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.
Highlights
The aim for theoretical precision predictions for the LHC requires next-to-next-to-leading order calculations for a number of processes
Numerical methods like numerical loop integration [1,2,3,4,5,6,7,8,9,10,11,12,13] combined with loop-tree duality [14,15,16,17,18,19,20,21,22,23] or methods based on numerical unitarity [24,25,26,27,28] are a promising path for this approach
Starting from two-loops, there are Feynman integrals with higher powers of the propagators. They arise from self-energy insertions on internal lines
Summary
The aim for theoretical precision predictions for the LHC requires next-to-next-to-leading order calculations for a number of processes. Starting from two-loops, there are Feynman integrals with higher powers of the propagators They arise from self-energy insertions on internal lines. If we would perform the one-loop calculation of the self-energy analytically and combine it with the counterterm, we would obtain a transcendental function, which vanishes quadratically in the on-shell limit. This will cancel the double pole and the residue will vanish. The main result of this paper is that when summed over all relevant diagrams (including counterterms from renormalization) residues due to higher poles from self-energy insertions on internal lines can be made to vanish at the integrand level. The Appendix lists the Feynman rules for the scalar φ3 theory
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
