Fractional Inversion in Krylov Space

The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is confined to an ellipse not including the origin, convergence is exponential, with the same rate as for Chebyshev inversion. The approximants can be improved recursively and lead to an iterative solver for $M^\gamma x = b$ in Krylov space. In case of $\gamma = 1/2$, the expansion is in terms of Legendre polynomials, and rigorous bounds for the truncation error are derived.Comment: Contribution to LAT97 proceedings, 3 page

Numerical Multi-Loop Calculations via Finite Integrals and One-Mass EW-QCD Drell-Yan Master Integrals

We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections to Drell-Yan lepton production with up to one massive vector boson in physical kinematics. As a reference, we evaluate these planar and non-planar integrals by the method of differential equations through to weight five. Choosing a basis of finite integrals for the numerical evaluation with SecDec3 leads to tremendous performance improvements and renders the otherwise problematic seven-line topologies numerically accessible. As another example, basis integrals for massless QCD three loop form factors are evaluated with FIESTA4. Here, employing a basis of finite integrals results in an overall speedup of more than an order of magnitude.Comment: 24 pages, 1 figure, 4 tables, 2 ancillary files with analytical results; in v2: minor improvements in the text with additional references added. v2 is the version published in JHE

A novel approach to integration by parts reduction

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta's algorithm. The key idea is to construct algebraic identities from numerical samples obtained from reductions over finite fields. We expect the method to be highly amenable to parallelization, show a low memory footprint during the reduction step, and allow for significantly better run-times.Comment: 4 pages. Version 2 is the final, published version of this articl

On the Limitations of the Color Dipole Picture

We discuss two aspects of the color dipole picture of high energy photon-proton scattering. First we present bounds on various ratios of deep inelastic structure functions resulting from the dipole picture that, together with the measured data, can be used to restrict the kinematical range of its applicability. The second issue that we address is the choice of energy variable in the dipole-proton cross section.Comment: 6 pages; talk presented by C.E. at 12th International Conference on Elastic and Diffractive Scattering (EDS07), DESY Hamburg, May 200

CP Violation in the General Two-Higgs-Doublet Model: a Geometric View

We discuss the CP properties of the potential in the general Two-Higgs-Doublet Model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.Comment: 19 pages, minor additions, minor typos corrected, results unchange

On the phenomenology of a two-Higgs-doublet model with maximal CP symmetry at the LHC - synopsis and addendum

Predictions for LHC physics are given for a two-Higgs-doublet model having four generalized CP symmetries. In this maximally-CP-symmetric model (MCPM) the first fermion family is, at tree level, uncoupled to the Higgs fields and thus massless. The second and third fermion families have a very symmetric coupling to the Higgs fields. But through the electroweak symmetry breaking a large mass hierarchy is generated between these fermion families. Thus, the fermion mass spectrum of the model presents a rough approximation to what is observed in Nature. In the MCPM the couplings of the Higgs bosons to the fermions are completely fixed. This allows us to present clear predictions for the production at the LHC and for the decays of the physical Higgs bosons. As salient feature we find rather large cross sections for Higgs-boson production via Drell-Yan type processes. In this paper we present a short outline of the model and extend a former study by the predictions at LHC for a center-of-mass energy of 7 TeV.Comment: 3 pages, 2 figure

Brushless dc motor and controller Final report, Sep. 1969 - Mar. 1970

Design, fabrication, and functional testing of brushless dc motors with split winding connected in series or paralle