Single-scale diagrams and multiple binomial sums

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.Comment: 10 pp LaTeX, misprints in app. A and minor misprints in the text correcte

The rate of cosmic ray showers at large zenith angles: a step towards the detection of ultra-high energy neutrinos by the Pierre Auger Observatory

It is anticipated that the Pierre Auger Observatory can be used to detect cosmic neutrinos of >10^19 eV that arrive at very large zenith angles. However showers created by neutrino interactions close to the detector must be picked out against a background of similar events initiated by cosmic ray nuclei. As a step towards understanding this background, we have made the first detailed analysis of air showers recorded at Haverah Park (an array which used similar detectors to those planned for the Auger Observatory) with zenith angles above 60 degs. We find that the differential shower rate from 60 degs to 80 degs. can be predicted accurately when we adopt the known primary energy spectrum above 10^17 eV and assume the QGSJET model and proton primaries. Details of the calculation are given.Comment: 22 pages, 12 figures, to appear in Astroparticle Physic

Two-loop self-energy master integrals on shell

Analytic results for the complete set of two-loop self-energy master integrals on shell with one mass are calculated.Comment: 14 pages, LaTeX, one eps-figure; in v5. misprints in the Eq.(2) and Table II correcte

Recursion relations for two-loop self-energy diagrams on-shell

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2 package is used for the calculation of special types of diagrams. A method of calculation of higher order \epsilon-expansion of master integrals is demonstrated.Comment: Talk given by J.Fleischer at 6th International Workshop on Software Engineering, Artificial Intelligence, Neural Nets, Genetic Algorithms, Symbolic Algebra, Automatic Calculation (AIHENP 99), Heraklion, Crete, Greece, 12-16 April, 1999; 8 pages, LaTeX, 3 eps-figure

Towards Automatic Analytic Evaluation of Diagrams with Masses

A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon ${{1/2}(g-2)}_{\mu}$. Presently, we confine ourselves to a ``toy'' model with only $\mu$, $\gamma$ and a heavy neutral scalar particle (Higgs). The algorithm is implemented as a FORM-based program package. For generating and automatically evaluating any number of two-loop self-energy diagrams, a special C-program has been written. This program creates the initial FORM-expression for every diagram generated by QGRAF, executes the corresponding subroutines and sums up the final results.Comment: LaTeX, 20 pages, 7 eps-figures included; extended version of talk given at AIHEN96, Lausanne, 1-6 Sept. 1996; detailed description of C-program is given; accepted for publication in Comp.Phys.Com