Modern Physics Letters A

A non-Abelian extension of electric-magnetic duality implies that dual to confined colour SU(3), there also ought to be a broken threefold symmetry which can play the role of fermion generations. A model constructed on these premises not only gives a raison d'être for 3 and only 3 generations as observed but also offers a natural explanation for the distinctive fermion mass and mixing patterns seen in experiment. A calculation to one-loop order in this model with only 3 fitted parameters already gives correct values, all within present experimental errors, for the following quantities: the mass ratios m_c/m_t, m_s/m_b, m_μ/m_τ, all 9 matrix elements of the CKM mixing matrix |V_rs| for quarks, plus the lepton MNS mixing matrix elements |U_μ3| and |U_e3| studied in neutrino oscillation experiments with respectively atmospheric and reactor neutrinos.

We have calculated the branching ratio and CP asymmetry of B → X_sγ decay within the family nonuniversal Z′ models. We have established certain bounds on the model parameters using the present experimental bounds. We also comment on the role of family nonuniversality in the hadronic decay modes of the B meson.

We study the fuzzy structure of the general Kähler coset space G/S ⊗ U(1)^k deformed by the Fedosov formalism. It is shown that the Killing potentials satisfy the fuzzy algebras working in the Darboux coordinates.

We advance the viewpoint that, only relevant modes of the vacuum fluctuations, namely, with wavelengths conditioned by the size, homogeneity, geometry and topology of the Universe, do contribute to the cosmological constant. A formula is derived which relates the cosmological constant with the size of the Universe and the three fundamental constants: the velocity of light, Planck and Newton gravitational constants. Then the current value of the cosmological constant remarkably agrees with the value indicated by distant supernovae observations, i.e. of the order of the critical density. Thus the cosmological constant had to be smaller than the matter density in the past and will be bigger in the future.

We consider three active flavor neutrino oscillations where both the mass-square differences play a role in atmospheric neutrino problem. We calculate the matter effects arising due to propagation through earth. We demonstrate that these effects improve the fit to the electron data vis-a-vis vacuum oscillations but make the fit to the muon data far worse, thus worsening the overall fit. The results of our analytical calculation verify the numerical investigations of this scheme presented earlier by Fogli et al.

The equations of motion for a particle with spin are derived from a simple Lagrangian. The spin is shown to be conserved on the particle's worldline. In the absence of a spin the equation coincides with that of a geodesic. The equations of motion are valid for massless particles as well, since mass does not enter the equations explicitly.

Using the notions of gauge symmetry and gauge connection on ordinary superspaces, we derive a class of generalized supertranslation algebras in the case of N = 1, D = 2 Euclidean superspace with a U(1) gauge group. This generalizes the ordinary algebra by inclusion of some additional bosonic and fermionic operators which are interpreted as the generators of the U(1) gauge symmetry on superspace. The generalized superalgebra closes only for very particular configurations of the gauge connection superfield. This provides a unified framework for a variety of generalizations of the ordinary superalgebra such as its central extension and its noncommutative deformation found in an earlier work.