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.

5+2 pages; v2: minor clarifications and typos, updating to published version

References in corpus (6)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Notes on cluster algebras and some all-loop Feynman integrals
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals

Cited by in corpus (6)

• Landau Discriminants
• Antipodal Self-Duality for a Four-Particle Form Factor
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• One-loop hexagon integral to higher orders in the dimensional regulator
• Probing multi-particle unitarity with the Landau equations