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

Kaluza-Klein Mesons in Universal Extra Dimensions

In models with universal extra dimensions, the isosinglet Kaluza-Klein (KK) quarks, q^1, have very narrow widths, of O(5-10) MeV, and will thus hadronize. Studies of KK-quarkonia, \bar{q}^1 q^1, show very sharp resonances and dramatic signatures at the Linear Collider. In this Brief Report, we consider the possibility of detecting KK-mesons, \bar{q}^1 q, and show that detection at a Linear Collider is unlikely.Comment: One paragraph regarding KK-meson annihilation added. Version to appear in Physical Review

Physical applications of second-order linear differential equations that admit polynomial solutions

Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation yield polynomial solutions are explicitly given. Some new classes of exactly solvable differential equation are also discussed. The results of this work are expressed in such way as to allow direct use, without preliminary analysis.Comment: 13 pages, no figure

Review of Linac-Ring Type Collider Proposals

There are three possibly types of particle colliders schemes: familiar (well known) ring-ring colliders, less familiar however sufficiently advanced linear colliders and less familiar and less advanced linac-ring type colliders. The aim of this paper is two-fold: to present possibly complete list of papers on linac-ring type collider proposals and to emphasize the role of linac-ring type machines for future HEP research.Comment: quality of figures is improved, some misprints are correcte

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

Fourth Generation Pseudoscalar Quarkonium Production and Observability at Hadron Colliders

The pseudoscalar quarkonium state, eta_4 1^S_0, formed by the Standard Model (SM) fourth generation quarks, is the best candidate among the fourth generation quarkonia to be produced at the LHC and VLHC. The production of this J^{PC} = 0^{-+} resonance is discussed and the background processes are studied to obtain the integrated luminosity limits for the discovery, depending on its mass.Comment: 13 pages, 4 figures, 5 table

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Quarkonium and hydrogen spectra with spin dependent relativistic wave equation

A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently the Dirac matrices and the k operator of Dirac's theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin 1/2 bound state single electron in Coulomb potential and then further extended to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.Comment: 14 pages, v7: Journal reference adde

Possible Discovery Channel for New Charged Leptons at the LHC

We propose a channel for the possible discovery of new charged leptons at the Large Hadron Collider. The proposed final state contains three same-sign leptons, making this new channel practically back- groundless. The method is illustrated for two different cases: the four-family Standard Model and the Grand Unified Theory based on the E6 gauge group. An example study taking 250 GeV as the charged lepton mass shows that in both models, about 8 signal events can be expected at 14 TeV center-of-mass energy with 1 fb^-1 of integrated luminosity. Although the event yield might not be sufficient for detailed measurements of the charged lepton properties, it would be sufficient to claim discovery through a counting experiment.Comment: 8 pages, 4 figures. v2 update includes an estimate of the backgrounds, consideration of the EW oblique parameters, and minor improvements. v3 update includes detector acceptance and ttbar backgroun