# Yangian Bootstrap for Massive Feynman Integrals

### Submission summary

 As Contributors: Florian Loebbert · Julian Miczajka · Dennis Müller · Hagen Münkler Preprint link: scipost_202011_00017v2 Date submitted: 2021-05-12 22:51 Submitted by: Miczajka, Julian Submitted to: SciPost Physics Academic field: Physics Specialties: Mathematical Physics High-Energy Physics - Theory Approach: Theoretical

### 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.

###### Current status:
Editor-in-charge assigned

### List of changes

- Added footnote 3 above (3.2).
- Added footnote 4 above (3.20).
- Added sentence "Notably, all integrals at higher loops that are expected to be Yangian invariant are related to planar diagrams. At this point there is no evidence that the Yangian symmetry of single Feynman diagrams can be generalized beyond planar integrals." at the end of section 3.2.
- Added footnote 6 on page 19.
- Added sentence "These constraints can come from e.g.\ permutation symmetry or kinematic limits that simplify the form of the integral, such as sending a mass to zero or an external point to infinity." to item 5 in section 4.2.
- Fixed a typo on page 26 (repetition "to to").
- Fixed a type in equation (7.9).