Vanishing Cycles and Analysis of Singularities of Feynman Diagrams

In this work, we analyze the vanishing cycles of Feynman loop integrals by the means of the Mayer–Vietoris spectral sequence. A complete classification of possible vanishing geometries is obtained. We use this result for establishing an asymptotic expansion for the loop integrals near their singularity locus and then give explicit formulas for the coefficients of such an expansion. Further development of this framework may potentially lead to exact calculations of one- and two-loop Feynman diagrams, as well as other next-to-leading and higher-order diagrams, in studies of radiative corrections for upcoming lepton–hadron scattering experiments.