Tuning FORM with large calculations

Some recent additions to FORM are discussed. In particular large file support and the tablebases are presented.Comment: 5 pages, LaTeX. Talk given at RADCOR02, Kloster Ban

The reaction e+e- --> hh recomputed

We notice that the existing literature about the reaction e+e- --> hh suffers from a mistake in the relative sign between the t-channel and u-channel graphs. Correcting this lowers the crosssections by about an order of magnitude.Comment: 7 pages, 5 figure

Mathematics for structure functions

We show some of the mathematics that is being developed for the computation of deep inelastic structure functions to three loops. These include harmonic sums, harmonic polylogarithms and a class of difference equations that can be solved with the use of harmonic sums.Comment: 6 pages LaTeX, uses axodraw.sty and npb.sty (included

The Mellin moments of deep inelastic structure functions at two loops

We perform the analytic calculation of the Mellin moments of the structure functions F_2 and F_L in perturbative QCD up to second order corrections and in leading twist approximation. We calculate the 2-loop contributions to the anomalous dimensions of the singlet and non-singlet operator matrix elements and the 2-loop coefficient functions of F_2 and F_L. Our results are in agreement with earlier calculations in the literature.Comment: 4 pages LaTeX, talk given at the QCD 99 Euroconference, Montpellier (France

Studying possible CP-violating Higgs couplings through top-quark pair productions at muon colliders

We study possible anomalous CP-violating Higgs couplings to mu mu-bar and t t-bar fully model-independent way through top-quark pair productions at muon colliders. Assuming additional non-standard neutral Higgs bosons, whose couplings with top-quark and muon are expressed in the most general covariant form, we carry out analyses of effects which they are expected to produce via CP-violating asymmetries and also the optimal-observable (OO) procedure under longitudinal and transverse muon polarizations. We find the measurement of the asymmetry for longitudinal beam polarization could be useful to catch some signal of CP violation, and an OO analysis might also be useful if we could reduce the number of unknown parameters with a help of other experiments and if the size of the parameters is at least O(1) ~ O(10).Comment: Final version (to appear in JHEP

ParFORM: recent development

We report on the status of our project of parallelization of the symbolic manipulation program FORM. We have now parallel versions of FORM running on Cluster- or SMP-architectures. These versions can be used to run arbitrary FORM programs in parallel.Comment: 5 pages, 6 Encapsulated postscript figures, LaTeX2e, uses espcrc2.sty (included). Talk given at ACAT0

Reduction and evaluation of two-loop graphs with arbitrary masses

We describe a general analytic-numerical reduction scheme for evaluating any 2-loop diagrams with general kinematics and general renormalizable interactions, whereby ten special functions form a complete set after tensor reduction. We discuss the symmetrical analytic structure of these special functions in their integral representation, which allows for optimized numerical integration. The process Z -> bb is used for illustration, for which we evaluate all the 3-point, non-factorizable g^2*alpha_s mixed electroweak-QCD graphs, which depend on the top quark mass. The isolation of infrared singularities is detailed, and numerical results are given for all two-loop three-point graphs involved in this process

FORM version 4.0

We present version 4.0 of the symbolic manipulation system FORM. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Groebner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Lastly, FORM 4.0 has become available as open source under the GNU General Public License version 3.Comment: 26 pages. Uses axodra

Three-Loop Results for Quark and Gluon Form Factors

We study the photon-quark-quark and Higgs-gluon-gluon form factors for on-shell massless quarks and gluons in perturbative QCD. Previous third-order results for the quark case are extended by calculating the fermion-loop contributions up to the finite terms in dimensional regularization. For the gluon case the complete set of infrared poles at three loops is derived. Using the exponentiation of the form factor, the latter results are employed to extract a function entering the infrared factorization of general third-order amplitudes. We evaluate the infrared finite absolute ratio of the time-like and space-like gluon form factors up to the fourth order in the strong coupling constant. The result supports previous indications that the perturbative expansion of the Higgs boson production rate at the LHC is under control.Comment: 9 pages, LaTeX. FORM file of main results appended to sourc

Forcer: a FORM program for 4-loop massless propagators

Algorithms and the Foundations of Software technolog