Non-singlet splitting functions in QED

Iterative solution of QED evolution equations for non-singlet electron structure functions is considered. Analytical expressions in the fourth and fifth orders are presented in terms of splitting functions. Relation to the existing exponentiated solution is discussed.Comment: 8 pages, LaTeX2

Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms \Li{a}{-t/s}, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.Comment: LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some explanations adde

Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q^2). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s,t and u, and simple finite two- and three fold Mellin--Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.Comment: 9 pages, LaTeX with axodraw.sty, minor changes in references, to appear in Physics Letters

Numerical evaluation of multiple polylogarithms

Multiple polylogarithms appear in analytic calculations of higher order corrections in quantum field theory. In this article we study the numerical evaluation of multiple polylogarithms. We provide algorithms, which allow the evaluation for arbitrary complex arguments and without any restriction on the weight. We have implemented these algorithms with arbitrary precision arithmetic in C++ within the GiNaC framework.Comment: 23 page

Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box

The dimensionally regularized massless on-shell planar triple box Feynman diagram with powers of propagators equal to one is analytically evaluated for general values of the Mandelstam variables s and t in a Laurent expansion in the parameter \ep=(4-d)/2 of dimensional regularization up to a finite part. An explicit result is expressed in terms of harmonic polylogarithms, with parameters 0 and 1, up to the sixth order. The evaluation is based on the method of Feynman parameters and multiple Mellin-Barnes representation. The same technique can be quite similarly applied to planar triple boxes with any numerators and integer powers of the propagators.Comment: 8 pages, LaTeX with axodraw.st

A Comparative Study of Automatic Localization Algorithms for Spherical Markers within 3D MRI Data

Localization of features and structures in images is an important task in medical image-processing. Characteristic structures and features are used in diagnostics and surgery planning for spatial adjustments of the volumetric data, including image registration or localization of bone-anchors and fiducials. Since this task is highly recurrent, a fast, reliable and automated approach without human interaction and parameter adjustment is of high interest. In this paper we propose and compare four image processing pipelines, including algorithms for automatic detection and localization of spherical features within 3D MRI data. We developed a convolution based method as well as algorithms based on connected-components labeling and analysis and the circular Hough-transform. A blob detection related approach, analyzing the Hessian determinant, was examined. Furthermore, we introduce a novel spherical MRI-marker design. In combination with the proposed algorithms and pipelines, this allows the detection and spatial localization, including the direction, of fiducials and bone-anchors

Phospholipid Scramblase 4 (PLSCR4) Regulates Adipocyte Differentiation via PIP3-Mediated AKT Activation

Phospholipid scramblase 4 (PLSCR4) is a member of a conserved enzyme family with high relevance for the remodeling of phospholipid distribution in the plasma membrane and the regulation of cellular signaling. While PLSCR1 and -3 are involved in the regulation of adipose-tissue expansion, the role of PLSCR4 is so far unknown. PLSCR4 is significantly downregulated in an adipose-progenitor-cell model of deficiency for phosphatase and tensin homolog (PTEN). PTEN acts as a tumor suppressor and antagonist of the growth and survival signaling phosphoinositide 3-kinase (PI3K)/AKT cascade by dephosphorylating phosphatidylinositol-3,4,5-trisphosphate (PIP3). Patients with PTEN germline deletion frequently develop lipomas. The underlying mechanism for this aberrant adipose-tissue growth is incompletely understood. PLSCR4 is most highly expressed in human adipose tissue, compared with other phospholipid scramblases, suggesting a specific role of PLSCR4 in adipose-tissue biology. In cell and mouse models of lipid accumulation, we found PLSCR4 to be downregulated. We observed increased adipogenesis in PLSCR4-knockdown adipose progenitor cells, while PLSCR4 overexpression attenuated lipid accumulation. PLSCR4 knockdown was associated with increased PIP3 levels and the activation of AKT. Our results indicated that PLSCR4 is a regulator of PI3K/AKT signaling and adipogenesis and may play a role in PTEN-associated adipose-tissue overgrowth and lipoma formation

DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory

We derive the DGLAP and BFKL evolution equations in the N=4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions \gamma of twist-2 operators in the non-physical points j=0,-1,... from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N=4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the Pomeron hamiltonian is violated, but the corresponding Bethe-Salpeter kernel has the property of a hermitian separability. The main singularities of anomalous dimensions \gamma at j=-r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles.Comment: 45 pages, latex. In the last version the expression (16) for the t-channel partial wave of the process e+e- --> \mu+\mu- in the double-logarithmic approximation at QED is corrected and its derivation is given in the Appendix

Two-Loop Vertices in Quantum Field Theory: Infrared and Collinear Divergent Configurations

A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic computations of next-to-next-to-leading corrections to physical observables is emphasised. A classification of infrared singular configurations, based on solutions of Landau equations, is introduced. Algorithms for the numerical evaluation of the residues of the infrared poles and of the infrared finite parts of diagrams are introduced and discussed within the scheme of dimensional regularization. Integral representations of Feynman diagrams which form a generalization of Nielsen - Goncharov polylogarithms are introduced and their numerical evaluation discussed. Numerical results are shown for all different families of multi-scale, two-loop, three-point infrared divergent diagrams and successful comparisons with analytical results, whenever available, are performed. Part of these results has already been included in a recent evaluation of electroweak pseudo-observables at the two-loop level.Comment: 62 pages, 15 figures, 16 table

NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories

We study next-to-leading corrections to the integral kernel of the BFKL equation for high energy cross-sections in QCD and in supersymmetric gauge theories. The eigenvalue of the BFKL kernel is calculated in an analytic form as a function of the anomalous dimension \gamma of the local gauge-invariant operators and their conformal spin n. For the case of an extended N=4 SUSY the kernel is significantly simplified. In particular, the terms non-analytic in n are canceled. We discuss the relation between the DGLAP and BFKL equations in the N=4 model.Comment: Latex, 26 pages, typos corrected, to be published in Nucl.Phys.