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.

Probing pseudoscalar and scalar mesons in semileptonic decays of $D_s^+$, D+ and D0

With the primary motivation of probing the quark substructure of scalar mesons, a generalized linear sigma model for the lowest and the next-to-lowest scalar and pseudoscalar mesons is employed to investigate several semileptonic decays of D mesons. The free parameters of the model (in its leading approximation) have been previously determined from fits to mass spectra and various low-energy parameters. With these fixed parameters, the model has already given encouraging predictions for different low-energy decays and scattering, as well as for semileptonic decay channels of [Formula: see text] that include a scalar meson in the final state. In the present work, we apply the same model (in its leading order with the same fixed parameters) to different semileptonic decay channels of [Formula: see text], D+ and D0. Although these decay channels produce only pseudoscalar mesons in the final states, since various properties of scalar mesons have been used in fixing the model parameters, this study further tests the model and its predictions for the quark substructure of both pseudoscalar as well as scalar mesons. We find that these predictions are in qualitative agreement with experiment.

BYPASSING THE AXIAL ANOMALIES

Many meson processes are related to the UA(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the Feynman graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.

LIMITS ON QUARK COMPOSITENESS FROM HIGH ENERGY JETS IN ${\bar P}P$ COLLISIONS AT 1.8 TEV

Events in [Formula: see text] collisions at 1.8 TeV with total transverse energy exceeding 500 GeV are used to set limits on quark substructure. The data are consistent with next-to-leading order QCD calculations. We set a lower limit of 2.0 TeV at 95% confidence on the energy scale ΛLL for compositeness in quarks, assuming a model with a left-left isoscalar contact interaction term. The limits on ΛLL are found to be insensitive to the sign of the interference term in the Lagrangian.

NUCLEON ELECTROMAGNETIC FORM FACTORS AND CHIRAL SINGULARITIES

Chiral singularities in both nucleon isovector radii are calculated in closed form. Within a one-meson-loop approximation we implement in an explicitly gauge invariant manner quark substructure in the γ π π and πNN vertex functions. The coefficients of log mπ and [Formula: see text] terms are directly related to gA and to the threshold behaviour of the πN amplitude A(-)(ν,0) which are 1 and 0, respectively, if only the N pole is considered in the πN scattering amplitude. This result is remarkably independent of the cut-off procedure. If mesonic substructure at the γ π π vertex is included, however, gA becomes slightly smaller than 1 and [Formula: see text] becomes moderately negative. This hints at important contributions to both gA and [Formula: see text] from the Δ(1232) and possibly other N*, Δ* resonances in this approach.