1,644 research outputs found
Fractional Inversion in Krylov Space
The fractional inverse (real ) of a matrix is
expanded in a series of Gegenbauer polynomials. If the spectrum of 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 in Krylov
space. In case of , 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
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
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