Minkowski Box from Yangian Bootstrap

TL;DR

This paper extends the Yangian bootstrap approach to Minkowski space for the one-loop box integral, deriving a compact, symmetry-constrained formula valid across all kinematic regions.

Contribution

It introduces a novel method to determine the one-loop box integral in Minkowski space using Yangian symmetry, expanding the bootstrap framework.

Findings

Derived a symmetry-constrained formula valid in all Minkowski kinematic regions.

Identified the space of Yangian invariants as spanned by the Bloch-Wigner function.

Explicitly fixed 12 constants in the integral's functional form.

Abstract

We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.