On the singular behaviour of scattering amplitudes in quantum field theory

Understand

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach.

• We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality.
• The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.