Yangian Bootstrap for Massive Feynman Integrals

TL;DR

This paper investigates the Yangian symmetry of massive Feynman integrals, establishing its relation to conformal symmetry, and uses these symmetries to derive new integral representations and conjectures for one-loop integrals in various dimensions.

Contribution

It extends the understanding of Yangian symmetry in massive Feynman integrals and employs this symmetry to bootstrap and conjecture new integral formulas.

Findings

Proved Yangian and conformal symmetry at one and two loops.

Derived hypergeometric expressions for massive integrals.

Conjectured series representations for all dual conformal one-loop integrals.

Abstract

We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we employ the conformal and Yangian constraints to bootstrap various one-loop examples of massive Feynman integrals. In particular, we explore the interplay between Yangian symmetry and hypergeometric expressions of the considered integrals. Based on these examples we conjecture single series representations for all dual conformal one-loop integrals in D spacetime dimensions with generic massive propagators.