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We present FEYNCALC 9.3, a new stable version of a powerful and versatile MATHEMAT-ICA package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and γ-matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds.

We present the calculation of the two-loop spin splitting functions P (1) ij (x) (i, j = q, g) contributing to the next-to-leading order corrected spin structure function g 1 (x, Q 2 ). These splitting functions, which are presented in the MS scheme, are derived from the order α 2 s contribution to the anomalous dimensions γ m ij (i, j = q, g). The latter correspond to the local operators which appear in the operator product expansion of two electromagnetic currents. Some of the properties of the anomalous dimensions will be discussed. In particular we find that in order α 2 s the supersymmetric relation γ m qq + γ m gq − γ m qg − γ m gg = 0 is violated.

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TARCER is an implementation of the recurrence algorithm of O.V. Tarasov for the reduction of two-loop propagator integrals with arbitrary masses to a small set of basis integrals. The tensor integral reduction scheme is adapted to moment integrals emerging in operator matrix element calculations.

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Abstract:Starting from the exact virtual and soft-photonic O() corrections to the dierential cross-section for on-shell W-pair production we derive a high-energy approximation valid for energies much higher than the W-boson mass. This approximation is improved by taking into account extra terms for large top-quark and Higgs-boson masses as well as the exact results for the leading low-energy universal corrections associated with the running of and the -parameter. For 90 scattering angle and in those situations where the cross-section is large, this approximation reproduces the full virtual and soft-photonic O() result to better than 1% for energies above 500 GeV. In the angular range 0:9 < cos < 0 : 9 it is better than 1% for energies above 1{3 TeV, depending on the polarization.