  Electroweak radiative corrections to the production of high-multiplicity
final states with several intermediate resonances in most cases can be
sufficiently well described by the leading contribution of an expansion about
the resonance poles. In this approach, also known as pole approximation,
corrections are classified into separately gauge-invariant factorizable and
non-factorizable corrections, where the former can be attributed to the
production and decay of the unstable particles on their mass shell. The
remaining non-factorizable corrections are induced by the exchange of soft
photons between different production and decay subprocesses. We give explicit
analytical results for the non-factorizable photonic virtual corrections to the
production of an arbitrary number of unstable particles at the one-loop level
and, thus, deliver an essential building block in the calculation of
next-to-leading-order electroweak corrections in pole approximation. The
remaining virtual factorizable corrections can be obtained with modern
automated one-loop matrix-element generators, while the evaluation of the
corresponding real photonic corrections can be evaluated with full matrix
elements by multi-purpose Monte Carlo generators. Our results can be easily
modified to non-factorizable QCD corrections, which are induced by soft-gluon
exchange.
