Energy-dependent point interactions in one dimension

We consider a new type of point interaction in one-dimensional quantum mechanics. It is characterized by a boundary condition at the origin that involves the second and/or higher order derivatives of the wavefunction. The interaction is effectively energy dependent. It leads to a unitary S-matrix for the transmission-reflection problem. The energy dependence of the interaction can be chosen such that any given unitary S-matrix (or the transmission and reflection coefficients) can be reproduced at all energies. Generalization of the results to coupled-channel cases is discussed.

Stop-lepton associated production at hadron colliders

At hadron colliders, the search for R-parity violating supersymmetry can probe scalar masses beyond what is covered by pair production processes. We evaluate the next-to-leading order SUSY-QCD corrections to the associated stop or sbottom production with a lepton through R-parity violating interactions. We show that higher order corrections render the theoretical predictions more stable with respect to variations of the renormalization and factorization scales and that the total cross section is enhanced by a factor up to 70% at the Tevatron and 50% at the LHC. We investigate in detail how the heavy supersymmetric states decouple from the next-to-leading order process, which gives rise to a theory with an additional scalar leptoquark. In this scenario the inclusion of higher order QCD corrections increases the Tevatron reach on leptoquark masses by up to 40 GeV and the LHC reach by up to 200 GeV. (C) 2003 Published by Elsevier B.V. B.V.

General soliton matrices in the Riemann-Hilbert problem for integrable nonlinear equations

We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix Riemann-Hilbert problem. We have applied these general results to the three-wave interaction system, and derived new classes of higher-order soliton and two-soliton solutions, in complement to those from our previous publication [Stud. Appl. Math. 110, 297 (2003)], where only the elementary higher-order zeros were considered. The higher-order solitons corresponding to nonelementary zeros generically describe the simultaneous breakup of a pumping wave (u(3)) into the other two components (u(1) and u(2)) and merger of u(1) and u(2) waves into the pumping u(3) wave. The two-soliton solutions corresponding to two simple zeros generically describe the breakup of the pumping u(3) wave into the u(1) and u(2) components, and the reverse process. In the nongeneric cases, these two-soliton solutions could describe the elastic interaction of the u(1) and u(2) waves, thus reproducing previous results obtained by Zakharov and Manakov [Zh. Eksp. Teor. Fiz. 69, 1654 (1975)] and Kaup [Stud. Appl. Math. 55, 9 (1976)]. (C) 2003 American Institute of Physics.

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to alpha'(3). Some partial results on N = 2, d = 10 and N = 1, d = 11 are also given.

Determination of the pole and (MS)over-bar masses of the top quark from the t(t)over-bar cross section

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Combination of t(t)over-bar cross section measurements and constraints on the mass of the top quark and its decays into charged Higgs bosons

We combine measurements of the top quark pair production cross section in p (p) over bar collisions in the l + jets, ll, and tau l final states ( where l is an electron or muon) at a center of mass energy of root s = 1.96 TeV in 1 fb(-1) of data collected with the D0 detector. For a top quark mass of 170 GeV/c(2), we obtain sigma(t (t) over bar) = 8.18(-0.87)(+0.98) pb in agreement with the theoretical prediction. Based on predictions from higher order quantum chromodynamics, we extract a mass for the top quark from the combined t (t) over bar cross section, consistent with the world average of the top quark mass. In addition, the ratios of t (t) over bar cross sections in different final states are used to set upper limits on the branching fractions B(t -> H(+)b -> tau(+) vb) and B(t -> H(+)b -> c (s) over barb) as a function of the charged Higgs boson mass.

Measurement of the t(t)over-bar production cross section in pp collisions at 7 TeV in lepton plus jets events using b-quark jet identification

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New class of spin projection operators for 3D models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Competition between suppression and production of Fermi acceleration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

Q-ANALOG REALIZATION OF NUCLEON PAIRING

A q-deformed analogue of zero-coupled nucleon pair states is constructed and the possibility of accounting for pairing correlations examined. For the single orbit case, the deformed pairs are found to be more strongly bound than the pairs with zero deformation, when a real-valued q parameter is used. It is found that an appropriately scaled deformation parameter reproduces the empirical few nucleon binding energies for nucleons in the 1f7/2 orbit and 1g9/2 orbit. The deformed pair Hamiltonian apparently accounts for many-body correlations, the strength of higher-order force terms being determined by the deformation parameter q. An extension to the multishell case, with deformed zero-coupled pairs distributed over several single particle orbits, has been realized. An analysis of calculated and experimental ground state energies and the energy spectra of three lowermost 0+ states, for even-A Ca isotopes, reveals that the deformation simulates the effective residual interaction to a large extent.

ANOMALIES OF VARIATIONAL PHASE-SHIFTS

It is demonstrated, contrary to various claims, that the phase shifts calculated via variational principles involving the Green function may exhibit anomalous behavior. These anomalies may appear in variational principles for the K matrix (Schwinger variational principle) of potential V, for (K-V) (Kohn-type and Newton variational principles), and other variational principles of higher order (Takatsuka-McKoy variational principle).

CHIRAL SCHWINGER MODEL WITH A PODOLSKY TERM AT FINITE-TEMPERATURE

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

The critical number of atoms for Bose-Einstein condensates with cylindrically symmetrical traps were calculated. The time evolution of the condensate was also studied at changing ground state. A conjecture on higher-order nonlinear effects was also discussed to determine its signal and strength. The results show that by exchanging frequencies, the geometry favors the condensation of larger number of particles.