Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space
Abstract
The Method of Regions is a systematic way to derive asymptotic expansions of Feynman integrals. For Euclidean integrals there is a well-established algorithm to determine the complete set of regions as facets of a Newton polytope defined by the graph polynomials. In many physically relevant Minkowski limits, additional regions known as hidden regions are needed to obtain the correct asymptotic expansion. By making a precise connection with pinch singularities in parameter space and the associated Landau conditions, we identify the general mechanism giving rise to these regions and devise an algorithm, the Hidden Region Finder, to determine them. We show that hidden regions arise through a delicate interplay between asymptotic scaling of the edge parameters, which enhances certain monomials of the graph polynomial, and cancellations amongst these monomials, which reduce their collective contribution to the same order as other terms in the polynomial. We explore massless four-, five- and six-point integrals in a variety of wide-angle mass-shell, planar, collinear, double-collinear and Regge limits. Across these different expansions, hidden regions recur in the same small set of seed topologies. In all cases studied, they can be traced to wide-angle configurations with multiple hard-scattering subdiagrams. Distinct kinematic limits of a given seed inherit a common singular locus, while each limit fixes its own scaling vector and cancellation depth. This exploratory study showcases the potential of the proposed algorithm both to uncover missing contributions to asymptotic expansions and to organise them through their underlying singular geometry.
Related
BibTeX
@misc{gardi2026hidden,
title = {{Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space}},
author = {Einan Gardi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29442},
eprint = {2609.29442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29442},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space
AU - Einan Gardi
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29442
UR - https://arxiv.org/abs/2609.29442
AB - The Method of Regions is a systematic way to derive asymptotic expansions of Feynman integrals. For Euclidean integrals there is a well-established algorithm to determine the complete set of regions as facets of a Newton polytope defined by the graph polynomials. In many physically relevant Minkowski limits, additional regions known as hidden regions are needed to obtain the correct asymptotic expansion. By making a precise connection with pinch singularities in parameter space and the associated Landau conditions, we identify the general mechanism giving rise to these regions and devise an algorithm, the Hidden Region Finder, to determine them. We show that hidden regions arise through a delicate interplay between asymptotic scaling of the edge parameters, which enhances certain monomials of the graph polynomial, and cancellations amongst these monomials, which reduce their collective contribution to the same order as other terms in the polynomial. We explore massless four-, five- and six-point integrals in a variety of wide-angle mass-shell, planar, collinear, double-collinear and Regge limits. Across these different expansions, hidden regions recur in the same small set of seed topologies. In all cases studied, they can be traced to wide-angle configurations with multiple hard-scattering subdiagrams. Distinct kinematic limits of a given seed inherit a common singular locus, while each limit fixes its own scaling vector and cancellation depth. This exploratory study showcases the potential of the proposed algorithm both to uncover missing contributions to asymptotic expansions and to organise them through their underlying singular geometry.
ER -