Techniques for the treatment of IR divergences in decay processes at NLO and application to the top-quark decay.

We present the extension of two general algorithms for the treatment of infrared singularities arising in electroweak corrections to decay processes at next-to-leading order: the dipole subtraction formalism and the one-cutoff slicing method. The former is extended to the case of decay kinematics which has not been considered in the literature so far. The latter is generalised to production and decay processes with more than two charged particles, where new "surface" terms arise. Arbitrary patterns of massive and massless external particles are considered, including the treatment of infrared singularities in dimensional or mass regularisation. As an application of the two techniques we present the calculation of the next-to-leading order QCD and electroweak corrections to the top-quark decay width including all off-shell and decay effects of intermediate [Formula: see text] bosons. The result, e.g., represents a building block of a future calculation of NLO electroweak effects to off-shell top-quark pair ([Formula: see text]) production. Moreover, this calculation can serve as the first step towards an event generator for top-quark decays at next-to-leading order accuracy, which can be used to attach top-quark decays to complicated many-particle top-quark processes, such as for [Formula: see text] or [Formula: see text].