# On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators

## TL;DR

This paper demonstrates that for renormalized on-shell quantities, residues of higher-power propagator cuts in loop integrals can be made to vanish at the integrand level, simplifying calculations in multi-loop quantum field theory.

## Contribution

It introduces a method to make certain residues vanish at the integrand level for higher-power propagators in multi-loop integrals within the on-shell renormalization scheme.

## Key findings

- Residues vanish at the integrand level for renormalized on-shell quantities.
- Applicable to two-loop and higher-loop integrals with raised propagators.
- Simplifies calculations in loop integrals with higher powers of propagators.

## Abstract

Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines. Within the loop-tree duality approach or within methods based on numerical unitarity one needs (among other things) the residue when a raised propagator goes on-shell. We show that for renormalised quantities in the on-shell scheme these residues can be made to vanish already at the integrand level.