Supersymmetry for Fermion Masses

It is proposed that supersymmetry (SUSY) maybe used to understand fermion mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic symmetry among the three generation SU(2) doublets. SUSY breaks at a high energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is unnaturally small. No additional global symmetry, like the R-parity, is imposed. The Yukawa couplings and R-parity violating couplings all take their natural values which are about (10^0-10^{-2}). Under the family symmetry, only the third generation charged fermions get their masses. This family symmetry is broken in the soft SUSY breaking terms which result in a hierarchical pattern of the fermion masses. It turns out that for the charged leptons, the tau mass is from the Higgs vacuum expectation value (VEV) and the sneutrino VEVs, the muon mass is due to the sneutrino VEVs, and the electron gains its mass due to both Z_{3L} and SUSY breaking. The large neutrino mixing are produced with neutralinos playing the partial role of right-handed neutrinos. |V_{e3}| which is for nu_e-nu_{tau} mixing is expected to be about 0.1. For the quarks, the third generation masses are from the Higgs VEVs, the second generation masses are from quantum corrections, and the down quark mass due to the sneutrino VEVs. It explains m_c/m_s, m_s/m_e, m_d > m_u and so on. Other aspects of the model are discussed.Comment: 25 pages, 3 figures, revtex4; neutrino oscillation and many discussions added, smallness of the electron mass due to supersymmetry pointed out; v3: numerical errors correcte

New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables

The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional generalization of well known one-dimensional P\"oschl-Teller model is proven to be exactly solvable for arbitrary integer value of parameter $p:$ all its bound state energy eigenvalues are found analytically, and the algorithm for analytical calculation of all wave functions is given. The shape invariance of the model and its integrability are of essential importance to obtain these results.Comment: 23 page

Quasi-classical path integral approach to supersymmetric quantum mechanics

{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet, Bandrauk and Campbell when SUSY is good. When SUSY is broken, we arrive at a new quantization formula, which is found as good as and even sometime better than the WKB formula in evaluating energy spectra for certain one-dimensional bound state problems. The wave functions in the stationary phase approximation are also derived for SUSY and broken SUSY cases. Insofar as a broken SUSY case is concerned, there are strong indications that the new quasi-classical approximation formula always overestimates the energy eigenvalues while WKB always underestimates.Comment: 13 pages + 5 figures, complete paper submitted as postscript file, to appear in Phys. Rev.

Physics of B_c mesons

In the framework of potential models for heavy quarkonium the mass spectrum for the system ($\bar b c$) is considered. Spin-dependent splittings, taking into account a change of a constant for effective coulomb interaction between the quarks, and widths of radiative transitions between the ($\bar b c$) levels are calculated. In the framework of QCD sum rules, masses of the lightest vector $B_c^*$ and pseudoscalar $B_c$ states are estimated, scaling relation for leptonic constants of heavy quarkonia is derived, and the leptonic constant $f_{B_c}$ is evaluated. The $B_c$ decays are considered in the framework of both the potential models and the QCD sum rules, where the significance of Coulomb-like corrections is shown. The relations, following from the approximate spin symmetry for the heavy quarks in the heavy quarkonium, are analysed for the form factors of the semileptonic weak exclusive decays of $B_c$. The $B_c$ lifetime is evaluated with the account of the corrections to the spectator mechanism of the decay, because of the quark binding into the meson. The total and differential cross sections of the $B_c$ production in different interactions are calculated. The analytic expressions for the fragmentational production cross sections of $B_c$ are derived. The possibility of the practical $B_c$ search in the current and future experiments at electron-positron and hadron colliders is analysed.Comment: 81 page, latex, ihep.sty is required and attached in the end of the file after \end{document}, figures are not availabl

Naturalness Bounds on Dipole Moments from New Physics

Assuming naturalness that the quantum corrections to the mass should not exceed the order of the observed mass, we derive and apply model-independent bounds on the anomalous magnetic moments and electric dipole moments of leptons and quarks due to new physics.Comment: 4 pages, 2 figure

Some Results on Cubic and Higher Order Extensions of the Poincar\'e Algebra

In these lectures we study some possible higher order (of degree greater than two) extensions of the Poincar\'e algebra. We first give some general properties of Lie superalgebras with some emphasis on the supersymmetric extension of the Poincar\'e algebra or Supersymmetry. Some general features on the so-called Wess-Zumino model (the simplest field theory invariant under Supersymmetry) are then given. We further introduce an additional algebraic structure called Lie algebras of order F, which naturally comprise the concepts of ordinary Lie algebras and superalgebras. This structure enables us to define various non-trivial extensions of the Poincar\'e algebra. These extensions are studied more precisely in two different contexts. The first algebra we are considering is shown to be an (infinite dimensional) higher order extension of the Poincar\'e algebra in $(1+2)-$dimensions and turns out to induce a symmetry which connects relativistic anyons. The second extension we are studying is related to a specific finite dimensional Lie algebra of order three, which is a cubic extension of the Poincar\'e algebra in $D-$space-time dimensions. Invariant Lagrangians are constructed.Comment: Mini course given at the Workshop higher symmetries in physics, Madrid, Spain, November 6-8, 200

Search for heavy long-lived charged R-hadrons with the ATLAS detector in 3.2 fb(-1) of proton-proton collision data at root s=13 TeV

A search for heavy long-lived charged R-hadrons is reported using a data sample corresponding to 3.2 fb−1 of proton–proton collisions at √s = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider at CERN. The search is based on observables related to large ionisation losses and slow propagation velocities, which are signatures of heavy charged particles travelling significantly slower than the speed of light. No significant deviations from the expected background are observed. Upper limits at 95% confidence level are provided on the production cross section of long-lived R-hadrons in the mass range from 600 GeV to 2000 GeV and gluino, bottom and top squark masses are excluded up to 1580 GeV, 805 GeV and 890 GeV, respectively