 1988
It is shown that Miyazawa's SU(6/21) superalgebra for hadrons can be applied to a bilocal quark-antiquark (q~) or quark-diquark (q-D) system resulting in multiplets that include the l = 1 mesons in the (35 + 1) representation of SU(6) and the 1 = 1 baryons (70-), in addition to the l = 0 mesons (35-+ 1-) and l= 0 baryons (56+). Alternatively, a nonsimple algebra that brings together the (35-+ 1 ) mesons and 56 + baryons is also proposed. This minimal scheme does not involve the D-D exotic mesons in the lowest hadronic supermultiplet. In both schemes color is incorporated through the algebra of split octonions.
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A superalgebra extracted from the Jordan algebra of the 27 and 27 dim. representations of the group E 6 is shown to be relevant to the description of the quark-antidiquark system. A bilocal baryon-meson field is constructed from two quark-antiquark fields. In the local approximation the hadron field is shown to exhibit supersymmetry which is then extended to hadronic mother trajectories and inclusion of multiquark states. Solving the spin-free Hamiltonian with light quark masses we develop a new kind of special function theory generalizing all existing mathematical theories of confluent hypergeometric type. The solution produces extra “ hidden ” quantum numbers relevant for description of supersymmetry and for generating new mass formulas. Normal 0 21 false false false CS X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Normalni tabulka"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-...
Journal of Physics: Conference Series, 2014
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 ∆ 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.
Algebraic Realization of Quark-Diquark Supersymmetry
Algebraic realizations of supersymmetry through SU(m,n) type superalgebras are developed. We show their applications to a bilocal quark-antiquark or a quark-diquark systems. A new scheme based on SU(6/1) is fully exploited and the bilocal approximation is shown to get carried unchanged into it. Color algebra based on octonions allows the introduction of a new larger algebra that puts quarks, diquarks and exotics in the same supermultiplet as hadrons and naturally suppresses quark configurations that are symmetrical in color space and antisymmetrical in remaining flavor, spin and position variables. A preliminary work on the first order relativistic formulation through the spin realization of Wess-Zumino super-Poincare algebra is presented.
Hadronic Supersymmetry from QCD
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The experimental search of standard model superpartners, and the derivation of the standard model from higher dimensional theories have been challenging for some time now. In this article these technologies are kept but they are applied to a simpler environment. A coherent scenario of particles based on Kaluza-Klein theory and unbroken supersymmetry is proposed. It offers an economic basis for constructing the standard model particles without the superpartner problem of the minimal supersymmetric standard model. With local supersymmetry one arrives at supergravity without Yang-Mills fields. A number of results in the literature would have to be reconsidered according to this model.
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1995
Abstract. A classification of hadrons and their interactions at low energies according to SU(4) allows to identify combinations of the fifteen mesons π, ω and ρ within the spin-isospin decomposition of the regular representation 15. Chirally symmetric SU(2)×SU(2) hadron interactions are then associated with transformations of a subgroup of SU(4). Nucleon and Delta resonance states are represented by a symmetric third rank tensor 20 whose spin-isospin decomposition leads to 4 ⊕ 16 ‘tower states ’ also known from the large-Nc limit of QCD. Towards a relativistic hadron theory, we consider possible generalizations of the stereographic projection S2 → C and the related complex spinorial calculus on the basis of the division algebras with unit element. Such a geometrical framework leads directly to transformations in a quaternionic projective ‘plane ’ and the related symmetry group SL(2,H). In exploiting the Lie algebra isomorphism sl(2,H) ∼ = su∗(4) ∼ = so(5,1), we focus on the Lie alge...
Relativistic Supersymmetric Quarks Model
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Considering the electromagnetic atom a topological structure of two intersecting (partially merged) manifolds (longitudinal waves or branes) vibrating with the same or opposite phases, their cobordian submanifolds created in and by such intersection will be the subatomic particles of the nucleus shared by this dual system, acting as fermions when the phases of variation of the intersecting manifolds are opposite and acting as bosons when those phases synchronize becoming equal. The quarks of the system - considered as the pushing forces caused by the displacement of the intersecting fields while vibrating - will be identical in the bosonic and fermionic times, that is to say, supersymmetric. The point of the intersection of the system, that remains the same during the whole phases but moving left to right in the fermionic phase and upward and downward in the bosonic one, will be the point of convergence of all the fermionic and bosonic strong and weak interactions naturally explaining the unification of the gauge couplings.
Supersymmetric preons and the standard model
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The experimental fact that standard model superpartners have not been observed compels one to consider an alternative implementation for supersymmetry. The basic supermultiplet proposed here consists of a photon and a charged spin 1/2 preon field, and their superpartners. These fields are shown to yield the standard model fermions, Higgs fields and gauge symmetries. Supersymmetry is defined for unbound preons only. Quantum group SLq(2) representations are introduced to classify topologically scalars, preons, quarks and leptons.
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