On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems

In this paper, we study the problem of robust stabilization for linear time-varying (LTV) systems subject to time-varying normalized coprime factor uncertainty. Operator theoretic results which generalize similar results known to hold for linear time-invariant (infinite-dimensional) systems are developed. In particular, we compute an upper bound for the maximal achievable stability margin under TV normalized coprime factor uncertainty in terms of the norm of an operator with a time-varying Hankel structure. We point to a necessary and sufficient condition which guarantees compactness of the TV Hankel operator, and in which case singular values and vectors can be used to compute the time-varying stability margin and TV controller. A connection between robust stabilization for LTV systems and an Operator Corona Theorem is also pointed out.Comment: 20 page

Two-Photon Decay Widths of Higgs Particles

Two--photon decays of Higgs bosons are important channels for the search of these particles in the intermediate mass range at the $pp$ colliders LHC and SSC. Dynamical aspects of the Higgs coupling to two photons can also be studied by means of the $\gamma \gamma$ fusion of Higgs particles at high--energy e$^+$e$^-$ linear colliders. Extending earlier analyses which had been restricted to the Standard Model, we present in this note the QCD radiative corrections to the $\gamma \gamma$ decay widths of scalar and pseudoscalar Higgs particles in multi--doublet extensions of the Higgs sector, as realized for instance in supersymmetric theories.Comment: 8pages + 3figures (not included, a hard copy is available from A.D. upon request), Prep. DESY 92-170 (to appear in Phys. Lett. B

Decays of Supersymmetric Particles: the program SUSY-HIT (SUspect-SdecaY-Hdecay-InTerface)

We present the program package SUSY-HIT for the computation of supersymmetric particle decays within the framework of the Minimal Supersymmetric extension of the Standard Model. The code is based on two existing programs HDECAY and SDECAY for the calculation of the decay widths and branching ratios of, respectively, the MSSM Higgs bosons and the SUSY particles, and calls a program for the calculation of the SUSY particle spectrum such as SuSpect. Including all important higher order effects, the package allows the consistent calculation of the MSSM particle spectrum and decays with the presently highest level of precision.Comment: 8 pages, no figure

Two-loop scalar self-energies and pole masses in a general renormalizable theory with massless gauge bosons

I present the two-loop self-energy functions for scalar bosons in a general renormalizable theory, within the approximation that vector bosons are treated as massless or equivalently that gauge symmetries are unbroken. This enables the computation of the two-loop physical pole masses of scalar particles in that approximation. The calculations are done simultaneously in the mass-independent \bar{MS}, \bar{DR}, and \bar{DR}' renormalization schemes, and with arbitrary covariant gauge fixing. As an example, I present the two-loop SUSYQCD corrections to squark masses, which can increase the known one-loop results by of order one percent. More generally, it is now straightforward to implement all two-loop sfermion pole mass computations in supersymmetry using the results given here, neglecting only the electroweak vector boson masses compared to the superpartner masses in the two-loop parts.Comment: 16 pages, 4 figures. v2: typo in eq. (5.30) fixe

Chargino and Neutralino Decays Revisited

We perform a comprehensive analysis of the decays of charginos and neutralinos in the Minimal Supersymmetric Standard Model where the neutralino $\chi_1^0$ is assumed to be the lightest supersymmetric particle. We focus, in particular, on the three-body decays of the next-to-lightest neutralino and the lightest chargino into the lightest neutralino and fermion-antifermion pairs and include vector boson, Higgs boson and sfermion exchange diagrams, where in the latter contribution the full mixing in the third generation is included. The radiative corrections to the heavy fermion and SUSY particle masses will be also taken into account. We present complete analytical formulae for the Dalitz densities and the integrated partial decay widths in the massless fermion case, as well as the expressions of the differential decay widths including the masses of the final fermions and the polarization of the decaying charginos and neutralinos. We then discuss these decay modes, in particular in scenarios where the parameter $\tan \beta$ is large and in models without universal gaugino masses at the Grand Unification scale where some new decay channels, such as decays into gluinos and $q\bar{q}$ pairs, open up.Comment: 51 pages with 13 figures, latex; uses axodraw.sty and epsfig.st

Production of MSSM Higgs Bosons in Photon-Photon Collisions

The heavy neutral Higgs bosons H, A in the minimal supersymmetric extension of the Standard Model can be produced as single resonances at high-energy gamma gamma colliders. We have studied the prospects of the search for these particles in b\bar b and neutralino-pair final states. The Higgs bosons can be found with masses up to 70-80% of the initial e^\pm e^- collider energy for medium values of tan(beta), i.e. in areas of the supersymmetric parameter space not accessible at other colliders.Comment: 9 pages, latex, 3 figure

HDECAY: a Program for Higgs Boson Decays in the Standard Model and its Supersymmetric Extension

We describe the Fortran code HDECAY which calculates the decay widths and the branching ratios of the Standard Model Higgs boson, and of the neutral and charged Higgs particles of the Minimal Supersymmetric extension of the Standard Model. The program is self-contained (with all subroutines included), easy to run, fast and calculates the decay widths and branching ratios according to the current theoretical knowledge.Comment: LaTeX, 26 pages, 3 ps figures include

Bosonic corrections to the effective leptonic weak mixing angle at the two-loop level

Details of the recent calculation of the two-loop bosonic corrections to the effective leptonic weak mixing angle are presented. In particular, the expansion in the difference of the W and Z boson masses is studied and some of the master integrals needed are given in analytic form.Comment: 5 pages, 4 figures, to appear in the proceedings of the 7th International Symposium on Radiative Corrections (RADCOR05), Shonan Village, Japan, 200

Search for a Higgs Boson Decaying into Two Photons with the L3 Detector at LEP

A search is performed for a Higgs boson, decaying into two photons, using the L3 data collected at centre of mass energies between $\sqrt s$ = 189 and 202 GeV, corresponding to an integrated luminosity of 400 pb$^{-1}$. The processes $e^{+}e^{-}\to {Zh} \to {q} \bar{q} \gamma \gamma$, $e^{+}e^{-}\to {Zh} \to \nu \bar{\nu} \gamma \gamma$, $e^{+}e^{-}\to {Zh} \to {l}^{+} {l}^{-} \gamma \gamma$ are considered. The observed data are found to be consistent with the expected background from standard physics processes. Limits on the branching fraction of the Higgs boson decay into two photons as a function of the Higgs mass are shown and a lower mass limit on a fermiophobic Higgs is derived.Comment: 3 pages, 2 postscript figures, Presented at the DPF2000 Conference, August 9-12, 2000, The Ohio State University, Columbus, Ohi