Fourth SM Family Manifestations at CLIC

The latest electroweak precision data allow the existence of additional chiral generations in the standard model. We study prospects of search for the fourth standard model family fermions and quarkonia at $e^{+}e^{-}$ and $\gamma \gamma$ options of CLIC. It is shown that CLIC will be powerfull machine for discovery and investigation of both fourth family leptons and quarkonia. Moreover, the formation of the fourth family quarkonia will give a new opportunity to investigate Higgs boson properties.Comment: 7 pages, 6 Table

The Fourth SM Family Neutrino at Future Linear Colliders

It is known that Flavor Democracy favors the existence of the fourth standard model (SM) family. In order to give nonzero masses for the first three family fermions Flavor Democracy has to be slightly broken. A parametrization for democracy breaking, which gives the correct values for fundamental fermion masses and, at the same time, predicts quark and lepton CKM matrices in a good agreement with the experimental data, is proposed. The pair productions of the fourth SM family Dirac $(\nu_{4})$ and Majorana $(N_{1})$ neutrinos at future linear colliders with $\sqrt{s}=500$ GeV, 1 TeV and 3 TeV are considered. The cross section for the process $e^{+}e^{-}\to\nu_{4}\bar {\nu_{4}}(N_{1}N_{1})$ and the branching ratios for possible decay modes of the both neutrinos are determined. The decays of the fourth family neutrinos into muon channels $(\nu_{4}(N_{1})\to\mu^{\pm}W^{\mp})$ provide cleanest signature at $e^{+}e^{-}$ colliders. Meanwhile, in our parametrization this channel is dominant. $W$ bosons produced in decays of the fourth family neutrinos will be seen in detector as either di-jets or isolated leptons. As an example we consider the production of 200 GeV mass fourth family neutrinos at $\sqrt{s}=500$ GeV linear colliders by taking into account di-muon plus four-jet events as signatures.Comment: 16 pages, 3 figures, 10 table

Spectral characteristics for a spherically confined -1/r + br^2 potential

We consider the analytical properties of the eigenspectrum generated by a class of central potentials given by V(r) = -a/r + br^2, b>0. In particular, scaling, monotonicity, and energy bounds are discussed. The potential $V(r)$ is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical boundary of radius R. With the aid of the asymptotic iteration method, several exact analytic results are obtained which exhibit the parametric dependence of energy on a, b, and R, under certain constraints. More general spectral characteristics are identified by use of a combination of analytical properties and accurate numerical calculations of the energies, obtained by both the generalized pseudo-spectral method, and the asymptotic iteration method. The experimental significance of the results for both the free and confined potential V(r) cases are discussed.Comment: 16 pages, 4 figure