The dipole subtraction method for calculating next-to-leading order corrections in QCD was originally only formulated for massless partons. In this paper we extend its definition to include massive partons, namely quarks, squarks and gluinos. We pay particular attention to the quasi-collinear region, which gives rise to terms that are enhanced by logarithms of the parton masses, M. By ensuring that our subtraction cross section matches the exact real cross section in all quasi-collinear regions we achieve uniform convergence both for hard scales Q ∼ M and Q ≫ M. Moreover, taking the masses to zero, we exactly reproduce the previously-calculated massless results. We give all the analytical formulae necessary to construct a numerical program to evaluate the next-to-leading order QCD corrections to arbitrary observables in an arbitrary process.

Abstract:We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e − → 4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex.

Neutral Higgs-boson-pair production provides the possibility of studying the trilinear Higgs couplings at future high-energy colliders. We present the QCD corrections to the gluon-initiated processes in the limit of a heavy top quark in the loops and the Drell-Yan-like pair production of scalar and pseudoscalar Higgs particles. The pp cross sections are discussed for CERN LHC energies within the standard model and its minimal supersymmetric extension. The QCD corrections are large, enhancing the total cross sections significantly.

The complete electroweak O(α) corrections have been calculated for the chargedcurrent four-fermion production processes e + e − → ν τ τ + µ −ν µ , udµ −ν µ , and udsc. Here, technical details of this calculation are presented. These include the algebraic reduction of spinor chains to a few standard structures and the consistent implementation of the finite width of the W boson. To this end, a generalization of the complex-mass scheme to the one-loop level is proposed, and the practical application of this method is described. Finally, the effects of the complete O(α) corrections to various differential cross sections of physical interest are discussed and compared to predictions based on the double-pole approximation, revealing that the latter approximation is not sufficient to fully exploit the potential of a future linear collider in an analysis of W-boson pairs at high energies.August 2011 1 Some of the problems appearing in a first attempt of such a calculation were already described in Ref. [ 25]. 2 The recently proposed approach [ 35] to describe unstable particles within an effective field theory is equivalent to a pole expansion.

A new method for the reduction of one-loop tensor 5-point integrals to related 4-point integrals is proposed. In contrast to the usual Passarino-Veltman reduction and other methods used in the literature, this reduction avoids the occurrence of inverse Gram determinants, which potentially cause severe numerical instabilities in practical calculations. Explicit results for the 5-point tensor coefficients are presented up to rank 4. The expressions for the reduction of the relevant 1-, 2-, 3-, and 4-point tensor coefficients to scalar integrals are also included; apart from these standard integrals no other integrals are needed.Comment: 24 pages, latex, some references adde