Residues on Permanent Pinches: Finite Integrals and Leading Divergences
Abstract
We study infrared (IR) divergences from the point of view of permanent pinches. We show how canceling permanent pinches allows us to form finite linear combinations of integrals. We further show how to compute scheme-independent leading IR divergences with- out introducing a regulator, by integrating certain residue forms along desingularizations of permanent pinch varieties. Our methods work for massless and mixed massive-massless inte- grals, for non-planar integrals with arbitrary numerators as well as for integrals with higher (integer) powers of propagators. We use this analysis to determine leading singular terms in some examples of box integrals. We further study examples of finite integrals at higher loops, and in particular provide a basis for finite non-evanescent integrals in a non-planar two-loop five-point topology.
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BibTeX
@misc{corradini2026residues,
title = {{Residues on Permanent Pinches: Finite Integrals and Leading Divergences}},
author = {Dimitri Corradini and Cristian Vergu and Shun-Qing Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02300},
eprint = {2609.02300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02300},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Residues on Permanent Pinches: Finite Integrals and Leading Divergences
AU - Dimitri Corradini
AU - Cristian Vergu
AU - Shun-Qing Zhang
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02300
UR - https://arxiv.org/abs/2609.02300
AB - We study infrared (IR) divergences from the point of view of permanent pinches. We show how canceling permanent pinches allows us to form finite linear combinations of integrals. We further show how to compute scheme-independent leading IR divergences with- out introducing a regulator, by integrating certain residue forms along desingularizations of permanent pinch varieties. Our methods work for massless and mixed massive-massless inte- grals, for non-planar integrals with arbitrary numerators as well as for integrals with higher (integer) powers of propagators. We use this analysis to determine leading singular terms in some examples of box integrals. We further study examples of finite integrals at higher loops, and in particular provide a basis for finite non-evanescent integrals in a non-planar two-loop five-point topology.
ER -