Two-Loop Threshold Singularities, Unstable Particles and Complex Masses

The effect of threshold singularities induced by unstable particles on two-loop observables is investigated and it is shown how to cure them working in the complex-mass scheme. The impact on radiative corrections around thresholds is thoroughly analyzed and shown to be relevant for two selected LHC and ILC applications: Higgs production via gluon fusion and decay into two photons at two loops in the Standard Model. Concerning Higgs production, it is essential to understand possible sources of large corrections in addition to the well-known QCD effects. It is shown that NLO electroweak corrections can incongruently reach a 10 % level around the WW vector-boson threshold without a complete implementation of the complex-mass scheme in the two-loop calculation.Comment: LaTeX, 12 pages, 7 figure

NNLO Computational Techniques: the Cases H -> gamma gamma and H -> g g

A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H -> gamma gamma and H -> g g. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H -> gamma gamma, g g are presented and discussed. When applied to the process pp -> gg + X -> H + X, the results show that the electroweak scaling factor for the cross section is between -4 % and + 6 % in the range 100 GeV < Mh < 500 GeV, without incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections under control.Comment: LaTeX, 70 pages, 8 eps figure

Multivariate Nonnegative Quadratic Mappings

In this paper we study several issues related to the characterization of speci c classes of multivariate quadratic mappings that are nonnegative over a given domain, with nonnegativity de ned by a pre-speci ed conic order.In particular, we consider the set (cone) of nonnegative quadratic mappings de ned with respect to the positive semide nite matrix cone, and study when it can be represented by linear matrix inequalities.We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models.In the latter application the implementational errors of the solution is taken into account, and the problem is formulated as a semide nite program.optimization;linear programming;models

Half-Megasecond Chandra Spectral Imaging of the Hot Circumgalactic Nebula around Quasar Mrk 231

A deep 400-ksec ACIS-S observation of the nearest quasar known, Mrk 231, is combined with archival 120-ksec data obtained with the same instrument and setup to carry out the first ever spatially resolved spectral analysis of a hot X-ray emitting circumgalactic nebula around a quasar. The 65 x 50 kpc X-ray nebula shares no resemblance with the tidal debris seen at optical wavelengths. One notable exception is the small tidal arc 3.5 kpc south of the nucleus where excess soft X-ray continuum emission and Si XIII 1.8 keV line emission are detected, consistent with star formation and its associated alpha-element enhancement, respectively. An X-ray shadow is also detected at the location of the 15-kpc northern tidal tail. The hard X-ray continuum emission within 6 kpc of the center is consistent with being due entirely to the bright central AGN. The soft X-ray spectrum of the outer (>6 kpc) portion of the nebula is best described as the sum of two thermal components with T~3 and ~8 million K and spatially uniform super-solar alpha element abundances, relative to iron. This result implies enhanced star formation activity over ~10^8 yrs accompanied with redistribution of the metals on large scale. The low-temperature thermal component is not present within 6 kpc of the nucleus, suggesting extra heating in this region from the circumnuclear starburst, the central quasar, or the wide-angle quasar-driven outflow identified from optical IFU spectroscopy on a scale of >3 kpc. Significant azimuthal variations in the soft X-ray intensity are detected in the inner region where the outflow is present. The soft X-ray emission is weaker in the western quadrant, coincident with a deficit of Halpha and some of the largest columns of neutral gas outflowing from the nucleus. Shocks created by the interaction of the wind with the ambient ISM may heat the gas to high temperatures at this location. (abridged)Comment: 43 pages, 11 figures, accepted for publication in the Astrophysical Journa

Reliability measurement during software development

During the development of data base software for a multi-sensor tracking system, reliability was measured. The failure ratio and failure rate were found to be consistent measures. Trend lines were established from these measurements that provided good visualization of the progress on the job as a whole as well as on individual modules. Over one-half of the observed failures were due to factors associated with the individual run submission rather than with the code proper. Possible application of these findings for line management, project managers, functional management, and regulatory agencies is discussed. Steps for simplifying the measurement process and for use of these data in predicting operational software reliability are outlined

Penning trap experiments for fundamental atomic physics

The possibility to store charged particles in Penning traps for long times basically at resthas enabled a rich variety of intriguing measurement opportunities. The purely staticmagnetic and electric fields, in combination with the extremely good vacuum in cryogenicPenning traps, largely decouples the ion from the complicated environment and thus givesa clear and unobscured view onto the fundamental properties of the ion. Moreover, thetheoretical calculations in atomic physics, using the quantum field theories of the StandardModel, have reached an impressive precision. Consequently, by measuring observables withsimilar precision we get the opportunity to test our most fundamental theories in physics.Here, highly charged ions (HCI) play a special role. The bound electrons in such HCI areexposed to the extremely strong electromagnetic fields of the nucleus - the strongest fieldswe have available in the laboratory in stable systems. Moreover, in HCI typically onlysingle or a few electrons are left and calculations of the atomic structure are relativelysimple and accurate. Consequently, HCI provide close to ideal conditions for stringent testsof the Standard Model, specifically quantum electrodynamics (QED). In the last years, mygroup at the Max Planck Institute for Nuclear Physics (MPIK), part of the “stored andcooled ions” division led by Klaus Blaum, has developed two experiments, Alphatrapand Liontrap. Liontrap is dedicated to the determination of the atomic masses of thelightest ions. We have provided world-leading values for the proton, the deuteron andthe HD+ molecular ion. This way, we have shed light on the puzzle of light ion masses,a long-standing discrepancy in the literature values of these fundamentally importantconstants. At Alphatrap and its predecessor experiment at Mainz we have performed aseries of measurements on the g-factor of the bound electron(s), among others the to datemost stringent test of QED in strong fields and the determination of the electron atomicmass from the g-factor of hydrogenlike carbon to 11 digits. Recently, we have connectedAlphatrap to the Heidelberg HD-EBIT high energy ion source and are now working onprogressing our experiments towards the heavy-HCI regime, where electric fields up to1016 V cm−1can be found. With this programme, Alphatrap is part of the CollaborativeResearch Centre 1225 ISOQUANT. Furthermore, new techniques enable performing preciselaser spectroscopy in HCI and other systems that are notoriously difficult to address,such as the molecular hydrogen ion. The development of sympathetic laser cooling ofions in separate traps will open up a precision regime that was previously beyond reach.Overall, we have a unique toolbox available, which will give us the opportunity to performintriguing measurements that will help to advance our understanding of fundamentalphysics

Knowing When a Higher Education Institution is in Trouble

This study investigates factors that measure the institutional viability of higher education organizations. The purpose of investigating these measures is to provide higher education officials with a means to predict the likelihood of the closure of a higher education institution. In this way, these viability measures can be used by administrators as a warning system for corrective action to ensure the continued viability of their institutions