Unregulated Divergences of Feynman Integrals

Feynman integrals can be expanded asymptotically with respect to some small parameters at the integrand level, a technique known as the expansion by regions. A naive expansion by regions may break down due to divergences not regulated by the spacetime dimension, exemplified by the rapidity divergences. A criterion to identify unregulated divergences is provided in this article. The analysis is conducted using both parametric and Mellin-Barnes representations, leading to a consistent conclusion. Based on this analysis, it is proven that { the presence of unregulated divergences implies the degeneracies of regions}, which may help to explain phenomena like the collinear anomaly.