Implications of the Landau Equations for Iterated Integrals

Abstract

We introduce a method for deriving constraints on the symbol of Feynman integrals from the form of their asymptotic expansions in the neighborhood of Landau loci. In particular, we show that the behavior of these integrals near singular points is directly related to the position in the symbol where one of the letters vanishes or becomes infinite. We illustrate this method on integrals with generic masses, and as a corollary prove the conjectured bound of $\lfloor \frac {D \ell} 2\rfloor$ on the transcendental weight of polylogarithmic $\ell$-loop integrals of this type in integer numbers of dimensions $D$. We also derive new constraints on the kinematic dependence of certain products of symbol letters that remain finite near singular points.