Implications of the Landau Equations for Iterated Integrals

TL;DR

This paper develops a method linking the asymptotic behavior of Feynman integrals near Landau singularities to constraints on their symbols, providing bounds on their transcendental weight and new insights into their kinematic structure.

Contribution

It introduces a novel approach connecting Landau equations to symbol constraints, proving a conjectured weight bound and deriving new kinematic constraints for Feynman integrals.

Findings

Bound of  rac {D \u221e  on transcendental weight.

Method relates asymptotics to symbol letters vanishing or diverging.

New constraints on kinematic dependence of symbol products.

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.