Ternary SU(3)-group symmetry and its possible applications in hadron-quark substructure. Towards a new spinor-fermion structure

The questions on the existence of the three color quark symmetry and three quark-lepton generations could have the origin associated with the new exotic symmetries outside the Cartan-Killing-Lie algebras/groups. Our long-term search for these symmetries has been began with our Calabi-Yau space classification on the basis of the n-ary algebra for the reflexive projective numbers and led us to the expansion of the binary n = 2 complex and hyper complex numbers in the framework of the n-ary complex and hyper-complex numbers with n = 3, 4, … where we constructed new Abelian and non-Abelian symmetries. We have studied then norm-division properties of the Abelian nary complex numbers and have built the infinite chain of the Abelian groups U(n–1) = [U(1) × … × U(1)](n–1). We have developed the n-ary holomorphic (polymorphic) analysis on the n-ary complex space NC{n}, which led us to the generalization of the quadratic Laplace equations for the harmonic functions. The generalized Laplace equations for the n-ary harmonic functions give us the n-th order homogeneous differential equations which are invariant with respect to the Abelian n-ary groups U(n–1) and with some new spatial properties. Further consideration of the non-Abelian n-ary hyper-complex numbers opens the infinite series of the non-Abelian TnSU(n)-Lie groups(n=3,4,…) and its corresponding tnsu(n) algebras. One of the exceptional features of these symmetry groups is the appearance of some new n-dimensional spinors that could lead to an extension of the concept of the SU(2)-spin, to the appearance of n-dimensional quantum structures -exotic “n-spinor” matter(n = 3, 4, … - maarcrions). It is natural to assume that these new exotic “quantum spinor states” could be candidates for the pra-matter of the quark-charge leptons or/and for the dark matter. We will be also interested in the detection of the exotic quantum ’n-spinor” matter in the neutrino and hadron experiments.

Theoretical Evaluations of Probability of Photons Yield Depending on Quantum Chromodynamics Theory

Aim of this research is the description with evaluation the photons rate probability at quark-gluon reactions processes theoretically depending on quantum color theory. In high energy physics as well as quantum field theory and quantum chromodynamics theory,they are very important for physical processes. In quark–gluon interaction there are many processes, the Compton scattering, annihilation pairs and quark–gluon plasma. There are many quantum features, each of three and systems that taken which could make a quark–gluon plasma in character system. First, electric quark charge and color quantum charge that’s satisfied by quantum number. Second, the critical temperature and photon energy. Moreover, for such three systems have variety quantum flavor numbers: 2, 3 and 4, the photons rate are evaluated at system energy limited with critical temperature: 144 MeV. However, due to the quark–gluon plasma producing in heavy ions collisions, the photons rate is increasing with decreasing of coupling constant and photons energy in quark-quark interaction systems.

Transverse charge and magnetization densities based on Regge parameterization

In this paper, we discuss the charge and magnetization densities for proton and neutron in the transverse plane, whereas there are links between the generalized parton distributions (GPDs) and elastic form factors by means of sum rules. We use the extended Regge parameterization for large momentum transfer region for calculating Dirac and Pauli form factors which have been described in the electromagnetic form factors data, so we want to calculate the charge and magnetization densities for proton and neutron in the transverse plane and we also calculate [Formula: see text] and [Formula: see text] quark charge and magnetization densities. The extracted results are compared with other previous parameterizations.