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

Role of Alpha Oscillations During Short Time Memory Task Investigated by Graph Based Partitioning

In this study, we investigate the clustering pattern of alpha band (8 Hz - 12 Hz) electroencephalogram (EEG) oscillations obtained from healthy individuals during a short time memory task with 3 different memory loads. The retention period during which subjects were asked to memorize a pattern in a square matrix is analyzed with a graph theoretical approach. The functional coupling among EEG electrodes are quantified via mutual information in the time-frequency plane. A spectral clustering algorithm followed by bootstrapping is used to parcellate memory related circuits and for identifying significant clusters in the brain. The main outcome of the study is that the size of the significant clusters formed by alpha oscillations decreases as the memory load increases. This finding corroborates the active inhibition hypothesis about alpha oscillations

Masses and decay constants of bound states containing fourth family quarks from QCD sum rules

The heavy fourth generation of quarks that have sufficiently small mixing with the three known SM families form hadrons. In the present work, we calculate the masses and decay constants of mesons containing either both quarks from the fourth generation or one from fourth family and the other from known third family SM quarks in the framework of the QCD sum rules. In the calculations, we take into account two gluon condensate diagrams as nonperturbative contributions. The obtained results reduce to the known masses and decay constants of the $\bar b b$ and $\bar c c$ quarkonia when the fourth family quark is replaced by the bottom or charm quark.Comment: 15 Pages, 9 Figures and 6 Table

Two-dimensional random walk in a bounded domain

In a recent Letter Ciftci and Cakmak [EPL 87, 60003 (2009)] showed that the two dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devil's staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function(PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the PDF bounding curve.Comment: 4 pages, 7 eps figures, revtex

Energies and wave functions for a soft-core Coulomb potential

For the family of model soft Coulomb potentials represented by V(r) = -\frac{Z}{(r^q+\beta^q)^{\frac{1}{q}}}, with the parameters Z>0, \beta>0, q \ge 1, it is shown analytically that the potentials and eigenvalues, E_{\nu\ell}, are monotonic in each parameter. The potential envelope method is applied to obtain approximate analytic estimates in terms of the known exact spectra for pure power potentials. For the case q =1, the Asymptotic Iteration Method is used to find exact analytic results for the eigenvalues E_{\nu\ell} and corresponding wave functions, expressed in terms of Z and \beta. A proof is presented establishing the general concavity of the scaled electron density near the nucleus resulting from the truncated potentials for all q. Based on an analysis of extensive numerical calculations, it is conjectured that the crossing between the pair of states [(\nu,\ell),(\nu',\ell')], is given by the condition \nu'\geq (\nu+1) and \ell' \geq (\ell+3). The significance of these results for the interaction of an intense laser field with an atom is pointed out. Differences in the observed level-crossing effects between the soft potentials and the hydrogen atom confined inside an impenetrable sphere are discussed.Comment: 13 pages, 5 figures, title change, minor revision