Computation of H→ggH\to gg in FDH and DRED: renormalization, operator mixing, and explicit two-loop results

The $H\to gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED

SCET approach to regularization-scheme dependence of QCD amplitudes

We investigate the regularization-scheme dependence of scattering amplitudes in massless QCD and find that the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED) are consistent at least up to NNLO in the perturbative expansion if renormalization is done appropriately. Scheme dependence is shown to be deeply linked to the structure of UV and IR singularities. We use jet and soft functions defined in soft-collinear effective theory (SCET) to efficiently extract the relevant anomalous dimensions in the different schemes. This result allows us to construct transition rules for scattering amplitudes between different schemes (CDR, HV, FDH, DRED) up to NNLO in massless QCD. We also show by explicit calculation that the hard, soft and jet functions in SCET are regularization-scheme independent.Comment: 46 pages, 6 figure

A Multifunctional Processing Board for the Fast Track Trigger of the H1 Experiment

The electron-proton collider HERA is being upgraded to provide higher luminosity from the end of the year 2001. In order to enhance the selectivity on exclusive processes a Fast Track Trigger (FTT) with high momentum resolution is being built for the H1 Collaboration. The FTT will perform a 3-dimensional reconstruction of curved tracks in a magnetic field of 1.1 Tesla down to 100 MeV in transverse momentum. It is able to reconstruct up to 48 tracks within 23 mus in a high track multiplicity environment. The FTT consists of two hardware levels L1, L2 and a third software level. Analog signals of 450 wires are digitized at the first level stage followed by a quick lookup of valid track segment patterns. For the main processing tasks at the second level such as linking, fitting and deciding, a multifunctional processing board has been developed by the ETH Zurich in collaboration with Supercomputing Systems (Zurich). It integrates a high-density FPGA (Altera APEX 20K600E) and four floating point DSPs (Texas Instruments TMS320C6701). This presentation will mainly concentrate on second trigger level hardware aspects and on the implementation of the algorithms used for linking and fitting. Emphasis is especially put on the integrated CAM (content addressable memory) functionality of the FPGA, which is ideally suited for implementing fast search tasks like track segment linking.Comment: 6 pages, 4 figures, submitted to TN

Structure of self-assembled Mn atom chains on Si(001)

Mn has been found to self-assemble into atomic chains running perpendicular to the surface dimer reconstruction on Si(001). They differ from other atomic chains by a striking asymmetric appearance in filled state scanning tunneling microscopy (STM) images. This has prompted complicated structural models involving up to three Mn atoms per chain unit. Combining STM, atomic force microscopy and density functional theory we find that a simple necklace-like chain of single Mn atoms reproduces all their prominent features, including their asymmetry not captured by current models. The upshot is a remarkably simpler structure for modelling the electronic and magnetic properties of Mn atom chains on Si(001).Comment: 5 pages, 4 figure

Ground States and Flux Configurations of the Two-dimensional Falicov-Kimball Model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an on-site potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions, for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram is studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finaly we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.Comment: 42 pages, uuencoded postscript file. Missing pages adde

The Mellin Transform Technique for the Extraction of the Gluon Density

A new method is presented to determine the gluon density in the proton from jet production in deeply inelastic scattering. By using the technique of Mellin transforms not only for the solution of the scale evolution equation of the parton densities but also for the evaluation of scattering cross sections, the gluon density can be extracted in next-to-leading order QCD. The method described in this paper is, however, more general, and can be used in situations where a repeated fast numerical evaluation of scattering cross sections for varying parton distribution functions is required.Comment: 13 pages (LaTeX); 2 figures are included via epsfig; the corresponding postscript files are uuencode

Saturation effects in the sub-Doppler spectroscopy of Cesium vapor confined in an Extremely Thin Cell

Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an Extremely Thin Cell (cell thickness $L < 1 \mu m$) are investigated experimentally and theoretically. The study is performed on the $D_{2}$ line ($\lambda ~= ~852 nm)$ of $Cs$ and concentrates on the two situations $L = \lambda /2$ and $L =\lambda$, the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For $L = \lambda /2$, the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for $L =\lambda$, sub-Doppler dips of reduced absorption at line-center appear on the broad absorption profile. For a fluorescence detection at $L =\lambda$, saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models, and are compared with numerical calculations based upon a two-level modelling that considers both a closed and an open system.Comment: 11 pages, 12 figure