Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able to calculat
e the number of zero modes in these systems for arbitrary given parameters in the semi-infinite limit. Moreover, we find that when suitable resonance condition is satisfied exact zero modes exist even in finite systems contrary to the common belief.
We investigate the prospects for the discovery of a neutral Higgs boson produced in association with a $b$ quark, followed by the Higgs decay into a pair of bottom quarks, $pp to bphi^0 to b bbar{b} +X$, at the CERN Large Hadron Collider (LHC) within
the framework of unified supersymmetric models. The Higgs boson $phi^0$ can be a heavy scalar $H^0$ or a pseudoscalar $A^0$. Furthermore, this direct discovery channel is compared with the indirect Higgs searches in the rare decay $B_s to mu^+mu^-$ at hadron colliders. Promising results are found for the minimal supergravity (mSUGRA) model, the anomaly mediated supersymmetry breaking (AMSB) model, and the gauge mediated supersymmetry breaking (GMSB) model. We find that the indirect search for $B(B_s to mu^+mu^-) ge 5times 10^{-9}$ is complementary to the direct search for $bphi^0 to bbbar{b}$ with $sqrt{s} = 14$ TeV and an integrated luminosity ($L$) of 300 fb$^{-1}$. In the AMSB and GMSB models, $bphi^0 to bbbar{b}$ with $L = 300$ fb$^{-1}$ covers a larger area in the parameter space than $B(B_s to mu^+mu^-) ge 5times 10^{-9}$. In addition, we present constraints from $b to sgamma$ and muon anomalous dipole moment ($Delta a_mu$) on the parameter space.
We investigate the prospects for discovering a top quark decaying into one light Higgs boson along with a charm quark in top quark pair production at the CERN Large Hadron Collider (LHC). A general two Higgs doublet model is adopted to study the sign
ature of flavor changing neutral Higgs decay $t to cphi^0$, %or $bar{t} to bar{c}phi^0$ where $phi^0$ could be CP-even ($H^0$) or CP-odd ($A^0$). The dominant physics background is evaluated with realistic acceptance cuts as well as tagging and mistagging efficiencies. For a reasonably large top-charm-Higgs coupling ($lambda_{tc}/lambda_{t} agt 0.09$), the abundance of signal events and the %that our acceptance cuts reduction in physics background allow us to establish a $5sigma$ signal for $M_phi sim 125$ GeV at the LHC with a center of mass energy ($sqrt{s}$) of 8 TeV and an integrated luminosity of 20 fb$^{-1}$. The discovery potential will be greatly enhanced with the full energy of $sqrt{s} = 14$ TeV.
We investigate the prospects for the discovery of massive color-octet vector bosons at the CERN Large Hadron Collider with $sqrt{s} = 14$ TeV. A phenomenological Lagrangian is adopted to evaluate the cross section of a pair of colored vector bosons (
colorons, $tilde{rho}$) decaying into four colored scalar resonances (hyper-pions, $tilde{pi}$), which then decay into eight gluons. We include the dominant physics background from the production of $8g,7g1q, 6g2q$, and $5g3q$, and determine the masses of $tilde{pi}$ and $tilde{rho}$ where discovery is possible. For example, we find that a 5$sigma$ signal can be established for $M_{tilde{pi}} alt 495$ GeV ($M_{tilde{rho}} alt 1650$ GeV). More generally we give the reach of this process for a selection of possible cuts and integrated luminosities.
We investigate the prospects for the discovery of massive hyper-gluons using data from the early runs of the CERN Large Hadron Collider with $sqrt{s} = 7$ TeV and assuming an integrated luminosity of 1 fb$^{-1}$. A phenomenological Lagrangian is adop
ted to evaluate the cross section of a pair of colored vector bosons (coloron, $tilde{rho}$) decaying into four colored scalar resonances (hyper-pion, $tilde{pi}$), which then decay into eight gluons. We include the dominant physics background from the production of $8g$, $7g1q$, $6g2q$, and $5g3q$. We find an abundance of signal events and that realistic cuts reduce the background enough to establish a $5sigma$ signal for $m_{tilde{pi}} alt 220$ GeV or $m_{tilde{rho}} alt 733$ GeV.
We investigate the prospects for the discovery of a neutral Higgs boson produced with one bottom quark followed by Higgs decay into a pair of bottom quarks at the CERN Large Hadron Collider (LHC) and the Fermilab Tevatron Collider. We work within the
framework of the minimal supersymmetric standard model. The dominant physics background is calculated with realistic acceptance cuts and efficiencies including the production of $bbbar{b}$, $bar{b}bbar{b}$, $jbbar{b}$ ($j = g, q, bar{q}$; $q = u, d, s, c$), $tbar{t} to bbar{b}jjell u$, and $tbar{t} to bbar{b}jjjj$. Promising results are found for the CP-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with masses up to 800 GeV for the LHC with an integrated luminosity ($L$) of 30 fb$^{-1}$ and up to 1 TeV for $L =$ 300 fb$^{-1}$.
We investigate the prospects for the discovery at the CERN Large Hadron Collider or at the Fermilab Tevatron of neutral Higgs bosons through the channel where the Higgs are produced together with a single bottom quark and the Higgs decays into a pair
of tau leptons, $bg to bphi^0 to btau^+tau^-, phi^0 = h^0, H^0, A^0$. We work within the framework of the minimal supersymmetric model. The dominant physics background from the production of $btau^+tau^-$, $jtau^+tau^-$ ($j = g, u, d, s, c$), $bbar{b}W^+W^-$, $W+2j$ and $Wbj$ is calculated with realistic acceptance cuts and efficiencies. Promising results are found for the CP-odd pseudoscalar ($A^0$) and the heavier CP-even scalar ($H^0$) Higgs bosons with masses up to one TeV.
We analytically calculate to second order the correction to the asymptotic form of quasinormal frequencies of four dimensional Schwarzschild black holes based on the monodromy analysis proposed by Motl and Neitzke. Our results are in good agreement with those obtained from numerical calculation.
