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

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

d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.Comment: 14 pages, no figures, to appear in J. Phys. A: Math. Ge

New exact solution of Dirac-Coulomb equation with exact boundary condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z > 137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.Comment: 12 pages,no figure

Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using √s=8 TeV proton-proton collision data

A search for squarks and gluinos in final states containing high-p T jets, missing transverse momentum and no electrons or muons is presented. The data were recorded in 2012 by the ATLAS experiment in s√=8 TeV proton-proton collisions at the Large Hadron Collider, with a total integrated luminosity of 20.3 fb−1. Results are interpreted in a variety of simplified and specific supersymmetry-breaking models assuming that R-parity is conserved and that the lightest neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 1330 GeV for a simplified model incorporating only a gluino and the lightest neutralino. For a simplified model involving the strong production of first- and second-generation squarks, squark masses below 850 GeV (440 GeV) are excluded for a massless lightest neutralino, assuming mass degenerate (single light-flavour) squarks. In mSUGRA/CMSSM models with tan β = 30, A 0 = −2m 0 and μ > 0, squarks and gluinos of equal mass are excluded for masses below 1700 GeV. Additional limits are set for non-universal Higgs mass models with gaugino mediation and for simplified models involving the pair production of gluinos, each decaying to a top squark and a top quark, with the top squark decaying to a charm quark and a neutralino. These limits extend the region of supersymmetric parameter space excluded by previous searches with the ATLAS detector

Measurement of the production of a W boson in association with a charm quark in pp collisions at √s = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at s√ = 7 TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q 2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio σ(W + +c¯¯)/σ(W − + c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s−s¯¯¯ quark asymmetry

Measurement of the top pair production cross section in 8 TeV proton-proton collisions using kinematic information in the lepton plus jets final state with ATLAS

A measurement is presented of the $t\bar{t}$ inclusive production cross-section in $pp$ collisions at a center-of-mass energy of $\sqrt{s}=8$ TeV using data collected by the ATLAS detector at the CERN Large Hadron Collider. The measurement was performed in the lepton+jets final state using a data set corresponding to an integrated luminosity of 20.3 fb$^{-1}$. The cross-section was obtained using a likelihood discriminant fit and $b$-jet identification was used to improve the signal-to-background ratio. The inclusive $t\bar{t}$ production cross-section was measured to be $260\pm 1{\textrm{(stat.)}} ^{+22}_{-23} {\textrm{(syst.)}}\pm 8{\textrm{(lumi.)}}\pm 4{\mathrm{(beam)}}$ pb assuming a top-quark mass of 172.5 GeV, in good agreement with the theoretical prediction of $253^{+13}_{-15}$ pb. The $t\bar{t}\to (e,\mu)+{\mathrm{jets}}$ production cross-section in the fiducial region determined by the detector acceptance is also reported.Comment: Published version, 19 pages plus author list (35 pages total), 3 figures, 2 tables, all figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/TOPQ-2013-06

Measurement of the top quark-pair production cross section with ATLAS in pp collisions at \sqrt{s}=7\TeV

A measurement of the production cross-section for top quark pairs(\ttbar) in $pp$ collisions at \sqrt{s}=7 \TeV is presented using data recorded with the ATLAS detector at the Large Hadron Collider. Events are selected in two different topologies: single lepton (electron $e$ or muon $\mu$) with large missing transverse energy and at least four jets, and dilepton ($ee$, $\mu\mu$ or $e\mu$) with large missing transverse energy and at least two jets. In a data sample of 2.9 pb-1, 37 candidate events are observed in the single-lepton topology and 9 events in the dilepton topology. The corresponding expected backgrounds from non-\ttbar Standard Model processes are estimated using data-driven methods and determined to be $12.2 \pm 3.9$ events and $2.5 \pm 0.6$ events, respectively. The kinematic properties of the selected events are consistent with SM \ttbar production. The inclusive top quark pair production cross-section is measured to be \sigmattbar=145 \pm 31 ^{+42}_{-27} pb where the first uncertainty is statistical and the second systematic. The measurement agrees with perturbative QCD calculations.Comment: 30 pages plus author list (50 pages total), 9 figures, 11 tables, CERN-PH number and final journal adde

Inclusive search for same-sign dilepton signatures in pp collisions at root s=7 TeV with the ATLAS detector

An inclusive search is presented for new physics in events with two isolated leptons (e or mu) having the same electric charge. The data are selected from events collected from p p collisions at root s = 7 TeV by the ATLAS detector and correspond to an integrated luminosity of 34 pb(-1). The spectra in dilepton invariant mass, missing transverse momentum and jet multiplicity are presented and compared to Standard Model predictions. In this event sample, no evidence is found for contributions beyond those of the Standard Model. Limits are set on the cross-section in a fiducial region for new sources of same-sign high-mass dilepton events in the ee, e mu and mu mu channels. Four models predicting same-sign dilepton signals are constrained: two descriptions of Majorana neutrinos, a cascade topology similar to supersymmetry or universal extra dimensions, and fourth generation d-type quarks. Assuming a new physics scale of 1 TeV, Majorana neutrinos produced by an effective operator V with masses below 460 GeV are excluded at 95% confidence level. A lower limit of 290 GeV is set at 95% confidence level on the mass of fourth generation d-type quarks