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

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

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

Conversion efficiency and luminosity for gamma-proton colliders based on the LHC-CLIC or LHC-ILC QCD Explorer scheme

Gamma-proton collisions allow unprecedented investigations of the low x and high $Q^{2}$ regions in quantum chromodynamics. In this paper, we investigate the luminosity for "ILC"$\times$LHC ($\sqrt{s_{ep}}=1.3$ TeV) and "CLIC"$\times$LHC ($\sqrt{s_{ep}}=1.45$ TeV) based $\gamma p$ colliders. Also we determine the laser properties required for high conversion efficiency.Comment: 16, 6 figure

Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Hydrothermal Deposition and Characterization of Heteroepitaxial BaTiO₃ Films on SrTiO₃ and LaAlO₃ Single Crystals

Heteroepitaxial BaTiO3 thin films were deposited in an aqueous solution under hydrothermal conditions on single crystal substrates of (100) SrTiO3 and (012) LaAlO3. The reactants consisted of fine TiO2 particles in a strongly alkaline solution of Ba(OH)2 at a temperature of 150°C. The growth of the films was studied by atomic force microscopy, high resolution scanning electron microscopy, and X-ray diffraction. The formation of the films occurred by nucleation of {001} faceted islands followed by three-dimensional growth of the islands to cover the substrate. Repeated hydrothermal treatment improved the film thickness and the surface coverage of the substrate at the expense of increased surface roughness. X-ray diffraction coupled with pole figure analysis showed that the films had the same in-plane and out-of-plane orientation as the substrate

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

Development of omega-3-rich \u3ci\u3eCamelina sativa\u3c/i\u3e seed oil emulsions

Camelina sativa seed is an underutilized oil source rich in omega-3 fatty acids; however, camelina oil is not fully explored for food applications. Its high omega-3 content makes it susceptible to oxidation, which may limit food applications. Therefore, the main objective of this study was to investigate the potential of camelina seed oil to form physically and oxidatively stable emulsions as a potential delivery system for omega-3 fatty acids. Effects of homogenization conditions, namely, pressure (15 MPa-30 MPa), number of passes (1,3,5, and 7), and type of homogenizers (high pressure and high shear) on the structural properties and stability of camelina seed oil emulsions stabilized with whey protein isolate were studied. High homogenization pressure (30 MPa) and number of passes (\u3e3) reduced the particle size (278 nm) and formed more physically and oxidatively stable emulsions compared to high shear homogenization; high shear homogenization generated bigger oil particles (~2,517 nm). Apparent viscosity and consistency index (k) decreased with increasing pressure, number of passes, and shear rate. Emulsions prepared with high pressure homogenization at both 15 and 30 MPa with 3 and more passes did not exhibit any peroxide formation over 28 days. Results indicated that camelina seed oil is a promising alternative oil source to form stable omega-3- rich emulsions for food applications

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way